Duvenaud, David; Rasmussen, Carl Edward
2011-01-01
We introduce a Gaussian process model of functions which are additive. An additive function is one which decomposes into a sum of low-dimensional functions, each depending on only a subset of the input variables. Additive GPs generalize both Generalized Additive Models, and the standard GP models which use squared-exponential kernels. Hyperparameter learning in this model can be seen as Bayesian Hierarchical Kernel Learning (HKL). We introduce an expressive but tractable parameterization of the kernel function, which allows efficient evaluation of all input interaction terms, whose number is exponential in the input dimension. The additional structure discoverable by this model results in increased interpretability, as well as state-of-the-art predictive power in regression tasks.
Stable and Efficient Gaussian Process Calculations
National Aeronautics and Space Administration — The use of Gaussian processes can be an effective approach to prediction in a supervised learning environment. For large data sets, the standard Gaussian process...
Gaussian process based recursive system identification
Prüher, Jakub; Šimandl, Miroslav
2014-12-01
This paper is concerned with the problem of recursive system identification using nonparametric Gaussian process model. Non-linear stochastic system in consideration is affine in control and given in the input-output form. The use of recursive Gaussian process algorithm for non-linear system identification is proposed to alleviate the computational burden of full Gaussian process. The problem of an online hyper-parameter estimation is handled using proposed ad-hoc procedure. The approach to system identification using recursive Gaussian process is compared with full Gaussian process in terms of model error and uncertainty as well as computational demands. Using Monte Carlo simulations it is shown, that the use of recursive Gaussian process with an ad-hoc learning procedure offers converging estimates of hyper-parameters and constant computational demands.
Palm distributions for log Gaussian Cox processes
DEFF Research Database (Denmark)
Coeurjolly, Jean-Francois; Møller, Jesper; Waagepetersen, Rasmus
This paper reviews useful results related to Palm distributions of spatial point processes and provides a new result regarding the characterization of Palm distributions for the class of log Gaussian Cox processes. This result is used to study functional summary statistics for a log Gaussian Cox...
GPstuff: Bayesian Modeling with Gaussian Processes
Vanhatalo, J.; Riihimaki, J.; Hartikainen, J.; Jylänki, P.P.; Tolvanen, V.; Vehtari, A.
2013-01-01
The GPstuff toolbox is a versatile collection of Gaussian process models and computational tools required for Bayesian inference. The tools include, among others, various inference methods, sparse approximations and model assessment methods.
Gaussian Process Techniques for Wireless Communications
Han, Mr Chong; Peters, Dr Gareth; Yuan, Prof Jinhong
2010-01-01
Bayesian filtering is a general framework for recursively estimating the state of a dynamical system. Classical solutions such that Kalman filter and Particle filter are introduced in this report. Gaussian processes have been introduced as a non-parametric technique for system estimation from supervision learning. For the thesis project, we intend to propose a new, general methodology for inference and learning in non-linear state-space models probabilistically incorporating with the Gaussian process model estimation.
Non-Gaussian Stochastic Processes.
1986-02-28
Underwriting Risk and Return Paradox Revisited," J. Risk and Insurance .24.L 621-627 (1982). P. Brockett and B. Arnold, "Identifiability for Dependent...Some Ruin Calculations," J. Risk and Insurance 5DIAL 727-731 (1983). P. Brockett, S. Cox, and R. Witt, "Self-Insurance and the Probability of...Financial Regret," J. Risk and Insurance 51(4) 720-729 (1984). P. Brockett, "The Likelihood Ratio Detector for Non-Gaussian Infinitely Divisible and Linear
MULTI-SCALE GAUSSIAN PROCESSES MODEL
Institute of Scientific and Technical Information of China (English)
Zhou Yatong; Zhang Taiyi; Li Xiaohe
2006-01-01
A novel model named Multi-scale Gaussian Processes (MGP) is proposed. Motivated by the ideas of multi-scale representations in the wavelet theory, in the new model, a Gaussian process is represented at a scale by a linear basis that is composed of a scale function and its different translations. Finally the distribution of the targets of the given samples can be obtained at different scales. Compared with the standard Gaussian Processes (GP) model, the MGP model can control its complexity conveniently just by adjusting the scale parameter. So it can trade-off the generalization ability and the empirical risk rapidly. Experiments verify the feasibility of the MGP model, and exhibit that its performance is superior to the GP model if appropriate scales are chosen.
Semisupervised Gaussian Process for Automated Enzyme Search.
Mellor, Joseph; Grigoras, Ioana; Carbonell, Pablo; Faulon, Jean-Loup
2016-06-17
Synthetic biology is today harnessing the design of novel and greener biosynthesis routes for the production of added-value chemicals and natural products. The design of novel pathways often requires a detailed selection of enzyme sequences to import into the chassis at each of the reaction steps. To address such design requirements in an automated way, we present here a tool for exploring the space of enzymatic reactions. Given a reaction and an enzyme the tool provides a probability estimate that the enzyme catalyzes the reaction. Our tool first considers the similarity of a reaction to known biochemical reactions with respect to signatures around their reaction centers. Signatures are defined based on chemical transformation rules by using extended connectivity fingerprint descriptors. A semisupervised Gaussian process model associated with the similar known reactions then provides the probability estimate. The Gaussian process model uses information about both the reaction and the enzyme in providing the estimate. These estimates were validated experimentally by the application of the Gaussian process model to a newly identified metabolite in Escherichia coli in order to search for the enzymes catalyzing its associated reactions. Furthermore, we show with several pathway design examples how such ability to assign probability estimates to enzymatic reactions provides the potential to assist in bioengineering applications, providing experimental validation to our proposed approach. To the best of our knowledge, the proposed approach is the first application of Gaussian processes dealing with biological sequences and chemicals, the use of a semisupervised Gaussian process framework is also novel in the context of machine learning applied to bioinformatics. However, the ability of an enzyme to catalyze a reaction depends on the affinity between the substrates of the reaction and the enzyme. This affinity is generally quantified by the Michaelis constant KM
Robust Filtering and Smoothing with Gaussian Processes
Deisenroth, Marc Peter; Turner, Ryan; Huber, Marco F.; Hanebeck, Uwe D.; Rasmussen, Carl Edward
2012-01-01
We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP) models. GPs are gaining increasing importance in signal processing, machine learning, robotics, and control for representing unknown system functions by posterior probability distributions. This modern way of "system identification" is more robust than finding p...
Convergence of posteriors for discretized log Gaussian Cox processes
DEFF Research Database (Denmark)
Waagepetersen, Rasmus Plenge
2004-01-01
In Markov chain Monte Carlo posterior computation for log Gaussian Cox processes (LGCPs) a discretization of the continuously indexed Gaussian field is required. It is demonstrated that approximate posterior expectations computed from discretized LGCPs converge to the exact posterior expectations...
Perfusion Quantification Using Gaussian Process Deconvolution
DEFF Research Database (Denmark)
Andersen, Irene Klærke; Have, Anna Szynkowiak; Rasmussen, Carl Edward
2002-01-01
The quantification of perfusion using dynamic susceptibility contrast MRI (DSC-MRI) requires deconvolution to obtain the residual impulse response function (IRF). In this work, a method using the Gaussian process for deconvolution (GPD) is proposed. The fact that the IRF is smooth is incorporated...... optimized according to the noise level in each voxel. The comparison is carried out using artificial data as well as data from healthy volunteers. It is shown that GPD is comparable to SVD with a variable optimized threshold when determining the maximum of the IRF, which is directly related to the perfusion...
Soft sensor modeling based on Gaussian processes
Institute of Scientific and Technical Information of China (English)
XIONG Zhi-hua; HUANG Guo-hong; SHAO Hui-he
2005-01-01
In order to meet the demand of online optimal running, a novel soft sensor modeling approach based on Gaussian processes was proposed. The approach is moderately simple to implement and use without loss of performance. It is trained by optimizing the hyperparameters using the scaled conjugate gradient algorithm with the squared exponential covariance function employed. Experimental simulations show that the soft sensor modeling approach has the advantage via a real-world example in a refinery. Meanwhile, the method opens new possibilities for application of kernel methods to potential fields.
Gravitational Wave Emulation Using Gaussian Process Regression
Doctor, Zoheyr; Farr, Ben; Holz, Daniel
2017-01-01
Parameter estimation (PE) for gravitational wave signals from compact binary coalescences (CBCs) requires reliable template waveforms which span the parameter space. Waveforms from numerical relativity are accurate but computationally expensive, so approximate templates are typically used for PE. These `approximants', while quick to compute, can introduce systematic errors and bias PE results. We describe a machine learning method for generating CBC waveforms and uncertainties using existing accurate waveforms as a training set. Coefficients of a reduced order waveform model are computed and each treated as arising from a Gaussian process. These coefficients and their uncertainties are then interpolated using Gaussian process regression (GPR). As a proof of concept, we construct a training set of approximant waveforms (rather than NR waveforms) in the two-dimensional space of chirp mass and mass ratio and interpolate new waveforms with GPR. We demonstrate that the mismatch between interpolated waveforms and approximants is below the 1% level for an appropriate choice of training set and GPR kernel hyperparameters.
Optimality of Poisson Processes Intensity Learning with Gaussian Processes
Kirichenko, A.; van Zanten, H.
2015-01-01
In this paper we provide theoretical support for the so-called "Sigmoidal Gaussian Cox Process" approach to learning the intensity of an inhomogeneous Poisson process on a d-dimensional domain. This method was proposed by Adams, Murray and MacKay (ICML, 2009), who developed a tractable computational
Optimality of Poisson Processes Intensity Learning with Gaussian Processes
A. Kirichenko; H. van Zanten
2015-01-01
In this paper we provide theoretical support for the so-called "Sigmoidal Gaussian Cox Process" approach to learning the intensity of an inhomogeneous Poisson process on a d-dimensional domain. This method was proposed by Adams, Murray and MacKay (ICML, 2009), who developed a tractable computational
Linear Latent Force Models using Gaussian Processes
Álvarez, Mauricio A; Lawrence, Neil D
2011-01-01
Purely data driven approaches for machine learning present difficulties when data is scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data driven modelling with a physical model of the system. We show how different, physically-inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology and geostatistics.
Bayesian nonparametric adaptive control using Gaussian processes.
Chowdhary, Girish; Kingravi, Hassan A; How, Jonathan P; Vela, Patricio A
2015-03-01
Most current model reference adaptive control (MRAC) methods rely on parametric adaptive elements, in which the number of parameters of the adaptive element are fixed a priori, often through expert judgment. An example of such an adaptive element is radial basis function networks (RBFNs), with RBF centers preallocated based on the expected operating domain. If the system operates outside of the expected operating domain, this adaptive element can become noneffective in capturing and canceling the uncertainty, thus rendering the adaptive controller only semiglobal in nature. This paper investigates a Gaussian process-based Bayesian MRAC architecture (GP-MRAC), which leverages the power and flexibility of GP Bayesian nonparametric models of uncertainty. The GP-MRAC does not require the centers to be preallocated, can inherently handle measurement noise, and enables MRAC to handle a broader set of uncertainties, including those that are defined as distributions over functions. We use stochastic stability arguments to show that GP-MRAC guarantees good closed-loop performance with no prior domain knowledge of the uncertainty. Online implementable GP inference methods are compared in numerical simulations against RBFN-MRAC with preallocated centers and are shown to provide better tracking and improved long-term learning.
Gaussian processes in non-commutative probability theory
Guţǎ, M.I.
2002-01-01
The generalisation of the notion of Gaussian processes from probability theory is investigated in the context of non-commutative probability theory. A non-commutative Gaussian process is viewed as a linear map from an infinite dimensional (real) Hilbert space into an algebra with involution and a po
Exponential Regret Bounds for Gaussian Process Bandits with Deterministic Observations
de Freitas, N.; Smola, A.J.; Zoghi, M.; Langford, J.; Pineau, J.
2012-01-01
This paper analyzes the problem of Gaussian process (GP) bandits with deterministic observations. The analysis uses a branch and bound algorithm that is related to the UCB algorithm of (Srinivas et al, 2010). For GPs with Gaussian observation noise, with variance strictly greater than zero, Srinivas
Method for generating two coupled Gaussian stochastic processes
Jamali, Tayeb
2016-01-01
Most processes in nature are coupled; however, extensive null models for generating such processes still lacks. We present a new method to generate two coupled Gaussian stochastic processes with arbitrary correlation functions. This method is developed by modifying the Fourier filtering method. The robustness of this method is proved by generating two coupled fractional Brownian motions and extending its range of application to Gaussian random fields.
Characterisation of random Gaussian and non-Gaussian stress processes in terms of extreme responses
Directory of Open Access Journals (Sweden)
Colin Bruno
2015-01-01
Full Text Available In the field of military land vehicles, random vibration processes generated by all-terrain wheeled vehicles in motion are not classical stochastic processes with a stationary and Gaussian nature. Non-stationarity of processes induced by the variability of the vehicle speed does not form a major difficulty because the designer can have good control over the vehicle speed by characterising the histogram of instantaneous speed of the vehicle during an operational situation. Beyond this non-stationarity problem, the hard point clearly lies in the fact that the random processes are not Gaussian and are generated mainly by the non-linear behaviour of the undercarriage and the strong occurrence of shocks generated by roughness of the terrain. This non-Gaussian nature is expressed particularly by very high flattening levels that can affect the design of structures under extreme stresses conventionally acquired by spectral approaches, inherent to Gaussian processes and based essentially on spectral moments of stress processes. Due to these technical considerations, techniques for characterisation of random excitation processes generated by this type of carrier need to be changed, by proposing innovative characterisation methods based on time domain approaches as described in the body of the text rather than spectral domain approaches.
ARC Code TI: Block-GP: Scalable Gaussian Process Regression
National Aeronautics and Space Administration — Block GP is a Gaussian Process regression framework for multimodal data, that can be an order of magnitude more scalable than existing state-of-the-art nonlinear...
Scalable Gaussian Processes and the search for exoplanets
CERN. Geneva
2015-01-01
Gaussian Processes are a class of non-parametric models that are often used to model stochastic behavior in time series or spatial data. A major limitation for the application of these models to large datasets is the computational cost. The cost of a single evaluation of the model likelihood scales as the third power of the number of data points. In the search for transiting exoplanets, the datasets of interest have tens of thousands to millions of measurements with uneven sampling, rendering naive application of a Gaussian Process model impractical. To attack this problem, we have developed robust approximate methods for Gaussian Process regression that can be applied at this scale. I will describe the general problem of Gaussian Process regression and offer several applicable use cases. Finally, I will present our work on scaling this model to the exciting field of exoplanet discovery and introduce a well-tested open source implementation of these new methods.
Non-negative matrix factorization with Gaussian process priors
DEFF Research Database (Denmark)
Schmidt, Mikkel Nørgaard; Laurberg, Hans
2008-01-01
We present a general method for including prior knowledge in a nonnegative matrix factorization (NMF), based on Gaussian process priors. We assume that the nonnegative factors in the NMF are linked by a strictly increasing function to an underlying Gaussian process specified by its covariance...... function. This allows us to find NMF decompositions that agree with our prior knowledge of the distribution of the factors, such as sparseness, smoothness, and symmetries. The method is demonstrated with an example from chemical shift brain imaging....
Non-negative matrix factorization with Gaussian process priors
DEFF Research Database (Denmark)
Schmidt, Mikkel Nørgaard; Laurberg, Hans
2008-01-01
We present a general method for including prior knowledge in a nonnegative matrix factorization (NMF), based on Gaussian process priors. We assume that the nonnegative factors in the NMF are linked by a strictly increasing function to an underlying Gaussian process specified by its covariance...... function. This allows us to find NMF decompositions that agree with our prior knowledge of the distribution of the factors, such as sparseness, smoothness, and symmetries. The method is demonstrated with an example from chemical shift brain imaging....
Recurrence plots of discrete-time Gaussian stochastic processes
Ramdani, Sofiane; Bouchara, Frédéric; Lagarde, Julien; Lesne, Annick
2016-09-01
We investigate the statistical properties of recurrence plots (RPs) of data generated by discrete-time stationary Gaussian random processes. We analytically derive the theoretical values of the probabilities of occurrence of recurrence points and consecutive recurrence points forming diagonals in the RP, with an embedding dimension equal to 1. These results allow us to obtain theoretical values of three measures: (i) the recurrence rate (REC) (ii) the percent determinism (DET) and (iii) RP-based estimation of the ε-entropy κ(ε) in the sense of correlation entropy. We apply these results to two Gaussian processes, namely first order autoregressive processes and fractional Gaussian noise. For these processes, we simulate a number of realizations and compare the RP-based estimations of the three selected measures to their theoretical values. These comparisons provide useful information on the quality of the estimations, such as the minimum required data length and threshold radius used to construct the RP.
Nonparametric estimation of stochastic differential equations with sparse Gaussian processes
García, Constantino A.; Otero, Abraham; Félix, Paulo; Presedo, Jesús; Márquez, David G.
2017-08-01
The application of stochastic differential equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we introduce a nonparametric method for estimating the drift and diffusion terms of SDEs from a densely observed discrete time series. The use of Gaussian processes as priors permits working directly in a function-space view and thus the inference takes place directly in this space. To cope with the computational complexity that requires the use of Gaussian processes, a sparse Gaussian process approximation is provided. This approximation permits the efficient computation of predictions for the drift and diffusion terms by using a distribution over a small subset of pseudosamples. The proposed method has been validated using both simulated data and real data from economy and paleoclimatology. The application of the method to real data demonstrates its ability to capture the behavior of complex systems.
Learning with Uncertainty - Gaussian Processes and Relevance Vector Machines
DEFF Research Database (Denmark)
Candela, Joaquin Quinonero
2004-01-01
This thesis is concerned with Gaussian Processes (GPs) and Relevance Vector Machines (RVMs), both of which are particular instances of probabilistic linear models. We look at both models from a Bayesian perspective, and are forced to adopt an approximate Bayesian treatment to learning for two...... family of approximations to Gaussian Processes, Reduced Rank Gaussian Processes (RRGPs), which take the form of nite extended linear models; we show that GPs are in general equivalent to in nite extended linear models. We also show that RRGPs result in degenerate GPs, which suffer, like RVMs...... reasons. The first reason is the analytical intractability of the full Bayesian treatment and the fact that we in principle do not want to resort to sampling methods. The second reason, which incidentally justifies our not wanting to sample, is that we are interested in computationally efficient models...
Bipower variation for Gaussian processes with stationary increments
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Corcuera, José Manuel; Podolskij, Mark
2009-01-01
Convergence in probability and central limit laws of bipower variation for Gaussian processes with stationary increments and for integrals with respect to such processes are derived. The main tools of the proofs are some recent powerful techniques of Wiener/Itô/Malliavin calculus for establishing...
Analysis of some methods for reduced rank Gaussian process regression
DEFF Research Database (Denmark)
Quinonero-Candela, J.; Rasmussen, Carl Edward
2005-01-01
While there is strong motivation for using Gaussian Processes (GPs) due to their excellent performance in regression and classification problems, their computational complexity makes them impractical when the size of the training set exceeds a few thousand cases. This has motivated the recent...... Gaussian Processes (RRGPs) are equivalent to finite sparse linear models. We also introduce the concept of degenerate GPs and show that they correspond to inappropriate priors. We show how to modify the RRGP to prevent it from being degenerate at test time. Training RRGPs consists both in learning...
Gaussian Process Structural Equation Models with Latent Variables
Silva, Ricardo
2010-01-01
In a variety of disciplines such as social sciences, psychology, medicine and economics, the recorded data are considered to be noisy measurements of latent variables connected by some causal structure. This corresponds to a family of graphical models known as the structural equation model with latent variables. While linear non-Gaussian variants have been well-studied, inference in nonparametric structural equation models is still underdeveloped. We introduce a sparse Gaussian process parameterization that defines a non-linear structure connecting latent variables, unlike common formulations of Gaussian process latent variable models. An efficient Markov chain Monte Carlo procedure is described. We evaluate the stability of the sampling procedure and the predictive ability of the model compared against the current practice.
Conditional simulation of extremal Gaussian processes
Dombry, Clément
2012-01-01
Recently the regular conditional distributions of max-infinitely divisible processes were derived by \\citet{Dombry2011} and although these conditional distributions have complicated closed forms, \\citet{Dombry2011b} introduce an algorithm to get conditional realizations of Brown-Resnick processes. In this paper we derive the regular conditional distributions of the max-stable process introduced by \\citet{Schlather2002} and adapt the framework of \\citet{Dombry2011b} to this specific process. We test the methods on simulated data and give an application to extreme temperatures in Switzerland. Results show that the proposed sampling scheme provide accurate conditional simulations and can handle real-sized problems.
Local times of N-parameter Gaussian processes
Institute of Scientific and Technical Information of China (English)
LIN Zhengyan; CHENG Zongmao
2005-01-01
An N-parameter Gaussian stationary process X = { X ( t ): t ∈ RN+ } is introduced and the existence and joint continuity of its local times is presented. And the moments of local times are estimated. Furthermore moduli of continuity and large increment results for the local times are established.
Predictive Information Rate in Discrete-time Gaussian Processes
Abdallah, Samer A
2012-01-01
We derive expressions for the predicitive information rate (PIR) for the class of autoregressive Gaussian processes AR(N), both in terms of the prediction coefficients and in terms of the power spectral density. The latter result suggests a duality between the PIR and the multi-information rate for processes with mutually inverse power spectra (i.e. with poles and zeros of the transfer function exchanged). We investigate the behaviour of the PIR in relation to the multi-information rate for some simple examples, which suggest, somewhat counter-intuitively, that the PIR is maximised for very `smooth' AR processes whose power spectra have multiple poles at zero frequency. We also obtain results for moving average Gaussian processes which are consistent with the duality conjectured earlier. One consequence of this is that the PIR is unbounded for MA(N) processes.
Predictive Active Set Selection Methods for Gaussian Processes
DEFF Research Database (Denmark)
Henao, Ricardo; Winther, Ole
2012-01-01
We propose an active set selection framework for Gaussian process classification for cases when the dataset is large enough to render its inference prohibitive. Our scheme consists of a two step alternating procedure of active set update rules and hyperparameter optimization based upon marginal...... likelihood maximization. The active set update rules rely on the ability of the predictive distributions of a Gaussian process classifier to estimate the relative contribution of a datapoint when being either included or removed from the model. This means that we can use it to include points with potentially...... high impact to the classifier decision process while removing those that are less relevant. We introduce two active set rules based on different criteria, the first one prefers a model with interpretable active set parameters whereas the second puts computational complexity first, thus a model...
Sparse-posterior Gaussian Processes for general likelihoods
Yuan,; Abdel-Gawad, Ahmed H; Minka, Thomas P
2012-01-01
Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate GP methods have been proposed that essentially map the large dataset into a small set of basis points. Among them, two state-of-the-art methods are sparse pseudo-input Gaussian process (SPGP) (Snelson and Ghahramani, 2006) and variablesigma GP (VSGP) Walder et al. (2008), which generalizes SPGP and allows each basis point to have its own length scale. However, VSGP was only derived for regression. In this paper, we propose a new sparse GP framework that uses expectation propagation to directly approximate general GP likelihoods using a sparse and smooth basis. It includes both SPGP and VSGP for regression as special cases. Plus as an EP algorithm, it inherits the ability to process data online. As a particular choice of approximating family, we blur each basis point with a...
Designing Multi-target Compound Libraries with Gaussian Process Models.
Bieler, Michael; Reutlinger, Michael; Rodrigues, Tiago; Schneider, Petra; Kriegl, Jan M; Schneider, Gisbert
2016-05-01
We present the application of machine learning models to selecting G protein-coupled receptor (GPCR)-focused compound libraries. The library design process was realized by ant colony optimization. A proprietary Boehringer-Ingelheim reference set consisting of 3519 compounds tested in dose-response assays at 11 GPCR targets served as training data for machine learning and activity prediction. We compared the usability of the proprietary data with a public data set from ChEMBL. Gaussian process models were trained to prioritize compounds from a virtual combinatorial library. We obtained meaningful models for three of the targets (5-HT2c , MCH, A1), which were experimentally confirmed for 12 of 15 selected and synthesized or purchased compounds. Overall, the models trained on the public data predicted the observed assay results more accurately. The results of this study motivate the use of Gaussian process regression on public data for virtual screening and target-focused compound library design.
Sound Event Detection for Music Signals Using Gaussian Processes
Directory of Open Access Journals (Sweden)
Pablo A. Alvarado-Durán
2013-11-01
Full Text Available In this paper we present a new methodology for detecting sound events in music signals using Gaussian Processes. Our method firstly takes a time-frequency representation, i.e. the spectrogram, of the input audio signal. Secondly the spectrogram dimension is reduced translating the linear Hertz frequency scale into the logarithmic Mel frequency scale using a triangular filter bank. Finally every short-time spectrum, i.e. every Mel spectrogram column, is classified as “Event” or “Not Event” by a Gaussian Processes Classifier. We compare our method with other event detection techniques widely used. To do so, we use MATLAB® to program each technique and test them using two datasets of music with different levels of complexity. Results show that the new methodology outperforms the standard approaches, getting an improvement by about 1.66 % on the dataset one and 0.45 % on the dataset two in terms of F-measure.
Adaptive Sampling for Learning Gaussian Processes Using Mobile Sensor Networks
Directory of Open Access Journals (Sweden)
Yunfei Xu
2011-03-01
Full Text Available This paper presents a novel class of self-organizing sensing agents that adaptively learn an anisotropic, spatio-temporal Gaussian process using noisy measurements and move in order to improve the quality of the estimated covariance function. This approach is based on a class of anisotropic covariance functions of Gaussian processes introduced to model a broad range of spatio-temporal physical phenomena. The covariance function is assumed to be unknown a priori. Hence, it is estimated by the maximum a posteriori probability (MAP estimator. The prediction of the field of interest is then obtained based on the MAP estimate of the covariance function. An optimal sampling strategy is proposed to minimize the information-theoretic cost function of the Fisher Information Matrix. Simulation results demonstrate the effectiveness and the adaptability of the proposed scheme.
Analysis of some methods for reduced rank Gaussian process regression
DEFF Research Database (Denmark)
Quinonero-Candela, J.; Rasmussen, Carl Edward
2005-01-01
While there is strong motivation for using Gaussian Processes (GPs) due to their excellent performance in regression and classification problems, their computational complexity makes them impractical when the size of the training set exceeds a few thousand cases. This has motivated the recent...... proliferation of a number of cost-effective approximations to GPs, both for classification and for regression. In this paper we analyze one popular approximation to GPs for regression: the reduced rank approximation. While generally GPs are equivalent to infinite linear models, we show that Reduced Rank...... Gaussian Processes (RRGPs) are equivalent to finite sparse linear models. We also introduce the concept of degenerate GPs and show that they correspond to inappropriate priors. We show how to modify the RRGP to prevent it from being degenerate at test time. Training RRGPs consists both in learning...
On the likelihood function of Gaussian max-stable processes
Genton, M. G.
2011-05-24
We derive a closed form expression for the likelihood function of a Gaussian max-stable process indexed by ℝd at p≤d+1 sites, d≥1. We demonstrate the gain in efficiency in the maximum composite likelihood estimators of the covariance matrix from p=2 to p=3 sites in ℝ2 by means of a Monte Carlo simulation study. © 2011 Biometrika Trust.
PSSGP : Program for Simulation of Stationary Gaussian Processes
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard
This report describes the computer program PSSGP. PSSGP can be used to simulate realizations of stationary Gaussian stochastic processes. The simulation algorithm can be coupled with some applications. One possibility is to use PSSGP to estimate the first-passage density function of a given system....... Another possibility is to estimate some measures relevant in a fatigue failure analysis of stochastically loadewd structures. The applications are used in two examples....
Multi-task Gaussian Process Learning of Robot Inverse Dynamics
Chai, Kian Ming; Williams, Christopher K. I.; Klanke, Stefan; Vijayakumar, Sethu
2008-01-01
The inverse dynamics problem for a robotic manipulator is to compute the torques needed at the joints to drive it along a given trajectory; it is beneficial to be able to learn this function for adaptive control. A robotic manipulator will often need to be controlled while holding different loads in its end effector, giving rise to a multi-task learning problem. By placing independent Gaussian process priors over the latent functions of the inverse dynamics, we obtain a multi-t...
Multistep Wind Speed Forecasting Based on Wavelet and Gaussian Processes
Niya Chen; Zheng Qian; Xiaofeng Meng
2013-01-01
Accurate wind speed forecasts are necessary for the safety and economy of the renewable energy utilization. The wind speed forecasts can be obtained by statistical model based on historical data. In this paper, a novel W-GP model (wavelet decomposition based Gaussian process learning paradigm) is proposed for short-term wind speed forecasting. The nonstationary and nonlinear original wind speed series is first decomposed into a set of better-behaved constitutive subseries by wavelet decomposi...
On bosonic non-Gaussian processes: photon-added Gaussian channels
Sabapathy, Krishna Kumar
2016-01-01
We present a framework for systematically studying linear bosonic non-Gaussian channels. Our emphasis is on a class of channels that we call as photon-added Gaussian channels and these are experimentally viable with current quantum-optical technologies. These channels are obtained by extending Gaussian channels with photon addition applied to the environment state (in its respective Stinespring unitary representation) giving rise to a one-parameter family of non-Gaussian channels indexed by photon number $n$ with $n=0$ corresponding to the underlying Gaussian channel. We then derive the corresponding operator-sum representation and observe that these channels are Fock-preserving, i.e., coherence non-generating on incoherent states in the Fock basis. Furthermore, noisy Gaussian channels can be expressed as a convex mixture of these non-Gaussian channels analogous to the Fock basis representation of a thermal state. We then report examples of activation of nonclassicality, using this method of photon-addition, ...
Nonlinear spectral unmixing of hyperspectral images using Gaussian processes
Altmann, Yoann; McLaughlin, Steve; Tourneret, Jean-Yves
2012-01-01
This paper presents an unsupervised algorithm for nonlinear unmixing of hyperspectral images. The proposed model assumes that the pixel reflectances result from a nonlinear function of the abundance vectors associated with the pure spectral components. We assume that the spectral signatures of the pure components and the nonlinear function are unknown. The first step of the proposed method consists of the Bayesian estimation of the abundance vectors for all the image pixels and the nonlinear function relating the abundance vectors to the observations. The endmembers are subsequently estimated using Gaussian process regression. The performance of the unmixing strategy is evaluated with simulations conducted on synthetic and real data.
Fault Tolerant Control Using Gaussian Processes and Model Predictive Control
Directory of Open Access Journals (Sweden)
Yang Xiaoke
2015-03-01
Full Text Available Essential ingredients for fault-tolerant control are the ability to represent system behaviour following the occurrence of a fault, and the ability to exploit this representation for deciding control actions. Gaussian processes seem to be very promising candidates for the first of these, and model predictive control has a proven capability for the second. We therefore propose to use the two together to obtain fault-tolerant control functionality. Our proposal is illustrated by several reasonably realistic examples drawn from flight control.
Sound Event Detection for Music Signals Using Gaussian Processes
Pablo A. Alvarado-Durán; Mauricio A. Álvarez-López; Álvaro A. Orozco-Gutiérrez
2013-01-01
In this paper we present a new methodology for detecting sound events in music signals using Gaussian Processes. Our method firstly takes a time-frequency representation, i.e. the spectrogram, of the input audio signal. Secondly the spectrogram dimension is reduced translating the linear Hertz frequency scale into the logarithmic Mel frequency scale using a triangular filter bank. Finally every short-time spectrum, i.e. every Mel spectrogram column, is classified as “Event” or “Not Event” by ...
The series product for gaussian quantum input processes
Gough, John E.; James, Matthew R.
2017-02-01
We present a theory for connecting quantum Markov components into a network with quantum input processes in a Gaussian state (including thermal and squeezed). One would expect on physical grounds that the connection rules should be independent of the state of the input to the network. To compute statistical properties, we use a version of Wicks' theorem involving fictitious vacuum fields (Fock space based representation of the fields) and while this aids computation, and gives a rigorous formulation, the various representations need not be unitarily equivalent. In particular, a naive application of the connection rules would lead to the wrong answer. We establish the correct interconnection rules, and show that while the quantum stochastic differential equations of motion display explicitly the covariances (thermal and squeezing parameters) of the Gaussian input fields we introduce the Wick-Stratonovich form which leads to a way of writing these equations that does not depend on these covariances and so corresponds to the universal equations written in terms of formal quantum input processes. We show that a wholly consistent theory of quantum open systems in series can be developed in this way, and as required physically, is universal and in particular representation-free.
Gaussian process style transfer mapping for historical Chinese character recognition
Feng, Jixiong; Peng, Liangrui; Lebourgeois, Franck
2015-01-01
Historical Chinese character recognition is very important to larger scale historical document digitalization, but is a very challenging problem due to lack of labeled training samples. This paper proposes a novel non-linear transfer learning method, namely Gaussian Process Style Transfer Mapping (GP-STM). The GP-STM extends traditional linear Style Transfer Mapping (STM) by using Gaussian process and kernel methods. With GP-STM, existing printed Chinese character samples are used to help the recognition of historical Chinese characters. To demonstrate this framework, we compare feature extraction methods, train a modified quadratic discriminant function (MQDF) classifier on printed Chinese character samples, and implement the GP-STM model on Dunhuang historical documents. Various kernels and parameters are explored, and the impact of the number of training samples is evaluated. Experimental results show that accuracy increases by nearly 15 percentage points (from 42.8% to 57.5%) using GP-STM, with an improvement of more than 8 percentage points (from 49.2% to 57.5%) compared to the STM approach.
Nudged elastic band calculations accelerated with Gaussian process regression
Koistinen, Olli-Pekka; Dagbjartsdóttir, Freyja B.; Ásgeirsson, Vilhjálmur; Vehtari, Aki; Jónsson, Hannes
2017-10-01
Minimum energy paths for transitions such as atomic and/or spin rearrangements in thermalized systems are the transition paths of largest statistical weight. Such paths are frequently calculated using the nudged elastic band method, where an initial path is iteratively shifted to the nearest minimum energy path. The computational effort can be large, especially when ab initio or electron density functional calculations are used to evaluate the energy and atomic forces. Here, we show how the number of such evaluations can be reduced by an order of magnitude using a Gaussian process regression approach where an approximate energy surface is generated and refined in each iteration. When the goal is to evaluate the transition rate within harmonic transition state theory, the evaluation of the Hessian matrix at the initial and final state minima can be carried out beforehand and used as input in the minimum energy path calculation, thereby improving stability and reducing the number of iterations needed for convergence. A Gaussian process model also provides an uncertainty estimate for the approximate energy surface, and this can be used to focus the calculations on the lesser-known part of the path, thereby reducing the number of needed energy and force evaluations to a half in the present calculations. The methodology is illustrated using the two-dimensional Müller-Brown potential surface and performance assessed on an established benchmark involving 13 rearrangement transitions of a heptamer island on a solid surface.
Transform Coding for Point Clouds Using a Gaussian Process Model.
De Queiroz, Ricardo; Chou, Philip A
2017-04-28
We propose using stationary Gaussian Processes (GPs) to model the statistics of the signal on points in a point cloud, which can be considered samples of a GP at the positions of the points. Further, we propose using Gaussian Process Transforms (GPTs), which are Karhunen-Lo`eve transforms of the GP, as the basis of transform coding of the signal. Focusing on colored 3D point clouds, we propose a transform coder that breaks the point cloud into blocks, transforms the blocks using GPTs, and entropy codes the quantized coefficients. The GPT for each block is derived from both the covariance function of the GP and the locations of the points in the block, which are separately encoded. The covariance function of the GP is parameterized, and its parameters are sent as side information. The quantized coefficients are sorted by eigenvalues of the GPTs, binned, and encoded using an arithmetic coder with bin-dependent Laplacian models whose parameters are also sent as side information. Results indicate that transform coding of 3D point cloud colors using the proposed GPT and entropy coding achieves superior compression performance on most of our data sets.
Modelling and control of dynamic systems using gaussian process models
Kocijan, Juš
2016-01-01
This monograph opens up new horizons for engineers and researchers in academia and in industry dealing with or interested in new developments in the field of system identification and control. It emphasizes guidelines for working solutions and practical advice for their implementation rather than the theoretical background of Gaussian process (GP) models. The book demonstrates the potential of this recent development in probabilistic machine-learning methods and gives the reader an intuitive understanding of the topic. The current state of the art is treated along with possible future directions for research. Systems control design relies on mathematical models and these may be developed from measurement data. This process of system identification, when based on GP models, can play an integral part of control design in data-based control and its description as such is an essential aspect of the text. The background of GP regression is introduced first with system identification and incorporation of prior know...
DEFF Research Database (Denmark)
Møller, Jesper; Jacobsen, Robert Dahl
We introduce a promising alternative to the usual hidden Markov tree model for Gaussian wavelet coefficients, where their variances are specified by the hidden states and take values in a finite set. In our new model, the hidden states have a similar dependence structure but they are jointly...... Gaussian, and the wavelet coefficients have log-variances equal to the hidden states. We argue why this provides a flexible model where frequentist and Bayesian inference procedures become tractable for estimation of parameters and hidden states. Our methodology is illustrated for denoising and edge...
Sequential Batch Design for Gaussian Processes Employing Marginalization †
Directory of Open Access Journals (Sweden)
Roland Preuss
2017-02-01
Full Text Available Within the Bayesian framework, we utilize Gaussian processes for parametric studies of long running computer codes. Since the simulations are expensive, it is necessary to exploit the computational budget in the best possible manner. Employing the sum over variances —being indicators for the quality of the fit—as the utility function, we establish an optimized and automated sequential parameter selection procedure. However, it is also often desirable to utilize the parallel running capabilities of present computer technology and abandon the sequential parameter selection for a faster overall turn-around time (wall-clock time. This paper proposes to achieve this by marginalizing over the expected outcomes at optimized test points in order to set up a pool of starting values for batch execution. For a one-dimensional test case, the numerical results are validated with the analytical solution. Eventually, a systematic convergence study demonstrates the advantage of the optimized approach over randomly chosen parameter settings.
a Gaussian Process Based Multi-Person Interaction Model
Klinger, T.; Rottensteiner, F.; Heipke, C.
2016-06-01
Online multi-person tracking in image sequences is commonly guided by recursive filters, whose predictive models define the expected positions of future states. When a predictive model deviates too much from the true motion of a pedestrian, which is often the case in crowded scenes due to unpredicted accelerations, the data association is prone to fail. In this paper we propose a novel predictive model on the basis of Gaussian Process Regression. The model takes into account the motion of every tracked pedestrian in the scene and the prediction is executed with respect to the velocities of all interrelated persons. As shown by the experiments, the model is capable of yielding more plausible predictions even in the presence of mutual occlusions or missing measurements. The approach is evaluated on a publicly available benchmark and outperforms other state-of-the-art trackers.
Reconstruct the Comic Distance Duality Relation by Gaussian Process
Zhang, Yi
2014-01-01
In this letter, the cosmic distance duality relation (CDDR) is reconstructed by gaussian process (GP) which is cosmological model independent. We will at least use GP two times to get a continuous $\\eta$ which denotes the deviation of the CDDR. The GP is needed to make the redshifts of the luminosity distance data (LD, $D_{L}$) and the angular diameter distance data (ADD, $D_{A}$) at the same point. Then, it is possible to construct the $\\eta$ sample. And, the GP is needed again to see the shape of the CDDR (or $\\eta$). The spherical sample of galaxy cluster (GC) which gives out the ADD data seems inconsistent with the CDDR. Our reconstructing results from the Union 2.1 and the elliptical sample of galaxy cluster show a nearly constant $\\eta$.
Variable sigma Gaussian processes: An expectation propagation perspective
Yuan,; Abdel-Gawad, Ahmed H; Minka, Thomas P
2009-01-01
Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate GP methods have been proposed that essentially map the large dataset into a small set of basis points. The most advanced of these, the variable-sigma GP (VSGP) (Walder et al., 2008), allows each basis point to have its own length scale. However, VSGP was only derived for regression. We describe how VSGP can be applied to classification and other problems, by deriving it as an expectation propagation algorithm. In this view, sparse GP approximations correspond to a KL-projection of the true posterior onto a compact exponential family of GPs. VSGP constitutes one such family, and we show how to enlarge this family to get additional accuracy. In particular, we show that endowing each basis point with its own full covariance matrix provides a significant increase in approximat...
Incorporating Side Information in Probabilistic Matrix Factorization with Gaussian Processes
Adams, Ryan Prescott; Murray, Iain
2010-01-01
Probabilistic matrix factorization (PMF) is a powerful method for modeling data associated with pairwise relationships, finding use in collaborative filtering, computational biology, and document analysis, among other areas. In many domains, there is additional information that can assist in prediction. For example, when modeling movie ratings, we might know when the rating occurred, where the user lives, or what actors appear in the movie. It is difficult, however, to incorporate this side information into the PMF model. We propose a framework for incorporating side information by coupling together multiple PMF problems via Gaussian process priors. We replace scalar latent features with functions that vary over the space of side information. The GP priors on these functions require them to vary smoothly and share information. We successfully use this new method to predict the scores of professional basketball games, where side information about the venue and date of the game are relevant for the outcome.
Inferring time derivatives including cell growth rates using Gaussian processes
Swain, Peter S.; Stevenson, Keiran; Leary, Allen; Montano-Gutierrez, Luis F.; Clark, Ivan B. N.; Vogel, Jackie; Pilizota, Teuta
2016-12-01
Often the time derivative of a measured variable is of as much interest as the variable itself. For a growing population of biological cells, for example, the population's growth rate is typically more important than its size. Here we introduce a non-parametric method to infer first and second time derivatives as a function of time from time-series data. Our approach is based on Gaussian processes and applies to a wide range of data. In tests, the method is at least as accurate as others, but has several advantages: it estimates errors both in the inference and in any summary statistics, such as lag times, and allows interpolation with the corresponding error estimation. As illustrations, we infer growth rates of microbial cells, the rate of assembly of an amyloid fibril and both the speed and acceleration of two separating spindle pole bodies. Our algorithm should thus be broadly applicable.
Prediction of plasma simulation data with the Gaussian process method
Energy Technology Data Exchange (ETDEWEB)
Preuss, R.; Toussaint, U. von, E-mail: udo.v.toussaint@ipp.mpg.de [Max-Planck-Institute for Plasma Physics, EURATOM Association, 85748 Garching (Germany)
2014-12-05
The simulation of plasma-wall interactions of fusion plasmas is extremely costly in computer power and time - the running time for a single parameter setting is easily in the order of weeks or months. We propose to exploit the already gathered results in order to predict the outcome for parametric studies within the high dimensional parameter space. For this we utilize Gaussian processes within the Bayesian framework and perform validation with one and two dimensional test cases from which we learn how to assess the outcome. Finally, the newly implemented method is applied to simulated data from the scrape-off layer of a fusion plasma. Uncertainties of the predictions are provided which point the way to parameter settings of further (expensive) simulations.
Dual Control with Active Learning using Gaussian Process Regression
Alpcan, Tansu
2011-01-01
In many real world problems, control decisions have to be made with limited information. The controller may have no a priori (or even posteriori) data on the nonlinear system, except from a limited number of points that are obtained over time. This is either due to high cost of observation or the highly non-stationary nature of the system. The resulting conflict between information collection (identification, exploration) and control (optimization, exploitation) necessitates an active learning approach for iteratively selecting the control actions which concurrently provide the data points for system identification. This paper presents a dual control approach where the information acquired at each control step is quantified using the entropy measure from information theory and serves as the training input to a state-of-the-art Gaussian process regression (Bayesian learning) method. The explicit quantification of the information obtained from each data point allows for iterative optimization of both identifica...
PASS-GP: Predictive active set selection for Gaussian processes
DEFF Research Database (Denmark)
Henao, Ricardo; Winther, Ole
2010-01-01
to the active set selection strategy and marginal likelihood optimization on the active set. We make extensive tests on the USPS and MNIST digit classification databases with and without incorporating invariances, demonstrating that we can get state-of-the-art results (e.g.0.86% error on MNIST) with reasonable......We propose a new approximation method for Gaussian process (GP) learning for large data sets that combines inline active set selection with hyperparameter optimization. The predictive probability of the label is used for ranking the data points. We use the leave-one-out predictive probability...... available in GPs to make a common ranking for both active and inactive points, allowing points to be removed again from the active set. This is important for keeping the complexity down and at the same time focusing on points close to the decision boundary. We lend both theoretical and empirical support...
Efficient preference learning with pairwise continuous observations and Gaussian Processes
DEFF Research Database (Denmark)
Jensen, Bjørn Sand; Nielsen, Jens Brehm; Larsen, Jan
2011-01-01
Human preferences can effectively be elicited using pairwise comparisons and in this paper current state-of-the-art based on binary decisions is extended by a new paradigm which allows subjects to convey their degree of preference as a continuous but bounded response. For this purpose, a novel...... Betatype likelihood is proposed and applied in a Bayesian regression framework using Gaussian Process priors. Posterior estimation and inference is performed using a Laplace approximation. The potential of the paradigm is demonstrated and discussed in terms of learning rates and robustness by evaluating...... the predictive performance under various noise conditions on a synthetic dataset. It is demonstrated that the learning rate of the novel paradigm is not only faster under ideal conditions, where continuous responses are naturally more informative than binary decisions, but also under adverse conditions where...
Facility Deployment Decisions through Warp Optimizaton of Regressed Gaussian Processes
Scopatz, Anthony
2015-01-01
A method for quickly determining deployment schedules that meet a given fuel cycle demand is presented here. This algorithm is fast enough to perform in situ within low-fidelity fuel cycle simulators. It uses Gaussian process regression models to predict the production curve as a function of time and the number of deployed facilities. Each of these predictions is measured against the demand curve using the dynamic time warping distance. The minimum distance deployment schedule is evaluated in a full fuel cycle simulation, whose generated production curve then informs the model on the next optimization iteration. The method converges within five to ten iterations to a distance that is less than one percent of the total deployable production. A representative once-through fuel cycle is used to demonstrate the methodology for reactor deployment.
Improving gravitational-wave parameter estimation using Gaussian process regression
Moore, Christopher J; Chua, Alvin J K; Gair, Jonathan R
2015-01-01
Folding uncertainty in theoretical models into Bayesian parameter estimation is necessary in order to make reliable inferences. A general means of achieving this is by marginalising over model uncertainty using a prior distribution constructed using Gaussian process regression (GPR). Here, we apply this technique to (simulated) gravitational-wave signals from binary black holes that could be observed using advanced-era gravitational-wave detectors. Unless properly accounted for, uncertainty in the gravitational-wave templates could be the dominant source of error in studies of these systems. We explain our approach in detail and provide proofs of various features of the method, including the limiting behaviour for high signal-to-noise, where systematic model uncertainties dominate over noise errors. We find that the marginalised likelihood constructed via GPR offers a significant improvement in parameter estimation over the standard, uncorrected likelihood. We also examine the dependence of the method on the ...
Detecting Damped Lyman-$\\alpha$ Absorbers with Gaussian Processes
Garnett, Roman; Bird, Simeon; Schneider, Jeff
2016-01-01
We develop an automated technique for detecting damped Lyman-$\\alpha$ absorbers (DLAs) along spectroscopic sightlines to quasi-stellar objects (QSOs or quasars). The detection of DLAs in large-scale spectroscopic surveys such as SDSS-III sheds light on galaxy formation at high redshift, showing the nucleation of galaxies from diffuse gas. We use nearly 50 000 QSO spectra to learn a novel tailored Gaussian process model for quasar emission spectra, which we apply to the DLA detection problem via Bayesian model selection. We propose models for identifying an arbitrary number of DLAs along a given line of sight. We demonstrate our method's effectiveness using a large-scale validation experiment, with excellent performance. We also provide a catalog of our results applied to 162 861 spectra from SDSS-III data release 12.
Next Generation Strong Lensing Time Delay Estimation with Gaussian Processes
Hojjati, Alireza
2014-01-01
Strong gravitational lensing forms multiple, time delayed images of cosmological sources, with the "focal length" of the lens serving as a cosmological distance probe. Robust estimation of the time delay distance can tightly constrain the Hubble constant as well as the matter density and dark energy. Current and next generation surveys will find hundreds to thousands of lensed systems but accurate time delay estimation from noisy, gappy lightcurves is potentially a limiting systematic. Using a large sample of blinded lightcurves from the Strong Lens Time Delay Challenge we develop and demonstrate a Gaussian Process crosscorrelation technique that delivers an average bias within 0.1% depending on the sampling, necessary for subpercent Hubble constant determination. The fits are accurate (80% of them within 1 day) for delays from 5-100 days and robust against cadence variations shorter than 6 days. We study the effects of survey characteristics such as cadence, season, and campaign length, and derive requiremen...
Learning with Uncertainty - Gaussian Processes and Relevance Vector Machines
DEFF Research Database (Denmark)
Candela, Joaquin Quinonero
2004-01-01
This thesis is concerned with Gaussian Processes (GPs) and Relevance Vector Machines (RVMs), both of which are particular instances of probabilistic linear models. We look at both models from a Bayesian perspective, and are forced to adopt an approximate Bayesian treatment to learning for two....... Computational efficiency is obtained through sparseness: sparse linear models have a significant number of their weights set to zero. For the RVM, which we treat in Chap. 2, we show that it is precisely the particular choice of Bayesian approximation that enforces sparseness. Probabilistic models have...... the important property of producing predictive distributions instead of point predictions. We also show that the resulting sparse probabilistic model implies counterintuitive priors over functions, and ultimately inappropriate predictive variances; the model is more certain about its predictions, the further...
SCALABLE TIME SERIES CHANGE DETECTION FOR BIOMASS MONITORING USING GAUSSIAN PROCESS
National Aeronautics and Space Administration — SCALABLE TIME SERIES CHANGE DETECTION FOR BIOMASS MONITORING USING GAUSSIAN PROCESS VARUN CHANDOLA AND RANGA RAJU VATSAVAI Abstract. Biomass monitoring,...
A Scalable Gaussian Process Analysis Algorithm for Biomass Monitoring
Energy Technology Data Exchange (ETDEWEB)
Chandola, Varun [ORNL; Vatsavai, Raju [ORNL
2011-01-01
Biomass monitoring is vital for studying the carbon cycle of earth's ecosystem and has several significant implications, especially in the context of understanding climate change and its impacts. Recently, several change detection methods have been proposed to identify land cover changes in temporal profiles (time series) of vegetation collected using remote sensing instruments, but do not satisfy one or both of the two requirements of the biomass monitoring problem, i.e., {\\em operating in online mode} and {\\em handling periodic time series}. In this paper, we adapt Gaussian process regression to detect changes in such time series in an online fashion. While Gaussian process (GP) have been widely used as a kernel based learning method for regression and classification, their applicability to massive spatio-temporal data sets, such as remote sensing data, has been limited owing to the high computational costs involved. We focus on addressing the scalability issues associated with the proposed GP based change detection algorithm. This paper makes several significant contributions. First, we propose a GP based online time series change detection algorithm and demonstrate its effectiveness in detecting different types of changes in {\\em Normalized Difference Vegetation Index} (NDVI) data obtained from a study area in Iowa, USA. Second, we propose an efficient Toeplitz matrix based solution which significantly improves the computational complexity and memory requirements of the proposed GP based method. Specifically, the proposed solution can analyze a time series of length $t$ in $O(t^2)$ time while maintaining a $O(t)$ memory footprint, compared to the $O(t^3)$ time and $O(t^2)$ memory requirement of standard matrix manipulation based methods. Third, we describe a parallel version of the proposed solution which can be used to simultaneously analyze a large number of time series. We study three different parallel implementations: using threads, MPI, and a
Local time and Tanaka formula for a Volterra-type multifractional Gaussian process
Boufoussi, Brahim; Marty, Renaud; 10.3150/10-BEJ261
2010-01-01
The stochastic calculus for Gaussian processes is applied to obtain a Tanaka formula for a Volterra-type multifractional Gaussian process. The existence and regularity properties of the local time of this process are obtained by means of Berman's Fourier analytic approach.
Multistep Wind Speed Forecasting Based on Wavelet and Gaussian Processes
Directory of Open Access Journals (Sweden)
Niya Chen
2013-01-01
Full Text Available Accurate wind speed forecasts are necessary for the safety and economy of the renewable energy utilization. The wind speed forecasts can be obtained by statistical model based on historical data. In this paper, a novel W-GP model (wavelet decomposition based Gaussian process learning paradigm is proposed for short-term wind speed forecasting. The nonstationary and nonlinear original wind speed series is first decomposed into a set of better-behaved constitutive subseries by wavelet decomposition. Then these sub-series are forecasted respectively by GP method, and the forecast results are summed to formulate an ensemble forecast for original wind speed series. Therefore, the previous process which obtains wind speed forecast result is named W-GP model. Finally, the proposed model is applied to short-term forecasting of the mean hourly and daily wind speed for a wind farm located in southern China. The prediction results indicate that the proposed W-GP model, which achieves a mean 13.34% improvement in RMSE (Root Mean Square Error compared to persistence method for mean hourly data and a mean 7.71% improvement for mean daily wind speed data, shows the best forecasting accuracy among several forecasting models.
Gaussian process regression for forecasting battery state of health
Richardson, Robert R.; Osborne, Michael A.; Howey, David A.
2017-07-01
Accurately predicting the future capacity and remaining useful life of batteries is necessary to ensure reliable system operation and to minimise maintenance costs. The complex nature of battery degradation has meant that mechanistic modelling of capacity fade has thus far remained intractable; however, with the advent of cloud-connected devices, data from cells in various applications is becoming increasingly available, and the feasibility of data-driven methods for battery prognostics is increasing. Here we propose Gaussian process (GP) regression for forecasting battery state of health, and highlight various advantages of GPs over other data-driven and mechanistic approaches. GPs are a type of Bayesian non-parametric method, and hence can model complex systems whilst handling uncertainty in a principled manner. Prior information can be exploited by GPs in a variety of ways: explicit mean functions can be used if the functional form of the underlying degradation model is available, and multiple-output GPs can effectively exploit correlations between data from different cells. We demonstrate the predictive capability of GPs for short-term and long-term (remaining useful life) forecasting on a selection of capacity vs. cycle datasets from lithium-ion cells.
Spectrum-based kernel length estimation for Gaussian process classification.
Wang, Liang; Li, Chuan
2014-06-01
Recent studies have shown that Gaussian process (GP) classification, a discriminative supervised learning approach, has achieved competitive performance in real applications compared with most state-of-the-art supervised learning methods. However, the problem of automatic model selection in GP classification, involving the kernel function form and the corresponding parameter values (which are unknown in advance), remains a challenge. To make GP classification a more practical tool, this paper presents a novel spectrum analysis-based approach for model selection by refining the GP kernel function to match the given input data. Specifically, we target the problem of GP kernel length scale estimation. Spectrums are first calculated analytically from the kernel function itself using the autocorrelation theorem as well as being estimated numerically from the training data themselves. Then, the kernel length scale is automatically estimated by equating the two spectrum values, i.e., the kernel function spectrum equals to the estimated training data spectrum. Compared with the classical Bayesian method for kernel length scale estimation via maximizing the marginal likelihood (which is time consuming and could suffer from multiple local optima), extensive experimental results on various data sets show that our proposed method is both efficient and accurate.
Bayesian site selection for fast Gaussian process regression
Pourhabib, Arash
2014-02-05
Gaussian Process (GP) regression is a popular method in the field of machine learning and computer experiment designs; however, its ability to handle large data sets is hindered by the computational difficulty in inverting a large covariance matrix. Likelihood approximation methods were developed as a fast GP approximation, thereby reducing the computation cost of GP regression by utilizing a much smaller set of unobserved latent variables called pseudo points. This article reports a further improvement to the likelihood approximation methods by simultaneously deciding both the number and locations of the pseudo points. The proposed approach is a Bayesian site selection method where both the number and locations of the pseudo inputs are parameters in the model, and the Bayesian model is solved using a reversible jump Markov chain Monte Carlo technique. Through a number of simulated and real data sets, it is demonstrated that with appropriate priors chosen, the Bayesian site selection method can produce a good balance between computation time and prediction accuracy: it is fast enough to handle large data sets that a full GP is unable to handle, and it improves, quite often remarkably, the prediction accuracy, compared with the existing likelihood approximations. © 2014 Taylor and Francis Group, LLC.
Scalable Indoor Localization via Mobile Crowdsourcing and Gaussian Process.
Chang, Qiang; Li, Qun; Shi, Zesen; Chen, Wei; Wang, Weiping
2016-03-16
Indoor localization using Received Signal Strength Indication (RSSI) fingerprinting has been extensively studied for decades. The positioning accuracy is highly dependent on the density of the signal database. In areas without calibration data, however, this algorithm breaks down. Building and updating a dense signal database is labor intensive, expensive, and even impossible in some areas. Researchers are continually searching for better algorithms to create and update dense databases more efficiently. In this paper, we propose a scalable indoor positioning algorithm that works both in surveyed and unsurveyed areas. We first propose Minimum Inverse Distance (MID) algorithm to build a virtual database with uniformly distributed virtual Reference Points (RP). The area covered by the virtual RPs can be larger than the surveyed area. A Local Gaussian Process (LGP) is then applied to estimate the virtual RPs' RSSI values based on the crowdsourced training data. Finally, we improve the Bayesian algorithm to estimate the user's location using the virtual database. All the parameters are optimized by simulations, and the new algorithm is tested on real-case scenarios. The results show that the new algorithm improves the accuracy by 25.5% in the surveyed area, with an average positioning error below 2.2 m for 80% of the cases. Moreover, the proposed algorithm can localize the users in the neighboring unsurveyed area.
Scalable Indoor Localization via Mobile Crowdsourcing and Gaussian Process
Directory of Open Access Journals (Sweden)
Qiang Chang
2016-03-01
Full Text Available Indoor localization using Received Signal Strength Indication (RSSI fingerprinting has been extensively studied for decades. The positioning accuracy is highly dependent on the density of the signal database. In areas without calibration data, however, this algorithm breaks down. Building and updating a dense signal database is labor intensive, expensive, and even impossible in some areas. Researchers are continually searching for better algorithms to create and update dense databases more efficiently. In this paper, we propose a scalable indoor positioning algorithm that works both in surveyed and unsurveyed areas. We first propose Minimum Inverse Distance (MID algorithm to build a virtual database with uniformly distributed virtual Reference Points (RP. The area covered by the virtual RPs can be larger than the surveyed area. A Local Gaussian Process (LGP is then applied to estimate the virtual RPs’ RSSI values based on the crowdsourced training data. Finally, we improve the Bayesian algorithm to estimate the user’s location using the virtual database. All the parameters are optimized by simulations, and the new algorithm is tested on real-case scenarios. The results show that the new algorithm improves the accuracy by 25.5% in the surveyed area, with an average positioning error below 2.2 m for 80% of the cases. Moreover, the proposed algorithm can localize the users in the neighboring unsurveyed area.
Gaussian Process Model for Collision Dynamics of Complex Molecules.
Cui, Jie; Krems, Roman V
2015-08-14
We show that a Gaussian process model can be combined with a small number (of order 100) of scattering calculations to provide a multidimensional dependence of scattering observables on the experimentally controllable parameters (such as the collision energy or temperature) as well as the potential energy surface (PES) parameters. For the case of Ar-C_{6}H_{6} collisions, we show that 200 classical trajectory calculations are sufficient to provide a ten-dimensional hypersurface, giving the dependence of the collision lifetimes on the collision energy, internal temperature, and eight PES parameters. This can be used for solving the inverse scattering problem, for the efficient calculation of thermally averaged observables, for reducing the error of the molecular dynamics calculations by averaging over the PES variations, and for the analysis of the sensitivity of the observables to individual parameters determining the PES. Trained by a combination of classical and quantum calculations, the model provides an accurate description of the quantum scattering cross sections, even near scattering resonances.
Computed tomography perfusion imaging denoising using Gaussian process regression
Zhu, Fan; Carpenter, Trevor; Rodriguez Gonzalez, David; Atkinson, Malcolm; Wardlaw, Joanna
2012-06-01
Brain perfusion weighted images acquired using dynamic contrast studies have an important clinical role in acute stroke diagnosis and treatment decisions. However, computed tomography (CT) images suffer from low contrast-to-noise ratios (CNR) as a consequence of the limitation of the exposure to radiation of the patient. As a consequence, the developments of methods for improving the CNR are valuable. The majority of existing approaches for denoising CT images are optimized for 3D (spatial) information, including spatial decimation (spatially weighted mean filters) and techniques based on wavelet and curvelet transforms. However, perfusion imaging data is 4D as it also contains temporal information. Our approach using Gaussian process regression (GPR), which takes advantage of the temporal information, to reduce the noise level. Over the entire image, GPR gains a 99% CNR improvement over the raw images and also improves the quality of haemodynamic maps allowing a better identification of edges and detailed information. At the level of individual voxel, GPR provides a stable baseline, helps us to identify key parameters from tissue time-concentration curves and reduces the oscillations in the curve. GPR is superior to the comparable techniques used in this study.
Multi-Scale Gaussian Processes: a Novel Model for Chaotic Time Series Prediction
Institute of Scientific and Technical Information of China (English)
ZHOU Ya-Tong; ZHANG Tai-Yi; SUN Jian-Cheng
2007-01-01
@@ Based on the classical Gaussian process (GP) model, we propose a multi-scale Gaussian process (MGP) model to predict the existence of chaotic time series. The MGP employs a covariance function that is constructed by a scaling function with its different dilations and translations, ensuring that the optimal hyperparameter is easy to determine.
Application of Gaussian Process Modeling to Analysis of Functional Unreliability
Energy Technology Data Exchange (ETDEWEB)
R. Youngblood
2014-06-01
This paper applies Gaussian Process (GP) modeling to analysis of the functional unreliability of a “passive system.” GPs have been used widely in many ways [1]. The present application uses a GP for emulation of a system simulation code. Such an emulator can be applied in several distinct ways, discussed below. All applications illustrated in this paper have precedents in the literature; the present paper is an application of GP technology to a problem that was originally analyzed [2] using neural networks (NN), and later [3, 4] by a method called “Alternating Conditional Expectations” (ACE). This exercise enables a multifaceted comparison of both the processes and the results. Given knowledge of the range of possible values of key system variables, one could, in principle, quantify functional unreliability by sampling from their joint probability distribution, and performing a system simulation for each sample to determine whether the function succeeded for that particular setting of the variables. Using previously available system simulation codes, such an approach is generally impractical for a plant-scale problem. It has long been recognized, however, that a well-trained code emulator or surrogate could be used in a sampling process to quantify certain performance metrics, even for plant-scale problems. “Response surfaces” were used for this many years ago. But response surfaces are at their best for smoothly varying functions; in regions of parameter space where key system performance metrics may behave in complex ways, or even exhibit discontinuities, response surfaces are not the best available tool. This consideration was one of several that drove the work in [2]. In the present paper, (1) the original quantification of functional unreliability using NN [2], and later ACE [3], is reprised using GP; (2) additional information provided by the GP about uncertainty in the limit surface, generally unavailable in other representations, is discussed
Vegetation Monitoring with Gaussian Processes and Latent Force Models
Camps-Valls, Gustau; Svendsen, Daniel; Martino, Luca; Campos, Manuel; Luengo, David
2017-04-01
Monitoring vegetation by biophysical parameter retrieval from Earth observation data is a challenging problem, where machine learning is currently a key player. Neural networks, kernel methods, and Gaussian Process (GP) regression have excelled in parameter retrieval tasks at both local and global scales. GP regression is based on solid Bayesian statistics, yield efficient and accurate parameter estimates, and provides interesting advantages over competing machine learning approaches such as confidence intervals. However, GP models are hampered by lack of interpretability, that prevented the widespread adoption by a larger community. In this presentation we will summarize some of our latest developments to address this issue. We will review the main characteristics of GPs and their advantages in vegetation monitoring standard applications. Then, three advanced GP models will be introduced. First, we will derive sensitivity maps for the GP predictive function that allows us to obtain feature ranking from the model and to assess the influence of examples in the solution. Second, we will introduce a Joint GP (JGP) model that combines in situ measurements and simulated radiative transfer data in a single GP model. The JGP regression provides more sensible confidence intervals for the predictions, respects the physics of the underlying processes, and allows for transferability across time and space. Finally, a latent force model (LFM) for GP modeling that encodes ordinary differential equations to blend data-driven modeling and physical models of the system is presented. The LFM performs multi-output regression, adapts to the signal characteristics, is able to cope with missing data in the time series, and provides explicit latent functions that allow system analysis and evaluation. Empirical evidence of the performance of these models will be presented through illustrative examples.
A sparse Gaussian process framework for photometric redshift estimation
Almosallam, Ibrahim A.; Lindsay, Sam N.; Jarvis, Matt J.; Roberts, Stephen J.
2016-01-01
Accurate photometric redshifts are a lynchpin for many future experiments to pin down the cosmological model and for studies of galaxy evolution. In this study, a novel sparse regression framework for photometric redshift estimation is presented. Synthetic data set simulating the Euclid survey and real data from SDSS DR12 are used to train and test the proposed models. We show that approaches which include careful data preparation and model design offer a significant improvement in comparison with several competing machine learning algorithms. Standard implementations of most regression algorithms use the minimization of the sum of squared errors as the objective function. For redshift inference, this induces a bias in the posterior mean of the output distribution, which can be problematic. In this paper, we directly minimize the target metric Δz = (zs - zp)/(1 + zs) and address the bias problem via a distribution-based weighting scheme, incorporated as part of the optimization objective. The results are compared with other machine learning algorithms in the field such as artificial neural networks (ANN), Gaussian processes (GPs) and sparse GPs. The proposed framework reaches a mean absolute Δz = 0.0026(1 + zs), over the redshift range of 0 ≤ zs ≤ 2 on the simulated data, and Δz = 0.0178(1 + zs) over the entire redshift range on the SDSS DR12 survey, outperforming the standard ANNz used in the literature. We also investigate how the relative size of the training sample affects the photometric redshift accuracy. We find that a training sample of >30 per cent of total sample size, provides little additional constraint on the photometric redshifts, and note that our GP formalism strongly outperforms ANNz in the sparse data regime for the simulated data set.
Gaussian process classification of superparamagnetic relaxometry data: Phantom study.
Sovizi, Javad; Mathieu, Kelsey B; Thrower, Sara L; Stefan, Wolfgang; Hazle, John D; Fuentes, David
2017-07-24
Superparamagnetic relaxometry (SPMR) is an emerging technology that holds potential for use in early cancer detection. Measurement of the magnetic field after the excitation of cancer-bound superparamagnetic iron oxide nanoparticles (SPIONs) enables the reconstruction of SPIONs spatial distribution and hence tumor detection. However, image reconstruction often requires solving an ill-posed inverse problem that is computationally challenging and sensitive to measurement uncertainty. Moreover, an additional image processing module is required to automatically detect and localize the tumor in the reconstructed image. Our goal is to examine the use of data-driven machine learning technique to detect a weak signal induced by a small cluster of SPIONs (surrogate tumor) in presence of background signal and measurement uncertainty. We aim to investigate the performance of both data-driven and image reconstruction models to characterize situations that one can replace the computationally-challenging reconstruction technique by the data-driven model. We utilize Gaussian process (GP) classification model and a physics-based image reconstruction method, tailored to SPMR datasets that are obtained from (i) in silico simulations designed based on mouse cancer models and (ii) phantom experiments using MagSense system (Imagion Biosystems, Inc.). We investigate the performance of the GP classifier against the reconstruction technique, for different levels of measurement noise, different scenarios of SPIONs distribution, and different concentrations of SPIONs at the surrogate tumor. In our in silico source detection analysis, we were able to achieve high sensitivity results using GP model that outperformed the image reconstruction model for various choices of SPIONs concentration at the surrogate tumor and measurement noise levels. Moreover, in our phantom studies we were able to detect the surrogate tumor phantoms with 5% and 7.3% of the total used SPIONs, surrounded by 9 low
Crevillén-García, D.; Wilkinson, R. D.; Shah, A. A.; Power, H.
2017-01-01
Numerical groundwater flow and dissolution models of physico-chemical processes in deep aquifers are usually subject to uncertainty in one or more of the model input parameters. This uncertainty is propagated through the equations and needs to be quantified and characterised in order to rely on the model outputs. In this paper we present a Gaussian process emulation method as a tool for performing uncertainty quantification in mathematical models for convection and dissolution processes in porous media. One of the advantages of this method is its ability to significantly reduce the computational cost of an uncertainty analysis, while yielding accurate results, compared to classical Monte Carlo methods. We apply the methodology to a model of convectively-enhanced dissolution processes occurring during carbon capture and storage. In this model, the Gaussian process methodology fails due to the presence of multiple branches of solutions emanating from a bifurcation point, i.e., two equilibrium states exist rather than one. To overcome this issue we use a classifier as a precursor to the Gaussian process emulation, after which we are able to successfully perform a full uncertainty analysis in the vicinity of the bifurcation point.
Way, M J; Gazis, P R; Srivastava, A N
2009-01-01
Expanding upon the work of Way & Srivastava 2006 we demonstrate how the use of training sets of comparable size continue to make Gaussian Process Regression a competitive and in many ways a superior approach to that of Neural Networks and other least-squares fitting methods. This is possible via new matrix inversion techniques developed for Gaussian Processes that do not require that the kernel matrix be sparse. This development, combined with a neural-network kernel function appears to give superior results for this problem. We demonstrate that there appears to be a minimum number of training set galaxies needed to obtain the optimal fit when using our Gaussian Process Regression rank-reduction methods. We also find that morphological information included with many photometric surveys appears, for the most part, to make the photometric redshift evaluation slightly worse rather than better. This would indicate that morphological information simply adds noise from the Gaussian Process point of view. In add...
Sparse Inverse Gaussian Process Regression with Application to Climate Network Discovery
National Aeronautics and Space Administration — Regression problems on massive data sets are ubiquitous in many application domains including the Internet, earth and space sciences, and finances. Gaussian Process...
SPATIALLY ADAPTIVE SEMI-SUPERVISED LEARNING WITH GAUSSIAN PROCESSES FOR HYPERSPECTRAL DATA ANALYSIS
National Aeronautics and Space Administration — SPATIALLY ADAPTIVE SEMI-SUPERVISED LEARNING WITH GAUSSIAN PROCESSES FOR HYPERSPECTRAL DATA ANALYSIS GOO JUN * AND JOYDEEP GHOSH* Abstract. A semi-supervised learning...
EigenGP: Sparse Gaussian process models with data-dependent eigenfunctions
Qi, Yuan; Dai, Bo; Zhu, Yao
2012-01-01
Gaussian processes (GPs) provide a nonparametric representation of functions. However, classical GP inference suffers from high computational cost and it is difficult to design nonstationary GP priors in practice. In this paper, we propose a sparse Gaussian process model, EigenGP, based on the Karhunen-Loeve (KL) expansion of a GP prior. We use the Nystrom approximation to obtain data dependent eigenfunctions and select these eigenfunctions by evidence maximization. This selection reduces the...
On Sparse Multi-Task Gaussian Process Priors for Music Preference Learning
DEFF Research Database (Denmark)
Nielsen, Jens Brehm; Jensen, Bjørn Sand; Larsen, Jan
In this paper we study pairwise preference learning in a music setting with multitask Gaussian processes and examine the effect of sparsity in the input space as well as in the actual judgments. To introduce sparsity in the inputs, we extend a classic pairwise likelihood model to support sparse...... simulation shows the performance on a real-world music preference dataset which motivates and demonstrates the potential of the sparse Gaussian process formulation for pairwise likelihoods....
EigenGP: Gaussian processes with sparse data-dependent eigenfunctions
Qi, Yuan; Zhu, Yao
2012-01-01
Gaussian processes (GPs) provide a nonparametric representation of functions. Given N training points, the exact GP inference incurs high computational cost. A variety of sparse GP methods have been proposed to speed up GP inference. These methods essentially trade prediction accuracy with computational effciency. In this paper, we address this problem from a new perspective: we define an exact Gaussian process model, EigenGP, whose covariance function has a sparse spectrum adaptive to data. Specifically, we estimate eigenfunctions of covariance function based on training data and use an empirical Bayesian approach to select these eigenfunctions. Thus, unlike the previous Nystrom-based methods, EigenGP defines an exact Gaussian process model with an data-dependent covariance function. To handle nonlinear likelihoods, we develop an efficient expectation propagation inference algorithm, and couple it with an active-set algorithm for evidence maximization. Because the selected eigenfunctions (based on Gaussian ...
Gaussian point processes and two-by-two random matrix theory.
Nieminen, John M
2007-10-01
The statistics of the multidimensional Gaussian point process are discussed in connection with the spacing statistics of eigenvalues of 2x2 random matrices. We consider the three-dimensional Gaussian point process when two of the coordinates of a point are randomly chosen from a Gaussian distribution having a mean of zero and a variance of sigma;{2}=1 but the third coordinate is chosen from a Gaussian distribution having a variance in the range of 0random point being at a distance r from the origin is shown to be closely related to the nearest-neighbor spacing distribution of eigenvalues coming from an ensemble of 2x2 matrices defined by the French-Kota-Pandey-Mehta two-matrix model of random matrix theory. An elementary explanation of this result is given.
Directory of Open Access Journals (Sweden)
Mei Congli
2016-01-01
Full Text Available Erythromycin fermentation process is a typical microbial fermentation process. Soft sensors can be used to estimate biomass of Erythromycin fermentation process for their relative low cost, simple development, and ability to predict difficult-to-measure variables. However, traditional soft sensors, e.g. artificial neural network (ANN soft sensors, support vector machine (SVM soft sensors, etc., cannot represent the uncertainty (measurement precision of outputs. That results in difficulties in practice. Gaussian process regression (GPR provides a novel framework to solve regression problems. The output uncertainty of a GPR model follows Gaussian distribution, expressed in terms of mean and variance. The mean represents the predicted output. The variance can be viewed as the measure of confidence in the predicted output that distinguishes the GPR from NN and SVM soft sensor models. We proposed a systematic approach based on GPR and principal component analysis (PCA to establish a soft sensor to estimate biomass of Erythromycin fermentation process. Simulations on industrial data from an Erythromycin fermentation process show the proposed GPR soft sensor has high performance of modeling the uncertainty of estimates.
Spatio-Temporal Data Analysis at Scale Using Models Based on Gaussian Processes
Energy Technology Data Exchange (ETDEWEB)
Stein, Michael [Univ. of Chicago, IL (United States)
2017-03-13
Gaussian processes are the most commonly used statistical model for spatial and spatio-temporal processes that vary continuously. They are broadly applicable in the physical sciences and engineering and are also frequently used to approximate the output of complex computer models, deterministic or stochastic. We undertook research related to theory, computation, and applications of Gaussian processes as well as some work on estimating extremes of distributions for which a Gaussian process assumption might be inappropriate. Our theoretical contributions include the development of new classes of spatial-temporal covariance functions with desirable properties and new results showing that certain covariance models lead to predictions with undesirable properties. To understand how Gaussian process models behave when applied to deterministic computer models, we derived what we believe to be the first significant results on the large sample properties of estimators of parameters of Gaussian processes when the actual process is a simple deterministic function. Finally, we investigated some theoretical issues related to maxima of observations with varying upper bounds and found that, depending on the circumstances, standard large sample results for maxima may or may not hold. Our computational innovations include methods for analyzing large spatial datasets when observations fall on a partially observed grid and methods for estimating parameters of a Gaussian process model from observations taken by a polar-orbiting satellite. In our application of Gaussian process models to deterministic computer experiments, we carried out some matrix computations that would have been infeasible using even extended precision arithmetic by focusing on special cases in which all elements of the matrices under study are rational and using exact arithmetic. The applications we studied include total column ozone as measured from a polar-orbiting satellite, sea surface temperatures over the
Asymptotic behavior of the likelihood function of covariance matrices of spatial Gaussian processes
DEFF Research Database (Denmark)
Zimmermann, Ralf
2010-01-01
The covariance structure of spatial Gaussian predictors (aka Kriging predictors) is generally modeled by parameterized covariance functions; the associated hyperparameters in turn are estimated via the method of maximum likelihood. In this work, the asymptotic behavior of the maximum likelihood......: optimally trained nondegenerate spatial Gaussian processes cannot feature arbitrary ill-conditioned correlation matrices. The implication of this theorem on Kriging hyperparameter optimization is exposed. A nonartificial example is presented, where maximum likelihood-based Kriging model training...
An empirical analysis of the distribution of overshoots in a stationary Gaussian stochastic process
Carter, M. C.; Madison, M. W.
1973-01-01
The frequency distribution of overshoots in a stationary Gaussian stochastic process is analyzed. The primary processes involved in this analysis are computer simulation and statistical estimation. Computer simulation is used to simulate stationary Gaussian stochastic processes that have selected autocorrelation functions. An analysis of the simulation results reveals a frequency distribution for overshoots with a functional dependence on the mean and variance of the process. Statistical estimation is then used to estimate the mean and variance of a process. It is shown that for an autocorrelation function, the mean and the variance for the number of overshoots, a frequency distribution for overshoots can be estimated.
Recursive Gaussian Process Regression Model for Adaptive Quality Monitoring in Batch Processes
Directory of Open Access Journals (Sweden)
Le Zhou
2015-01-01
Full Text Available In chemical batch processes with slow responses and a long duration, it is time-consuming and expensive to obtain sufficient normal data for statistical analysis. With the persistent accumulation of the newly evolving data, the modelling becomes adequate gradually and the subsequent batches will change slightly owing to the slow time-varying behavior. To efficiently make use of the small amount of initial data and the newly evolving data sets, an adaptive monitoring scheme based on the recursive Gaussian process (RGP model is designed in this paper. Based on the initial data, a Gaussian process model and the corresponding SPE statistic are constructed at first. When the new batches of data are included, a strategy based on the RGP model is used to choose the proper data for model updating. The performance of the proposed method is finally demonstrated by a penicillin fermentation batch process and the result indicates that the proposed monitoring scheme is effective for adaptive modelling and online monitoring.
Institute of Scientific and Technical Information of China (English)
Zuo Xiang PENG; Jin Jun TONG; Zhi Chao WENG
2012-01-01
In this paper,we study the joint limit distributions of point processes of exceedances and partial sums of multivariate Gaussian sequences and show that the point processes and partial sums are asymptotically independent under some mild conditions.As a result,for a sequence of standardized stationary Gaussian vectors,we obtain that the point process of exceedances formed by the sequence (centered at the sample mean) converges in distribution to a Poisson process and it is asymptotically independent of the partial sums.The asymptotic joint limit distributions of order statistics and partial sums are also investigated under different conditions.
How big are the increments of 1~p-valued Gaussian processes?
Institute of Scientific and Technical Information of China (English)
林正炎
1997-01-01
be a sequence of independent Gaussian processes with σk2 (h)The large increments for Y(·) with boundedσ (p, h ) are investigated. As an example the large increments of infinite-dimensional fractional Ornstein-Uhlenbeck process in 1p are given. The method can also be applied to certain processes with stationary increments.
A Monte Carlo simulation model for stationary non-Gaussian processes
DEFF Research Database (Denmark)
Grigoriu, M.; Ditlevsen, Ove Dalager; Arwade, S. R.
2003-01-01
includes translation processes and is useful for both Monte Carlo simulation and analytical studies. As for translation processes, the mixture of translation processes can have a wide range of marginal distributions and correlation functions. Moreover, these processes can match a broader range of second...... athe proposed Monte Carlo algorithm and compare features of translation processes and mixture of translation processes. Keywords: Monte Carlo simulation, non-Gaussian processes, sampling theorem, stochastic processes, translation processes......A class of stationary non-Gaussian processes, referred to as the class of mixtures of translation processes, is defined by their finite dimensional distributions consisting of mixtures of finite dimensional distributions of translation processes. The class of mixtures of translation processes...
STABLE SUB-GAUSSIAN MODELS CONSTRUCTED BY POISSON PROCESSES
Institute of Scientific and Technical Information of China (English)
Dai Hongshuai; Li Yuqiang
2011-01-01
In this paper,we first prove that one-parameter standard α-stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity.Then we extend this result to the two-parameter processes.At last,we consider the approximation of the subordinated fractional Brownian motion.
Multiple Human Tracking Using Particle Filter with Gaussian Process Dynamical Model
Directory of Open Access Journals (Sweden)
Wang Jing
2008-01-01
Full Text Available Abstract We present a particle filter-based multitarget tracking method incorporating Gaussian process dynamical model (GPDM to improve robustness in multitarget tracking. With the particle filter Gaussian process dynamical model (PFGPDM, a high-dimensional target trajectory dataset of the observation space is projected to a low-dimensional latent space in a nonlinear probabilistic manner, which will then be used to classify object trajectories, predict the next motion state, and provide Gaussian process dynamical samples for the particle filter. In addition, Histogram-Bhattacharyya, GMM Kullback-Leibler, and the rotation invariant appearance models are employed, respectively, and compared in the particle filter as complimentary features to coordinate data used in GPDM. The simulation results demonstrate that the approach can track more than four targets with reasonable runtime overhead and performance. In addition, it can successfully deal with occasional missing frames and temporary occlusion.
On Sparse Multi-Task Gaussian Process Priors for Music Preference Learning
DEFF Research Database (Denmark)
Nielsen, Jens Brehm; Jensen, Bjørn Sand; Larsen, Jan
In this paper we study pairwise preference learning in a music setting with multitask Gaussian processes and examine the effect of sparsity in the input space as well as in the actual judgments. To introduce sparsity in the inputs, we extend a classic pairwise likelihood model to support sparse, ...... simulation shows the performance on a real-world music preference dataset which motivates and demonstrates the potential of the sparse Gaussian process formulation for pairwise likelihoods.......In this paper we study pairwise preference learning in a music setting with multitask Gaussian processes and examine the effect of sparsity in the input space as well as in the actual judgments. To introduce sparsity in the inputs, we extend a classic pairwise likelihood model to support sparse...
On Sparse Multi-Task Gaussian Process Priors for Music Preference Learning
DEFF Research Database (Denmark)
Nielsen, Jens Brehm; Jensen, Bjørn Sand; Larsen, Jan
, multi-task Gaussian process priors based on the pseudo-input formulation. Sparsity in the actual pairwise judgments is potentially obtained by a sequential experimental design approach, and we discuss the combination of the sequential approach with the pseudo-input preference model. A preliminary......In this paper we study pairwise preference learning in a music setting with multitask Gaussian processes and examine the effect of sparsity in the input space as well as in the actual judgments. To introduce sparsity in the inputs, we extend a classic pairwise likelihood model to support sparse...
On the maximum likelihood training of gradient-enhanced spatial Gaussian processes
DEFF Research Database (Denmark)
Zimmermann, Ralf
2013-01-01
Spatial Gaussian processes, alias spatial linear models or Kriging estimators, are a powerful and well-established tool for the design and analysis of computer experiments in a multitude of engineering applications. A key challenge in constructing spatial Gaussian processes is the training...... to incorporate the cross-correlations between the function values and their partial deriva- tives in the maximum likelihood estimation. In this paper it is proved that in consistency with the model assumptions, both the autocorrelations and the aforementioned cross-correlations must be considered when optimizing...
Modeling non-Gaussian time-varying vector autoregressive process
National Aeronautics and Space Administration — We present a novel and general methodology for modeling time-varying vector autoregressive processes which are widely used in many areas such as modeling of chemical...
Multi-scale Gaussian normalization for solar image processing
Morgan, Huw; Druckmüller, Miloslav
2014-01-01
Extreme ultra-violet images of the corona contain information over a wide range of spatial scales, and different structures such as active regions, quiet Sun, and filament channels contain information at very different brightness regimes. Processing of these images is important to reveal information, often hidden within the data, without introducing artefacts or bias. It is also important that any process be computationally efficient, particularly given the fine spatial and temporal resolutio...
Multi-scale Gaussian normalization for solar image processing
Morgan, Huw
2014-01-01
Extreme UltraViolet images of the corona contain information over a large range of spatial scales, and different structures such as active regions, quiet Sun and filament channels contain information at very different brightness regimes. Processing of these images is important to reveal information, often hidden within the data, without introducing artifacts or bias. It is also important that any process be computationally efficient, particularly given the fine spatial and temporal resolution of Atmospheric Imaging Assembly on the Solar Dynamics Observatory (AIA/SDO) , and consideration of future higher-resolution observations. A very efficient process is described here which is based on localized normalizing of the data at many different spatial scales. The method reveals information at the finest scales, whilst maintaining enough of the larger-scale information to provide context. It also intrinsically flattens noisy regions and can reveal structure in off-limb regions out to the edge of the field of view. ...
Power variation for Gaussian processes with stationary increments
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Corcuera, J.M.; Podolskij, Mark
2009-01-01
of the process we prove the convergence in probability for the properly normalised realised power variation. Moreover, under a further assumption on the Hölder index of the path of , we show an associated stable central limit theorem. The main tool is a general central limit theorem, due essentially to Hu...
Krems, Roman; Cui, Jie; Li, Zhiying
2016-05-01
We show how statistical learning techniques based on kriging (Gaussian Process regression) can be used for improving the predictions of classical and/or quantum scattering theory. In particular, we show how Gaussian Process models can be used for: (i) efficient non-parametric fitting of multi-dimensional potential energy surfaces without the need to fit ab initio data with analytical functions; (ii) obtaining scattering observables as functions of individual PES parameters; (iii) using classical trajectories to interpolate quantum results; (iv) extrapolation of scattering observables from one molecule to another; (v) obtaining scattering observables with error bars reflecting the inherent inaccuracy of the underlying potential energy surfaces. We argue that the application of Gaussian Process models to quantum scattering calculations may potentially elevate the theoretical predictions to the same level of certainty as the experimental measurements and can be used to identify the role of individual atoms in determining the outcome of collisions of complex molecules. We will show examples and discuss the applications of Gaussian Process models to improving the predictions of scattering theory relevant for the cold molecules research field. Work supported by NSERC of Canada.
Analysis of multi-species point patterns using multivariate log Gaussian Cox processes
DEFF Research Database (Denmark)
Waagepetersen, Rasmus; Guan, Yongtao; Jalilian, Abdollah;
Multivariate log Gaussian Cox processes are flexible models for multivariate point patterns. However, they have so far only been applied in bivariate cases. In this paper we move beyond the bivariate case in order to model multi-species point patterns of tree locations. In particular we address...
DEFF Research Database (Denmark)
Malzahn, Dorthe; Opper, Manfred
2003-01-01
We employ the replica method of statistical physics to study the average case performance of learning systems. The new feature of our theory is that general distributions of data can be treated, which enables applications to real data. For a class of Bayesian prediction models which are based on ...... on Gaussian processes, we discuss Bootstrap estimates for learning curves....
Multi-Scale Gaussian Normalization for Solar Image Processing.
Morgan, Huw; Druckmüller, Miloslav
Extreme ultra-violet images of the corona contain information over a wide range of spatial scales, and different structures such as active regions, quiet Sun, and filament channels contain information at very different brightness regimes. Processing of these images is important to reveal information, often hidden within the data, without introducing artefacts or bias. It is also important that any process be computationally efficient, particularly given the fine spatial and temporal resolution of Atmospheric Imaging Assembly on the Solar Dynamics Observatory (AIA/SDO), and consideration of future higher resolution observations. A very efficient process is described here, which is based on localised normalising of the data at many different spatial scales. The method reveals information at the finest scales whilst maintaining enough of the larger-scale information to provide context. It also intrinsically flattens noisy regions and can reveal structure in off-limb regions out to the edge of the field of view. We also applied the method successfully to a white-light coronagraph observation.
Institute of Scientific and Technical Information of China (English)
Yao Weixiong; Yang Yi; Zeng Bin
2009-01-01
High pressure die casting (HPDC) is a versatile material processing method for mass-production of metal parts with complex geometries,and this method has been widely used in manufacturing various products of excellent dimensional accuracy and productivity. In order to ensure the quality of the components,a number of variables need to be properly set. A novel methodology for high pressure die casting process optimization was developed,validated and applied to selection of optimal parameters,which incorporate design of experiment (DOE),Gaussian process (GP) regression technique and genetic algorithms (GA). This new approach was applied to process optimization for cast magnesium alloy notebook shell. After being trained,using data generated by PROCAST (FEM-based simulation software),the GP model approximated well with the simulation by extracting useful information from the simulation results. With the help of MATLAB,the GP/GA based approach has achieved the optimum solution of die casting process condition settings.
Full extremal process, cluster law and freezing for two-dimensional discrete Gaussian Free Field
Biskup, Marek; Louidor, Oren
2016-01-01
We study the extremal process associated with the Discrete Gaussian Free Field (DGFF) in scaled-up (square-)lattice versions of bounded open planar domains subject to mild regularity conditions on the boundary. We prove that, in the scaling limit, this process tends to a Cox process decorated by independent, correlated clusters whose distribution is completely characterized. As an application, we control the scaling limit of the discrete supercritical Liouville measure, extract a Poisson-Diri...
A Bayesian optimal design for degradation tests based on the inverse Gaussian process
Energy Technology Data Exchange (ETDEWEB)
Peng, Weiwen; Liu, Yu; Li, Yan Feng; Zhu, Shun Peng; Huang, Hong Zhong [University of Electronic Science and Technology of China, Chengdu (China)
2014-10-15
The inverse Gaussian process is recently introduced as an attractive and flexible stochastic process for degradation modeling. This process has been demonstrated as a valuable complement for models that are developed on the basis of the Wiener and gamma processes. We investigate the optimal design of the degradation tests on the basis of the inverse Gaussian process. In addition to an optimal design with pre-estimated planning values of model parameters, we also address the issue of uncertainty in the planning values by using the Bayesian method. An average pre-posterior variance of reliability is used as the optimization criterion. A trade-off between sample size and number of degradation observations is investigated in the degradation test planning. The effects of priors on the optimal designs and on the value of prior information are also investigated and quantified. The degradation test planning of a GaAs Laser device is performed to demonstrate the proposed method.
Discussion: the design and analysis of the Gaussian process model
Energy Technology Data Exchange (ETDEWEB)
Williams, Brian J [Los Alamos National Laboratory; Loeppky, Jason L [UNIV OF BC-OKANAGAN
2008-01-01
The investigation of complex physical systems utilizing sophisticated computer models has become commonplace with the advent of modern computational facilities. In many applications, experimental data on the physical systems of interest is extremely expensive to obtain and hence is available in limited quantities. The mathematical systems implemented by the computer models often include parameters having uncertain values. This article provides an overview of statistical methodology for calibrating uncertain parameters to experimental data. This approach assumes that prior knowledge about such parameters is represented as a probability distribution, and the experimental data is used to refine our knowledge about these parameters, expressed as a posterior distribution. Uncertainty quantification for computer model predictions of the physical system are based fundamentally on this posterior distribution. Computer models are generally not perfect representations of reality for a variety of reasons, such as inadequacies in the physical modeling of some processes in the dynamic system. The statistical model includes components that identify and adjust for such discrepancies. A standard approach to statistical modeling of computer model output for unsampled inputs is introduced for the common situation where limited computer model runs are available. Extensions of the statistical methods to functional outputs are available and discussed briefly.
Lasko, Thomas A
2014-07-01
The episodic, irregular and asynchronous nature of medical data render them difficult substrates for standard machine learning algorithms. We would like to abstract away this difficulty for the class of time-stamped categorical variables (or events) by modeling them as a renewal process and inferring a probability density over non-parametric longitudinal intensity functions that modulate the process. Several methods exist for inferring such a density over intensity functions, but either their constraints prevent their use with our potentially bursty event streams, or their time complexity renders their use intractable on our long-duration observations of high-resolution events, or both. In this paper we present a new efficient and flexible inference method that uses direct numeric integration and smooth interpolation over Gaussian processes. We demonstrate that our direct method is up to twice as accurate and two orders of magnitude more efficient than the best existing method (thinning). Importantly, our direct method can infer intensity functions over the full range of bursty to memoryless to regular events, which thinning and many other methods cannot do. Finally, we apply the method to clinical event data and demonstrate a simple example application facilitated by the abstraction.
A unified formulation of Gaussian vs. sparse stochastic processes - Part I: Continuous-domain theory
Unser, Michael; Sun, Qiyu
2011-01-01
We introduce a general distributional framework that results in a unifying description and characterization of a rich variety of continuous-time stochastic processes. The cornerstone of our approach is an innovation model that is driven by some generalized white noise process, which may be Gaussian or not (e.g., Laplace, impulsive Poisson or alpha stable). This allows for a conceptual decoupling between the correlation properties of the process, which are imposed by the whitening operator L, and its sparsity pattern which is determined by the type of noise excitation. The latter is fully specified by a Levy measure. We show that the range of admissible innovation behavior varies between the purely Gaussian and super-sparse extremes. We prove that the corresponding generalized stochastic processes are well-defined mathematically provided that the (adjoint) inverse of the whitening operator satisfies some Lp bound for p>=1. We present a novel operator-based method that yields an explicit characterization of all...
Large-Deviation Results for Discriminant Statistics of Gaussian Locally Stationary Processes
Directory of Open Access Journals (Sweden)
Junichi Hirukawa
2012-01-01
Full Text Available This paper discusses the large-deviation principle of discriminant statistics for Gaussian locally stationary processes. First, large-deviation theorems for quadratic forms and the log-likelihood ratio for a Gaussian locally stationary process with a mean function are proved. Their asymptotics are described by the large deviation rate functions. Second, we consider the situations where processes are misspecified to be stationary. In these misspecified cases, we formally make the log-likelihood ratio discriminant statistics and derive the large deviation theorems of them. Since they are complicated, they are evaluated and illustrated by numerical examples. We realize the misspecification of the process to be stationary seriously affecting our discrimination.
Modeling Sea-Level Change using Errors-in-Variables Integrated Gaussian Processes
Cahill, Niamh; Parnell, Andrew; Kemp, Andrew; Horton, Benjamin
2014-05-01
We perform Bayesian inference on historical and late Holocene (last 2000 years) rates of sea-level change. The data that form the input to our model are tide-gauge measurements and proxy reconstructions from cores of coastal sediment. To accurately estimate rates of sea-level change and reliably compare tide-gauge compilations with proxy reconstructions it is necessary to account for the uncertainties that characterize each dataset. Many previous studies used simple linear regression models (most commonly polynomial regression) resulting in overly precise rate estimates. The model we propose uses an integrated Gaussian process approach, where a Gaussian process prior is placed on the rate of sea-level change and the data itself is modeled as the integral of this rate process. The non-parametric Gaussian process model is known to be well suited to modeling time series data. The advantage of using an integrated Gaussian process is that it allows for the direct estimation of the derivative of a one dimensional curve. The derivative at a particular time point will be representative of the rate of sea level change at that time point. The tide gauge and proxy data are complicated by multiple sources of uncertainty, some of which arise as part of the data collection exercise. Most notably, the proxy reconstructions include temporal uncertainty from dating of the sediment core using techniques such as radiocarbon. As a result of this, the integrated Gaussian process model is set in an errors-in-variables (EIV) framework so as to take account of this temporal uncertainty. The data must be corrected for land-level change known as glacio-isostatic adjustment (GIA) as it is important to isolate the climate-related sea-level signal. The correction for GIA introduces covariance between individual age and sea level observations into the model. The proposed integrated Gaussian process model allows for the estimation of instantaneous rates of sea-level change and accounts for all
Palacios, Julia A; Minin, Vladimir N
2013-03-01
Changes in population size influence genetic diversity of the population and, as a result, leave a signature of these changes in individual genomes in the population. We are interested in the inverse problem of reconstructing past population dynamics from genomic data. We start with a standard framework based on the coalescent, a stochastic process that generates genealogies connecting randomly sampled individuals from the population of interest. These genealogies serve as a glue between the population demographic history and genomic sequences. It turns out that only the times of genealogical lineage coalescences contain information about population size dynamics. Viewing these coalescent times as a point process, estimating population size trajectories is equivalent to estimating a conditional intensity of this point process. Therefore, our inverse problem is similar to estimating an inhomogeneous Poisson process intensity function. We demonstrate how recent advances in Gaussian process-based nonparametric inference for Poisson processes can be extended to Bayesian nonparametric estimation of population size dynamics under the coalescent. We compare our Gaussian process (GP) approach to one of the state-of-the-art Gaussian Markov random field (GMRF) methods for estimating population trajectories. Using simulated data, we demonstrate that our method has better accuracy and precision. Next, we analyze two genealogies reconstructed from real sequences of hepatitis C and human Influenza A viruses. In both cases, we recover more believed aspects of the viral demographic histories than the GMRF approach. We also find that our GP method produces more reasonable uncertainty estimates than the GMRF method.
Estimation for Non-Gaussian Locally Stationary Processes with Empirical Likelihood Method
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Hiroaki Ogata
2012-01-01
Full Text Available An application of the empirical likelihood method to non-Gaussian locally stationary processes is presented. Based on the central limit theorem for locally stationary processes, we give the asymptotic distributions of the maximum empirical likelihood estimator and the empirical likelihood ratio statistics, respectively. It is shown that the empirical likelihood method enables us to make inferences on various important indices in a time series analysis. Furthermore, we give a numerical study and investigate a finite sample property.
Bayesian electron density inference from JET lithium beam emission spectra using Gaussian processes
Kwak, Sehyun; Brix, M; Ghim, Y -c
2016-01-01
A Bayesian model to infer edge electron density profiles is developed for the JET lithium beam emission spectroscopy system, measuring Li I line radiation using 26 channels with ~1 cm spatial resolution and 10~20 ms temporal resolution. The density profile is modelled using a Gaussian process prior, and the uncertainty of the density profile is calculated by a Markov Chain Monte Carlo (MCMC) scheme. From the spectra measured by the transmission grating spectrometer, the Li line intensities are extracted, and modelled as a function of the plasma density by a multi-state model which describes the relevant processes between neutral lithium beam atoms and plasma particles. The spectral model fully takes into account interference filter and instrument effects, that are separately estimated, again using Gaussian processes. The line intensities are inferred based on a spectral model consistent with the measured spectra within their uncertainties, which includes photon statistics and electronic noise. Our newly devel...
A unified formulation of Gaussian vs. sparse stochastic processes - Part II: Discrete-domain theory
Unser, Michael; Amini, Arash; Kirshner, Hagai
2011-01-01
This paper is devoted to the characterization of an extended family of CARMA (continuous-time autoregressive moving average) processes that are solutions of stochastic differential equations driven by white Levy noise. These are completely specified by: (1) a set of poles and zeros that fixes their correlation structure, and (2) a canonical infinitely-divisible probability distribution that controls their degree of sparsity (with the Gaussian model corresponding to the least sparse scenario). The generalized CARMA processes are either stationary or non-stationary, depending on the location of the poles in the complex plane. The most basic non-stationary representatives (with a single pole at the origin) are the Levy processes, which are the non-Gaussian counterparts of Brownian motion. We focus on the general analog-to-discrete conversion problem and introduce a novel spline-based formalism that greatly simplifies the derivation of the correlation properties and joint probability distributions of the discrete...
Computationally efficient algorithm for Gaussian Process regression in case of structured samples
Belyaev, M.; Burnaev, E.; Kapushev, Y.
2016-04-01
Surrogate modeling is widely used in many engineering problems. Data sets often have Cartesian product structure (for instance factorial design of experiments with missing points). In such case the size of the data set can be very large. Therefore, one of the most popular algorithms for approximation-Gaussian Process regression-can be hardly applied due to its computational complexity. In this paper a computationally efficient approach for constructing Gaussian Process regression in case of data sets with Cartesian product structure is presented. Efficiency is achieved by using a special structure of the data set and operations with tensors. Proposed algorithm has low computational as well as memory complexity compared to existing algorithms. In this work we also introduce a regularization procedure allowing to take into account anisotropy of the data set and avoid degeneracy of regression model.
Bayesian Smoothing with Gaussian Processes Using Fourier Basis Functions in the spectralGP Package
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Christopher J. Paciorek
2007-04-01
Full Text Available The spectral representation of stationary Gaussian processes via the Fourier basis provides a computationally efficient specification of spatial surfaces and nonparametric regression functions for use in various statistical models. I describe the representation in detail and introduce the spectralGP package in R for computations. Because of the large number of basis coefficients, some form of shrinkage is necessary; I focus on a natural Bayesian approach via a particular parameterized prior structure that approximates stationary Gaussian processes on a regular grid. I review several models from the literature for data that do not lie on a grid, suggest a simple model modification, and provide example code demonstrating MCMC sampling using the spectralGP package. I describe reasons that mixing can be slow in certain situations and provide some suggestions for MCMC techniques to improve mixing, also with example code, and some general recommendations grounded in experience.
Invariant Gaussian Process Latent Variable Models and Application in Causal Discovery
Zhang, Kun; Janzing, Dominik
2012-01-01
In nonlinear latent variable models or dynamic models, if we consider the latent variables as confounders (common causes), the noise dependencies imply further relations between the observed variables. Such models are then closely related to causal discovery in the presence of nonlinear confounders, which is a challenging problem. However, generally in such models the observation noise is assumed to be independent across data dimensions, and consequently the noise dependencies are ignored. In this paper we focus on the Gaussian process latent variable model (GPLVM), from which we develop an extended model called invariant GPLVM (IGPLVM), which can adapt to arbitrary noise covariances. With the Gaussian process prior put on a particular transformation of the latent nonlinear functions, instead of the original ones, the algorithm for IGPLVM involves almost the same computational loads as that for the original GPLVM. Besides its potential application in causal discovery, IGPLVM has the advantage that its estimat...
Dropka, Natasha; Holena, Martin
2017-08-01
In directional solidification of silicon, the solid-liquid interface shape plays a crucial role for the quality of crystals. The interface shape can be influenced by forced convection using travelling magnetic fields. Up to now, there is no general and explicit methodology to identify the relation and the optimum combination of magnetic and growth parameters e.g., frequency, phase shift, current magnitude and interface deflection in a buoyancy regime. In the present study, 2D CFD modeling was used to generate data for the design and training of artificial neural networks and for Gaussian process modeling. The aim was to quickly assess the complex nonlinear dependences among the parameters and to optimize them for the interface flattening. The first encouraging results are presented and the pros and cons of artificial neural networks and Gaussian process modeling discussed.
Shi, J Q; Wang, B; Will, E J; West, R M
2012-11-20
We propose a new semiparametric model for functional regression analysis, combining a parametric mixed-effects model with a nonparametric Gaussian process regression model, namely a mixed-effects Gaussian process functional regression model. The parametric component can provide explanatory information between the response and the covariates, whereas the nonparametric component can add nonlinearity. We can model the mean and covariance structures simultaneously, combining the information borrowed from other subjects with the information collected from each individual subject. We apply the model to dose-response curves that describe changes in the responses of subjects for differing levels of the dose of a drug or agent and have a wide application in many areas. We illustrate the method for the management of renal anaemia. An individual dose-response curve is improved when more information is included by this mechanism from the subject/patient over time, enabling a patient-specific treatment regime.
José Luis Gómez-Dans; Philip Edward Lewis; Mathias Disney
2016-01-01
There is an increasing need to consistently combine observations from different sensors to monitor the state of the land surface. In order to achieve this, robust methods based on the inversion of radiative transfer (RT) models can be used to interpret the satellite observations. This typically results in an inverse problem, but a major drawback of these methods is the computational complexity. We introduce the concept of Gaussian Process (GP) emulators: surrogate functions that accurately ap...
Generalized Inferences about the Mean Vector of Several Multivariate Gaussian Processes
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Pilar Ibarrola
2015-01-01
Full Text Available We consider in this paper the problem of comparing the means of several multivariate Gaussian processes. It is assumed that the means depend linearly on an unknown vector parameter θ and that nuisance parameters appear in the covariance matrices. More precisely, we deal with the problem of testing hypotheses, as well as obtaining confidence regions for θ. Both methods will be based on the concepts of generalized p value and generalized confidence region adapted to our context.
celerite: Scalable 1D Gaussian Processes in C++, Python, and Julia
Foreman-Mackey, Daniel; Agol, Eric; Ambikasaran, Sivaram; Angus, Ruth
2017-09-01
celerite provides fast and scalable Gaussian Process (GP) Regression in one dimension and is implemented in C++, Python, and Julia. The celerite API is designed to be familiar to users of george and, like george, celerite is designed to efficiently evaluate the marginalized likelihood of a dataset under a GP model. This is then be used alongside a non-linear optimization or posterior inference library for the best results.
Gaussian process based intelligent sampling for measuring nano-structure surfaces
Sun, L. J.; Ren, M. J.; Yin, Y. H.
2016-09-01
Nanotechnology is the science and engineering that manipulate matters at nano scale, which can be used to create many new materials and devices with a vast range of applications. As the nanotech product increasingly enters the commercial marketplace, nanometrology becomes a stringent and enabling technology for the manipulation and the quality control of the nanotechnology. However, many measuring instruments, for instance scanning probe microscopy, are limited to relatively small area of hundreds of micrometers with very low efficiency. Therefore some intelligent sampling strategies should be required to improve the scanning efficiency for measuring large area. This paper presents a Gaussian process based intelligent sampling method to address this problem. The method makes use of Gaussian process based Bayesian regression as a mathematical foundation to represent the surface geometry, and the posterior estimation of Gaussian process is computed by combining the prior probability distribution with the maximum likelihood function. Then each sampling point is adaptively selected by determining the position which is the most likely outside of the required tolerance zone among the candidates and then inserted to update the model iteratively. Both simulationson the nominal surface and manufactured surface have been conducted on nano-structure surfaces to verify the validity of the proposed method. The results imply that the proposed method significantly improves the measurement efficiency in measuring large area structured surfaces.
Spatio-temporal learning with the online finite and infinite echo-state Gaussian processes.
Soh, Harold; Demiris, Yiannis
2015-03-01
Successful biological systems adapt to change. In this paper, we are principally concerned with adaptive systems that operate in environments where data arrives sequentially and is multivariate in nature, for example, sensory streams in robotic systems. We contribute two reservoir inspired methods: 1) the online echostate Gaussian process (OESGP) and 2) its infinite variant, the online infinite echostate Gaussian process (OIESGP) Both algorithms are iterative fixed-budget methods that learn from noisy time series. In particular, the OESGP combines the echo-state network with Bayesian online learning for Gaussian processes. Extending this to infinite reservoirs yields the OIESGP, which uses a novel recursive kernel with automatic relevance determination that enables spatial and temporal feature weighting. When fused with stochastic natural gradient descent, the kernel hyperparameters are iteratively adapted to better model the target system. Furthermore, insights into the underlying system can be gleamed from inspection of the resulting hyperparameters. Experiments on noisy benchmark problems (one-step prediction and system identification) demonstrate that our methods yield high accuracies relative to state-of-the-art methods, and standard kernels with sliding windows, particularly on problems with irrelevant dimensions. In addition, we describe two case studies in robotic learning-by-demonstration involving the Nao humanoid robot and the Assistive Robot Transport for Youngsters (ARTY) smart wheelchair.
Yun, Yuqi; Zevin, Michael; Sampson, Laura; Kalogera, Vassiliki
2017-01-01
With more observations from LIGO in the upcoming years, we will be able to construct an observed mass distribution of black holes to compare with binary evolution simulations. This will allow us to investigate the physics of binary evolution such as the effects of common envelope efficiency and wind strength, or the properties of the population such as the initial mass function.However, binary evolution codes become computationally expensive when running large populations of binaries over a multi-dimensional grid of input parameters, and may simulate accurately only for a limited combination of input parameter values. Therefore we developed a fast machine-learning method that utilizes Gaussian Mixture Model (GMM) and Gaussian Process (GP) regression, which together can predict distributions over the entire parameter space based on a limited number of simulated models. Furthermore, Gaussian Process regression naturally provides interpolation errors in addition to interpolation means, which could provide a means of targeting the most uncertain regions of parameter space for running further simulations.We also present a case study on applying this new method to predicting chirp mass distributions for binary black hole systems (BBHs) in Milky-way like galaxies of different metallicities.
Fast Direct Methods for Gaussian Processes and the Analysis of NASA Kepler Mission Data
Ambikasaran, Sivaram; Greengard, Leslie; Hogg, David W; O'Neil, Michael
2014-01-01
A number of problems in probability and statistics can be addressed using the multivariate normal (or multivariate Gaussian) distribution. In the one-dimensional case, computing the probability for a given mean and variance simply requires the evaluation of the corresponding Gaussian density. In the $n$-dimensional setting, however, it requires the inversion of an $n \\times n$ covariance matrix, $C$, as well as the evaluation of its determinant, $\\det(C)$. In many cases, the covariance matrix is of the form $C = \\sigma^2 I + K$, where $K$ is computed using a specified kernel, which depends on the data and additional parameters (called hyperparameters in Gaussian process computations). The matrix $C$ is typically dense, causing standard direct methods for inversion and determinant evaluation to require $\\mathcal O(n^3)$ work. This cost is prohibitive for large-scale modeling. Here, we show that for the most commonly used covariance functions, the matrix $C$ can be hierarchically factored into a product of bloc...
Institute of Scientific and Technical Information of China (English)
Xuan Yang; Xiao'e Ruan
2016-01-01
In this paper, a reinforced gradient-type iterative learning control profile is proposed by making use of system matrices and a proper learning step to improve the tracking performance of batch processes disturbed by exter-nal Gaussian white noise. The robustness is analyzed and the range of the step is specified by means of statistical technique and matrix theory. Compared with the conventional one, the proposed algorithm is more efficient to resist external noise. Numerical simulations of an injection molding process il ustrate that the proposed scheme is feasible and effective.
Gaussian Process Based Independent Analysis for Temporal Source Separation in fMRI.
Hald, Ditte Høvenhoff; Henao, Ricardo; Winther, Ole
2017-02-26
Functional Magnetic Resonance Imaging (fMRI) gives us a unique insight into the processes of the brain, and opens up for analyzing the functional activation patterns of the underlying sources. Task-inferred supervised learning with restrictive assumptions in the regression set-up, restricts the exploratory nature of the analysis. Fully unsupervised independent component analysis (ICA) algorithms, on the other hand, can struggle to detect clear classifiable components on single-subject data. We attribute this shortcoming to inadequate modeling of the fMRI source signals by failing to incorporate its temporal nature. fMRI source signals, biological stimuli and non-stimuli-related artifacts are all smooth over a time-scale compatible with the sampling time (TR). We therefore propose Gaussian process ICA (GPICA), which facilitates temporal dependency by the use of Gaussian process source priors. On two fMRI data sets with different sampling frequency, we show that the GPICA-inferred temporal components and associated spatial maps allow for a more definite interpretation than standard temporal ICA methods. The temporal structures of the sources are controlled by the covariance of the Gaussian process, specified by a kernel function with an interpretable and controllable temporal length scale parameter. We propose a hierarchical model specification, considering both instantaneous and convolutive mixing, and we infer source spatial maps, temporal patterns and temporal length scale parameters by Markov Chain Monte Carlo. A companion implementation made as a plug-in for SPM can be downloaded from https://github.com/dittehald/GPICA.
Measuring the Mass of Kepler-78b Using a Gaussian Process Model
Grunblatt, Samuel Kai; Howard, Andrew; Haywood, Raphaëlle
2015-01-01
Kepler-78b is a transiting planet that is 1.2 times the size of Earth and orbits a young K dwarf every 8 hours. Howard et al. (2013) and Pepe et al. (2013) independently reported the mass of Kepler-78b based on radial velocity measurements using the HIRES and HARPS-N spectrographs, respectively. In this study, a nonparametric model of the stellar activity observed in radial velocity measurements is made using Gaussian process regression, a novel technique in the field of radial velocity analysis, allowing the planetary Doppler signal to be modeled more accurately. By fitting the stellar activity with various Gaussian process regression models, we find a more precise measurement of the planet Doppler amplitude. We identify a superior Gaussian process model, and reanalyze both radial velocity datasets acquired by Howard et al. (2013) and Pepe et al. (2013) with this new technique. The Doppler amplitude of Kepler-78b is measured to be 1.92 +/- 0.25 m s-1, which corresponds to a mass of 1.93 +/- 0.27 ME, a 2.5-sigma improvement on the measurement of Howard et al (2013). This corresponds to a density of 6.1+1.9/-1.4 g cm-3, and an iron mass fraction of 0.32 +/- 0.26, assuming a two component rock-iron composition. This is consistent with an Earth-like composition, with uncertainties ranging from Moon-like to Mercury-like. Better understanding of the composition of Kepler-78b is an integral part of understanding rocky planet formation.
The Limit Theorems for Maxima of Stationary Gaussian Processes with Random Index
Institute of Scientific and Technical Information of China (English)
Zhong Quan TAN
2014-01-01
Let {X(t), t ≥ 0} be a standard (zero-mean, unit-variance) stationary Gaussian process with correlation function r(·) and continuous sample paths. In this paper, we consider the maxima M (T ) = max{X (t),∀t ∈ [0, T ]} with random index TT , where TT/T converges to a non-degenerate distribution or to a positive random variable in probability, and show that the limit distribution of M (TT ) exists under some additional conditions related to the correlation function r(·).
Using Gaussian Process Annealing Particle Filter for 3D Human Tracking
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Michael Rudzsky
2008-01-01
Full Text Available We present an approach for human body parts tracking in 3D with prelearned motion models using multiple cameras. Gaussian process annealing particle filter is proposed for tracking in order to reduce the dimensionality of the problem and to increase the tracker's stability and robustness. Comparing with a regular annealed particle filter-based tracker, we show that our algorithm can track better for low frame rate videos. We also show that our algorithm is capable of recovering after a temporal target loss.
Derrida, Bernard; Hakim, Vincent; Zeitak, Reuven
1996-09-01
The fraction r\\(t\\) of spins which have never flipped up to time t is studied within a linear diffusion approximation to phase ordering. Numerical simulations show that r\\(t\\) decays with time like a power law with a nontrivial exponent θ which depends on the space dimension. The dynamics is a special case of a stationary Gaussian process of known correlation function. The exponent θ is given by the asymptotic decay of the probability distribution of intervals between consecutive zero crossings. An approximation based on the assumption that successive zero crossings are independent random variables gives values of θ in close agreement with the results of simulations.
Uniform approximation of Gaussian wavelet for biomedical signal processing in analog domain.
Makkena, Goutham; Bvvsn, Prabhakara Rao; Srinivas, M B
2013-01-01
Signal processing in analog domain is favorable when power consumption is a critical design constraint. Continuous Wavelet Transform (CWT), which is increasingly being used in characterizing biomedical signals, when implemented in analog domain consumes less power provided the mother wavelet is properly approximated. This paper presents an approximation of Gaussian wavelet by making use of the Uniform approximation. Simulations of the approximated wavelet and the actual wavelet in MATLAB are performed and the results discussed. Simulations show that (i) approximation obtained closely matches the mother wavelet chosen and (ii) a stable approximation which helps in physical realization using any circuit design methodology.
Remaining Useful Life Prediction for Lithium-Ion Batteries Based on Gaussian Processes Mixture
Li, Lingling; Wang, Pengchong; Chao, Kuei-Hsiang; Zhou, Yatong; Xie, Yang
2016-01-01
The remaining useful life (RUL) prediction of Lithium-ion batteries is closely related to the capacity degeneration trajectories. Due to the self-charging and the capacity regeneration, the trajectories have the property of multimodality. Traditional prediction models such as the support vector machines (SVM) or the Gaussian Process regression (GPR) cannot accurately characterize this multimodality. This paper proposes a novel RUL prediction method based on the Gaussian Process Mixture (GPM). It can process multimodality by fitting different segments of trajectories with different GPR models separately, such that the tiny differences among these segments can be revealed. The method is demonstrated to be effective for prediction by the excellent predictive result of the experiments on the two commercial and chargeable Type 1850 Lithium-ion batteries, provided by NASA. The performance comparison among the models illustrates that the GPM is more accurate than the SVM and the GPR. In addition, GPM can yield the predictive confidence interval, which makes the prediction more reliable than that of traditional models. PMID:27632176
Image interpolation and denoising for division of focal plane sensors using Gaussian processes.
Gilboa, Elad; Cunningham, John P; Nehorai, Arye; Gruev, Viktor
2014-06-16
Image interpolation and denoising are important techniques in image processing. These methods are inherent to digital image acquisition as most digital cameras are composed of a 2D grid of heterogeneous imaging sensors. Current polarization imaging employ four different pixelated polarization filters, commonly referred to as division of focal plane polarization sensors. The sensors capture only partial information of the true scene, leading to a loss of spatial resolution as well as inaccuracy of the captured polarization information. Interpolation is a standard technique to recover the missing information and increase the accuracy of the captured polarization information. Here we focus specifically on Gaussian process regression as a way to perform a statistical image interpolation, where estimates of sensor noise are used to improve the accuracy of the estimated pixel information. We further exploit the inherent grid structure of this data to create a fast exact algorithm that operates in ����(N(3/2)) (vs. the naive ���� (N³)), thus making the Gaussian process method computationally tractable for image data. This modeling advance and the enabling computational advance combine to produce significant improvements over previously published interpolation methods for polarimeters, which is most pronounced in cases of low signal-to-noise ratio (SNR). We provide the comprehensive mathematical model as well as experimental results of the GP interpolation performance for division of focal plane polarimeter.
Nested polynomial trends for the improvement of Gaussian process-based predictors
Perrin, G.; Soize, C.; Marque-Pucheu, S.; Garnier, J.
2017-10-01
The role of simulation keeps increasing for the sensitivity analysis and the uncertainty quantification of complex systems. Such numerical procedures are generally based on the processing of a huge amount of code evaluations. When the computational cost associated with one particular evaluation of the code is high, such direct approaches based on the computer code only, are not affordable. Surrogate models have therefore to be introduced to interpolate the information given by a fixed set of code evaluations to the whole input space. When confronted to deterministic mappings, the Gaussian process regression (GPR), or kriging, presents a good compromise between complexity, efficiency and error control. Such a method considers the quantity of interest of the system as a particular realization of a Gaussian stochastic process, whose mean and covariance functions have to be identified from the available code evaluations. In this context, this work proposes an innovative parametrization of this mean function, which is based on the composition of two polynomials. This approach is particularly relevant for the approximation of strongly non linear quantities of interest from very little information. After presenting the theoretical basis of this method, this work compares its efficiency to alternative approaches on a series of examples.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Jiangjiang [College of Environmental and Resource Sciences, Zhejiang University, Hangzhou China; Li, Weixuan [Pacific Northwest National Laboratory, Richland Washington USA; Zeng, Lingzao [College of Environmental and Resource Sciences, Zhejiang University, Hangzhou China; Wu, Laosheng [Department of Environmental Sciences, University of California, Riverside California USA
2016-08-01
Surrogate models are commonly used in Bayesian approaches such as Markov Chain Monte Carlo (MCMC) to avoid repetitive CPU-demanding model evaluations. However, the approximation error of a surrogate may lead to biased estimations of the posterior distribution. This bias can be corrected by constructing a very accurate surrogate or implementing MCMC in a two-stage manner. Since the two-stage MCMC requires extra original model evaluations, the computational cost is still high. If the information of measurement is incorporated, a locally accurate approximation of the original model can be adaptively constructed with low computational cost. Based on this idea, we propose a Gaussian process (GP) surrogate-based Bayesian experimental design and parameter estimation approach for groundwater contaminant source identification problems. A major advantage of the GP surrogate is that it provides a convenient estimation of the approximation error, which can be incorporated in the Bayesian formula to avoid over-confident estimation of the posterior distribution. The proposed approach is tested with a numerical case study. Without sacrificing the estimation accuracy, the new approach achieves about 200 times of speed-up compared to our previous work using two-stage MCMC.
Infinite Shift-invariant Grouped Multi-task Learning for Gaussian Processes
Wang, Yuyang; Protopapas, Pavlos
2012-01-01
Multi-task learning leverages shared information among data sets to improve the learning performance of individual tasks. The paper applies this framework for data where each task is a phase-shifted periodic time series. In particular, we develop a novel Bayesian nonparametric model capturing a mixture of Gaussian processes where each task is a sum of a group-specific function and a component capturing individual variation, in addition to each task being phase shifted. We develop an efficient \\textsc{em} algorithm to learn the parameters of the model. As a special case we obtain the Gaussian mixture model and \\textsc{em} algorithm for phased-shifted periodic time series. Furthermore, we extend the proposed model by using a Dirichlet Process prior and thereby leading to an infinite mixture model that is capable of doing automatic model selection. A Variational Bayesian approach is developed for inference in this model. Experiments in regression, classification and class discovery demonstrate the performance of...
Buis, Arjan
2016-01-01
Elevated skin temperature at the body/device interface of lower-limb prostheses is one of the major factors that affect tissue health. The heat dissipation in prosthetic sockets is greatly influenced by the thermal conductive properties of the hard socket and liner material employed. However, monitoring of the interface temperature at skin level in lower-limb prosthesis is notoriously complicated. This is due to the flexible nature of the interface liners used which requires consistent positioning of sensors during donning and doffing. Predicting the residual limb temperature by monitoring the temperature between socket and liner rather than skin and liner could be an important step in alleviating complaints on increased temperature and perspiration in prosthetic sockets. To predict the residual limb temperature, a machine learning algorithm – Gaussian processes is employed, which utilizes the thermal time constant values of commonly used socket and liner materials. This Letter highlights the relevance of thermal time constant of prosthetic materials in Gaussian processes technique which would be useful in addressing the challenge of non-invasively monitoring the residual limb skin temperature. With the introduction of thermal time constant, the model can be optimised and generalised for a given prosthetic setup, thereby making the predictions more reliable. PMID:27695626
Silversides, Katherine L.; Melkumyan, Arman
2017-03-01
Machine learning techniques such as Gaussian Processes can be used to identify stratigraphically important features in geophysical logs. The marker shales in the banded iron formation hosted iron ore deposits of the Hamersley Ranges, Western Australia, form distinctive signatures in the natural gamma logs. The identification of these marker shales is important for stratigraphic identification of unit boundaries for the geological modelling of the deposit. Machine learning techniques each have different unique properties that will impact the results. For Gaussian Processes (GPs), the output values are inclined towards the mean value, particularly when there is not sufficient information in the library. The impact that these inclinations have on the classification can vary depending on the parameter values selected by the user. Therefore, when applying machine learning techniques, care must be taken to fit the technique to the problem correctly. This study focuses on optimising the settings and choices for training a GPs system to identify a specific marker shale. We show that the final results converge even when different, but equally valid starting libraries are used for the training. To analyse the impact on feature identification, GP models were trained so that the output was inclined towards a positive, neutral or negative output. For this type of classification, the best results were when the pull was towards a negative output. We also show that the GP output can be adjusted by using a standard deviation coefficient that changes the balance between certainty and accuracy in the results.
On the Bayesian Treed Multivariate Gaussian Process with Linear Model of Coregionalization
Energy Technology Data Exchange (ETDEWEB)
Konomi, Bledar A.; Karagiannis, Georgios; Lin, Guang
2015-02-01
The Bayesian treed Gaussian process (BTGP) has gained popularity in recent years because it provides a straightforward mechanism for modeling non-stationary data and can alleviate computational demands by fitting models to less data. The extension of BTGP to the multivariate setting requires us to model the cross-covariance and to propose efficient algorithms that can deal with trans-dimensional MCMC moves. In this paper we extend the cross-covariance of the Bayesian treed multivariate Gaussian process (BTMGP) to that of linear model of Coregionalization (LMC) cross-covariances. Different strategies have been developed to improve the MCMC mixing and invert smaller matrices in the Bayesian inference. Moreover, we compare the proposed BTMGP with existing multiple BTGP and BTMGP in test cases and multiphase flow computer experiment in a full scale regenerator of a carbon capture unit. The use of the BTMGP with LMC cross-covariance helped to predict the computer experiments relatively better than existing competitors. The proposed model has a wide variety of applications, such as computer experiments and environmental data. In the case of computer experiments we also develop an adaptive sampling strategy for the BTMGP with LMC cross-covariance function.
Cui, Jie; Li, Zhiying; Krems, Roman V
2015-10-21
We consider a problem of extrapolating the collision properties of a large polyatomic molecule A-H to make predictions of the dynamical properties for another molecule related to A-H by the substitution of the H atom with a small molecular group X, without explicitly computing the potential energy surface for A-X. We assume that the effect of the -H →-X substitution is embodied in a multidimensional function with unknown parameters characterizing the change of the potential energy surface. We propose to apply the Gaussian Process model to determine the dependence of the dynamical observables on the unknown parameters. This can be used to produce an interval of the observable values which corresponds to physical variations of the potential parameters. We show that the Gaussian Process model combined with classical trajectory calculations can be used to obtain the dependence of the cross sections for collisions of C6H5CN with He on the unknown parameters describing the interaction of the He atom with the CN fragment of the molecule. The unknown parameters are then varied within physically reasonable ranges to produce a prediction uncertainty of the cross sections. The results are normalized to the cross sections for He - C6H6 collisions obtained from quantum scattering calculations in order to provide a prediction interval of the thermally averaged cross sections for collisions of C6H5CN with He.
Revisiting Gaussian Process Regression Modeling for Localization in Wireless Sensor Networks.
Richter, Philipp; Toledano-Ayala, Manuel
2015-09-08
Signal strength-based positioning in wireless sensor networks is a key technology for seamless, ubiquitous localization, especially in areas where Global Navigation Satellite System (GNSS) signals propagate poorly. To enable wireless local area network (WLAN) location fingerprinting in larger areas while maintaining accuracy, methods to reduce the effort of radio map creation must be consolidated and automatized. Gaussian process regression has been applied to overcome this issue, also with auspicious results, but the fit of the model was never thoroughly assessed. Instead, most studies trained a readily available model, relying on the zero mean and squared exponential covariance function, without further scrutinization. This paper studies the Gaussian process regression model selection for WLAN fingerprinting in indoor and outdoor environments. We train several models for indoor/outdoor- and combined areas; we evaluate them quantitatively and compare them by means of adequate model measures, hence assessing the fit of these models directly. To illuminate the quality of the model fit, the residuals of the proposed model are investigated, as well. Comparative experiments on the positioning performance verify and conclude the model selection. In this way, we show that the standard model is not the most appropriate, discuss alternatives and present our best candidate.
Revisiting Gaussian Process Regression Modeling for Localization in Wireless Sensor Networks
Directory of Open Access Journals (Sweden)
Philipp Richter
2015-09-01
Full Text Available Signal strength-based positioning in wireless sensor networks is a key technology for seamless, ubiquitous localization, especially in areas where Global Navigation Satellite System (GNSS signals propagate poorly. To enable wireless local area network (WLAN location fingerprinting in larger areas while maintaining accuracy, methods to reduce the effort of radio map creation must be consolidated and automatized. Gaussian process regression has been applied to overcome this issue, also with auspicious results, but the fit of the model was never thoroughly assessed. Instead, most studies trained a readily available model, relying on the zero mean and squared exponential covariance function, without further scrutinization. This paper studies the Gaussian process regression model selection for WLAN fingerprinting in indoor and outdoor environments. We train several models for indoor/outdoor- and combined areas; we evaluate them quantitatively and compare them by means of adequate model measures, hence assessing the fit of these models directly. To illuminate the quality of the model fit, the residuals of the proposed model are investigated, as well. Comparative experiments on the positioning performance verify and conclude the model selection. In this way, we show that the standard model is not the most appropriate, discuss alternatives and present our best candidate.
Silversides, Katherine L.; Melkumyan, Arman
2016-12-01
Machine learning techniques such as Gaussian Processes can be used to identify stratigraphically important features in geophysical logs. The marker shales in the banded iron formation hosted iron ore deposits of the Hamersley Ranges, Western Australia, form distinctive signatures in the natural gamma logs. The identification of these marker shales is important for stratigraphic identification of unit boundaries for the geological modelling of the deposit. Machine learning techniques each have different unique properties that will impact the results. For Gaussian Processes (GPs), the output values are inclined towards the mean value, particularly when there is not sufficient information in the library. The impact that these inclinations have on the classification can vary depending on the parameter values selected by the user. Therefore, when applying machine learning techniques, care must be taken to fit the technique to the problem correctly. This study focuses on optimising the settings and choices for training a GPs system to identify a specific marker shale. We show that the final results converge even when different, but equally valid starting libraries are used for the training. To analyse the impact on feature identification, GP models were trained so that the output was inclined towards a positive, neutral or negative output. For this type of classification, the best results were when the pull was towards a negative output. We also show that the GP output can be adjusted by using a standard deviation coefficient that changes the balance between certainty and accuracy in the results.
Multi-fidelity Gaussian process regression for prediction of random fields
Energy Technology Data Exchange (ETDEWEB)
Parussini, L. [Department of Engineering and Architecture, University of Trieste (Italy); Venturi, D., E-mail: venturi@ucsc.edu [Department of Applied Mathematics and Statistics, University of California Santa Cruz (United States); Perdikaris, P. [Department of Mechanical Engineering, Massachusetts Institute of Technology (United States); Karniadakis, G.E. [Division of Applied Mathematics, Brown University (United States)
2017-05-01
We propose a new multi-fidelity Gaussian process regression (GPR) approach for prediction of random fields based on observations of surrogate models or hierarchies of surrogate models. Our method builds upon recent work on recursive Bayesian techniques, in particular recursive co-kriging, and extends it to vector-valued fields and various types of covariances, including separable and non-separable ones. The framework we propose is general and can be used to perform uncertainty propagation and quantification in model-based simulations, multi-fidelity data fusion, and surrogate-based optimization. We demonstrate the effectiveness of the proposed recursive GPR techniques through various examples. Specifically, we study the stochastic Burgers equation and the stochastic Oberbeck–Boussinesq equations describing natural convection within a square enclosure. In both cases we find that the standard deviation of the Gaussian predictors as well as the absolute errors relative to benchmark stochastic solutions are very small, suggesting that the proposed multi-fidelity GPR approaches can yield highly accurate results.
On small deviations of stationary Gaussian processes and related analytic inequalities
Weber, Michel J G
2011-01-01
Let $ \\{X_j, j\\in \\Z\\}$ be a Gaussian stationary sequence having a spectral function $F$ of infinite type. Then for all $n$ and $z\\ge 0$,$$ \\P\\Big\\{\\sup_{j=1}^n |X_j|\\le z \\Big\\}\\le \\Big(\\int_{-z/\\sqrt{G(f)}}^{z/\\sqrt{G(f)}} e^{-x^2/2}\\frac{\\dd x}{\\sqrt{2\\pi}} \\Big)^n,$$ where $ G(f)$ is the geometric mean of the Radon Nycodim derivative of the absolutely continuous part $f$ of $F$. The proof uses properties of finite Toeplitz forms. Let $ \\{X(t), t\\in \\R\\}$ be a sample continuous stationary Gaussian process with covariance function $\\g(u) $. We also show that there exists an absolute constant $K$ such that for all $T>0$, $a>0$ with $T\\ge \\e(a)$, $$\\P\\Big\\{\\sup_{0\\le s,t\\le T} |X(s)-X(t)|\\le a\\Big\\} \\le \\exp \\Big \\{-{KT \\over \\e(a) p(\\e(a))}\\Big\\} ,$$ where $\\e (a)= \\min\\big\\{b>0: \\d (b)\\ge a\\big\\}$, $\\d (b)=\\min_{u\\ge 1}\\{\\sqrt{2(1-\\g((ub))}, u\\ge 1\\}$, and $ p(b) = 1+\\sum_{j=2}^\\infty {|2\\g (jb)-\\g ((j-1)b)-\\g ((j+1)b)| \\over 2(1-\\g(b))}$. The proof is based on some decoupling inequalities arising from Bras...
Alborzpour, Jonathan P.; Tew, David P.; Habershon, Scott
2016-11-01
Solution of the time-dependent Schrödinger equation using a linear combination of basis functions, such as Gaussian wavepackets (GWPs), requires costly evaluation of integrals over the entire potential energy surface (PES) of the system. The standard approach, motivated by computational tractability for direct dynamics, is to approximate the PES with a second order Taylor expansion, for example centred at each GWP. In this article, we propose an alternative method for approximating PES matrix elements based on PES interpolation using Gaussian process regression (GPR). Our GPR scheme requires only single-point evaluations of the PES at a limited number of configurations in each time-step; the necessity of performing often-expensive evaluations of the Hessian matrix is completely avoided. In applications to 2-, 5-, and 10-dimensional benchmark models describing a tunnelling coordinate coupled non-linearly to a set of harmonic oscillators, we find that our GPR method results in PES matrix elements for which the average error is, in the best case, two orders-of-magnitude smaller and, in the worst case, directly comparable to that determined by any other Taylor expansion method, without requiring additional PES evaluations or Hessian matrices. Given the computational simplicity of GPR, as well as the opportunities for further refinement of the procedure highlighted herein, we argue that our GPR methodology should replace methods for evaluating PES matrix elements using Taylor expansions in quantum dynamics simulations.
Tancret, F.
2013-06-01
A new alloy design procedure is proposed, combining in a single computational tool several modelling and predictive techniques that have already been used and assessed in the field of materials science and alloy design: a genetic algorithm is used to optimize the alloy composition for target properties and performance on the basis of the prediction of mechanical properties (estimated by Gaussian process regression of data on existing alloys) and of microstructural constitution, stability and processability (evaluated by computational themodynamics). These tools are integrated in a unique Matlab programme. An example is given in the case of the design of a new nickel-base superalloy for future power plant applications (such as the ultra-supercritical (USC) coal-fired plant, or the high-temperature gas-cooled nuclear reactor (HTGCR or HTGR), where the selection criteria include cost, oxidation and creep resistance around 750 °C, long-term stability at service temperature, forgeability, weldability, etc.
Gaussian process based independent analysis for temporal source separation in fMRI
DEFF Research Database (Denmark)
Hald, Ditte Høvenhoff; Henao, Ricardo; Winther, Ole
2017-01-01
Functional Magnetic Resonance Imaging (fMRI) gives us a unique insight into the processes of the brain, and opens up for analyzing the functional activation patterns of the underlying sources. Task-inferred supervised learning with restrictive assumptions in the regression set-up, restricts......MRI data sets with different sampling frequency, we show that the GPICA-inferred temporal components and associated spatial maps allow for a more definite interpretation than standard temporal ICA methods. The temporal structures of the sources are controlled by the covariance of the Gaussian process......, specified by a kernel function with an interpretable and controllable temporal length scale parameter. We propose a hierarchical model specification, considering both instantaneous and convolutive mixing, and we infer source spatial maps, temporal patterns and temporal length scale parameters by Markov...
Bayesian electron density inference from JET lithium beam emission spectra using Gaussian processes
Kwak, Sehyun; Svensson, J.; Brix, M.; Ghim, Y.-C.; Contributors, JET
2017-03-01
A Bayesian model to infer edge electron density profiles is developed for the JET lithium beam emission spectroscopy (Li-BES) system, measuring Li I (2p-2s) line radiation using 26 channels with ∼1 cm spatial resolution and 10∼ 20 ms temporal resolution. The density profile is modelled using a Gaussian process prior, and the uncertainty of the density profile is calculated by a Markov Chain Monte Carlo (MCMC) scheme. From the spectra measured by the transmission grating spectrometer, the Li I line intensities are extracted, and modelled as a function of the plasma density by a multi-state model which describes the relevant processes between neutral lithium beam atoms and plasma particles. The spectral model fully takes into account interference filter and instrument effects, that are separately estimated, again using Gaussian processes. The line intensities are inferred based on a spectral model consistent with the measured spectra within their uncertainties, which includes photon statistics and electronic noise. Our newly developed method to infer JET edge electron density profiles has the following advantages in comparison to the conventional method: (i) providing full posterior distributions of edge density profiles, including their associated uncertainties, (ii) the available radial range for density profiles is increased to the full observation range (∼26 cm), (iii) an assumption of monotonic electron density profile is not necessary, (iv) the absolute calibration factor of the diagnostic system is automatically estimated overcoming the limitation of the conventional technique and allowing us to infer the electron density profiles for all pulses without preprocessing the data or an additional boundary condition, and (v) since the full spectrum is modelled, the procedure of modulating the beam to measure the background signal is only necessary for the case of overlapping of the Li I line with impurity lines.
Low-Level and Successive Large-Level Excursions of a Stationary Gaussian Process
Nguyen, Van Minh
2012-01-01
The present work investigates two properties of level crossings of a stationary Gaussian process $X(t)$ with autocorrelation function $R_X(\\tau)$. We show firstly that if $R_X(\\tau)$ admits finite second and fourth derivatives at the origin, the length of up-excursions above a low level $-\\gamma$ is asymptotically exponential as $-\\gamma \\to -\\infty$. Secondly, assume that $R_X(\\tau)$ admits a finite second derivative at the origin and some defined properties, we derive the mean number of crossings as well as the length of successive excursions above two adjacent large levels. The asymptotic results are showed to be effective even for practical values of crossing levels. An application of the developed results is proposed to derive the probability of successive excursions above adjacent levels during a time window.
Wan, Zhong Yi
2016-01-01
We formulate a reduced-order strategy for efficiently forecasting complex high-dimensional dynamical systems entirely based on data streams. The first step of our method involves reconstructing the dynamics in a reduced-order subspace of choice using Gaussian Process Regression (GPR). GPR simultaneously allows for reconstruction of the vector field and more importantly, estimation of local uncertainty. The latter is due to i) local interpolation error and ii) truncation of the high-dimensional phase space. This uncertainty component can be analytically quantified in terms of the GPR hyperparameters. In the second step we formulate stochastic models that explicitly take into account the reconstructed dynamics and their uncertainty. For regions of the attractor which are not sufficiently sampled for our GPR framework to be effective, an adaptive blended scheme is formulated to enforce correct statistical steady state properties, matching those of the real data. We examine the effectiveness of the proposed metho...
Bilionis, Ilias; Gonzalez, Marcial
2016-01-01
The prohibitive cost of performing Uncertainty Quantification (UQ) tasks with a very large number of input parameters can be addressed, if the response exhibits some special structure that can be discovered and exploited. Several physical responses exhibit a special structure known as an active subspace (AS), a linear manifold of the stochastic space characterized by maximal response variation. The idea is that one should first identify this low dimensional manifold, project the high-dimensional input onto it, and then link the projection to the output. In this work, we develop a probabilistic version of AS which is gradient-free and robust to observational noise. Our approach relies on a novel Gaussian process regression with built-in dimensionality reduction with the AS represented as an orthogonal projection matrix that serves as yet another covariance function hyper-parameter to be estimated from the data. To train the model, we design a two-step maximum likelihood optimization procedure that ensures the ...
Reconstructing interaction between dark energy and dark matter using Gaussian Processes
Cai, Rong-Gen; Yang, Tao
2015-01-01
We present a non-parametric approach to reconstruct the interaction between dark energy and dark matter directly from SNIa Union 2.1 data using Gaussian Processes, which is a fully Bayesian approach for smoothing data. In this method, once the equation of state ($w$) of dark energy is specified, the interaction can be reconstructed with respect to redshift. For the decaying vacuum energy case with $w=-1$, the reconstructed interaction is consistent with the $\\Lambda$CDM model, namely, there is no evidence for the interaction. This also holds for the constant $w$ cases from $-0.9$ to $-1.1$ and for the CPL parameterization case. If the equation of state deviates obviously from $-1$, the reconstructed interaction exits at $95\\%$ confidence level. This shows the degeneracy between the interaction and the equation of state of dark energy when they get constraints from the observational data.
Gaussian process surrogates for failure detection: A Bayesian experimental design approach
Wang, Hongqiao; Lin, Guang; Li, Jinglai
2016-05-01
An important task of uncertainty quantification is to identify the probability of undesired events, in particular, system failures, caused by various sources of uncertainties. In this work we consider the construction of Gaussian process surrogates for failure detection and failure probability estimation. In particular, we consider the situation that the underlying computer models are extremely expensive, and in this setting, determining the sampling points in the state space is of essential importance. We formulate the problem as an optimal experimental design for Bayesian inferences of the limit state (i.e., the failure boundary) and propose an efficient numerical scheme to solve the resulting optimization problem. In particular, the proposed limit-state inference method is capable of determining multiple sampling points at a time, and thus it is well suited for problems where multiple computer simulations can be performed in parallel. The accuracy and performance of the proposed method is demonstrated by both academic and practical examples.
Gibson, N P; Roberts, S; Evans, T M; Osborne, M; Pont, F
2011-01-01
Transmission spectroscopy, which consists of measuring the wavelength-dependent absorption of starlight by a planet's atmosphere during a transit, is a powerful probe of atmospheric composition. However, the expected signal is typically orders of magnitude smaller than instrumental systematics, and the results are crucially dependent on the treatment of the latter. In this paper, we propose a new method to infer transit parameters in the presence of systematic noise using Gaussian processes, a technique widely used in the machine learning community for Bayesian regression and classification problems. Our method makes use of auxiliary information about the state of the instrument, but does so in a non-parametric manner, without imposing a specific dependence of the systematics on the instrumental parameters, and naturally allows for the correlated nature of the noise. We give an example application of the method to archival NICMOS transmission spectroscopy of the hot Jupiter HD 189733, which goes some way towa...
STANDARDIZING TYPE Ia SUPERNOVA ABSOLUTE MAGNITUDES USING GAUSSIAN PROCESS DATA REGRESSION
Energy Technology Data Exchange (ETDEWEB)
Kim, A. G.; Aldering, G.; Aragon, C.; Bailey, S.; Childress, M.; Fakhouri, H. K.; Nordin, J. [Physics Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720 (United States); Thomas, R. C. [Computational Cosmology Center, Computational Research Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road MS 50B-4206, Berkeley, CA 94720 (United States); Antilogus, P.; Bongard, S.; Canto, A.; Cellier-Holzem, F.; Guy, J. [Laboratoire de Physique Nucleaire et des Hautes Energies, Universite Pierre et Marie Curie Paris 6, Universite Denis Diderot Paris 7, CNRS-IN2P3, 4 place Jussieu, F-75252 Paris Cedex 05 (France); Baltay, C. [Department of Physics, Yale University, New Haven, CT 06250-8121 (United States); Buton, C.; Kerschhaggl, M.; Kowalski, M. [Physikalisches Institut, Universitaet Bonn, Nussallee 12, D-53115 Bonn (Germany); Chotard, N. [Tsinghua Center for Astrophysics, Tsinghua University, Beijing 100084 (China); Copin, Y.; Gangler, E. [Universite de Lyon, F-69622 Lyon (France); and others
2013-04-01
We present a novel class of models for Type Ia supernova time-evolving spectral energy distributions (SEDs) and absolute magnitudes: they are each modeled as stochastic functions described by Gaussian processes. The values of the SED and absolute magnitudes are defined through well-defined regression prescriptions, so that data directly inform the models. As a proof of concept, we implement a model for synthetic photometry built from the spectrophotometric time series from the Nearby Supernova Factory. Absolute magnitudes at peak B brightness are calibrated to 0.13 mag in the g band and to as low as 0.09 mag in the z = 0.25 blueshifted i band, where the dispersion includes contributions from measurement uncertainties and peculiar velocities. The methodology can be applied to spectrophotometric time series of supernovae that span a range of redshifts to simultaneously standardize supernovae together with fitting cosmological parameters.
Standardizing Type Ia Supernova Absolute Magnitudes Using Gaussian Process Data Regression
Kim, A G; Aldering, G; Antilogus, P; Aragon, C; Bailey, S; Baltay, C; Bongard, S; Buton, C; Canto, A; Cellier-Holzem, F; Childress, M; Chotard, N; Copin, Y; Fakhouri, H K; Gangler, E; Guy, J; Kerschhaggl, M; Kowalski, M; Nordin, J; Nugent, P; Paech, K; Pain, R; Pécontal, E; Pereira, R; Perlmutter, S; Rabinowitz, D; Rigault, M; Runge, K; Saunders, C; Scalzo, R; Smadja, G; Tao, C; Weaver, B A; Wu, C
2013-01-01
We present a novel class of models for Type Ia supernova time-evolving spectral energy distributions (SED) and absolute magnitudes: they are each modeled as stochastic functions described by Gaussian processes. The values of the SED and absolute magnitudes are defined through well-defined regression prescriptions, so that data directly inform the models. As a proof of concept, we implement a model for synthetic photometry built from the spectrophotometric time series from the Nearby Supernova Factory. Absolute magnitudes at peak $B$ brightness are calibrated to 0.13 mag in the $g$-band and to as low as 0.09 mag in the $z=0.25$ blueshifted $i$-band, where the dispersion includes contributions from measurement uncertainties and peculiar velocities. The methodology can be applied to spectrophotometric time series of supernovae that span a range of redshifts to simultaneously standardize supernovae together with fitting cosmological parameters.
Laser Raman detection for oral cancer based on a Gaussian process classification method
Du, Zhanwei; Yang, Yongjian; Bai, Yuan; Wang, Lijun; Zhang, Chijun; Chen, He; Luo, Yusheng; Su, Le; Chen, Yong; Li, Xianchang; Zhou, Xiaodong; Jia, Jun; Shen, Aiguo; Hu, Jiming
2013-06-01
Oral squamous cell carcinoma is the most common neoplasm of the oral cavity. The incidence rate accounts for 80% of total oral cancer and shows an upward trend in recent years. It has a high degree of malignancy and is difficult to detect in terms of differential diagnosis, as a consequence of which the timing of treatment is always delayed. In this work, Raman spectroscopy was adopted to differentially diagnose oral squamous cell carcinoma and oral gland carcinoma. In total, 852 entries of raw spectral data which consisted of 631 items from 36 oral squamous cell carcinoma patients, 87 items from four oral gland carcinoma patients and 134 items from five normal people were collected by utilizing an optical method on oral tissues. The probability distribution of the datasets corresponding to the spectral peaks of the oral squamous cell carcinoma tissue was analyzed and the experimental result showed that the data obeyed a normal distribution. Moreover, the distribution characteristic of the noise was also in compliance with a Gaussian distribution. A Gaussian process (GP) classification method was utilized to distinguish the normal people and the oral gland carcinoma patients from the oral squamous cell carcinoma patients. The experimental results showed that all the normal people could be recognized. 83.33% of the oral squamous cell carcinoma patients could be correctly diagnosed and the remaining ones would be diagnosed as having oral gland carcinoma. For the classification process of oral gland carcinoma and oral squamous cell carcinoma, the correct ratio was 66.67% and the erroneously diagnosed percentage was 33.33%. The total sensitivity was 80% and the specificity was 100% with the Matthews correlation coefficient (MCC) set to 0.447 213 595. Considering the numerical results above, the application prospects and clinical value of this technique are significantly impressive.
Huang, Yi-Fei; Golding, G Brian
2014-01-01
A critical question in biology is the identification of functionally important amino acid sites in proteins. Because functionally important sites are under stronger purifying selection, site-specific substitution rates tend to be lower than usual at these sites. A large number of phylogenetic models have been developed to estimate site-specific substitution rates in proteins and the extraordinarily low substitution rates have been used as evidence of function. Most of the existing tools, e.g. Rate4Site, assume that site-specific substitution rates are independent across sites. However, site-specific substitution rates may be strongly correlated in the protein tertiary structure, since functionally important sites tend to be clustered together to form functional patches. We have developed a new model, GP4Rate, which incorporates the Gaussian process model with the standard phylogenetic model to identify slowly evolved regions in protein tertiary structures. GP4Rate uses the Gaussian process to define a nonparametric prior distribution of site-specific substitution rates, which naturally captures the spatial correlation of substitution rates. Simulations suggest that GP4Rate can potentially estimate site-specific substitution rates with a much higher accuracy than Rate4Site and tends to report slowly evolved regions rather than individual sites. In addition, GP4Rate can estimate the strength of the spatial correlation of substitution rates from the data. By applying GP4Rate to a set of mammalian B7-1 genes, we found a highly conserved region which coincides with experimental evidence. GP4Rate may be a useful tool for the in silico prediction of functionally important regions in the proteins with known structures.
Using Gaussian Processes to Model Noise in Eclipsing Binary Light Curves
Prsa, Andrej; Hambleton, Kelly M.
2017-01-01
The most precise data we have at hand arguably comes from NASA's Kepler mission, for which there is no good flux calibration available since it was designed to measure relative flux changes down to ~20ppm level. Instrumental artifacts thus abound in the data, and they vary with the module, location on the CCD, target brightness, electronic cross-talk, etc. In addition, Kepler's near-uninterrupted mode of observation reveals astrophysical signals and transient phenomena (i.e. spots, flares, protuberances, pulsations, magnetic field features, etc) that are not accounted for in the models. These "nuisance" signals, along with instrumental artifacts, are considered noise when modeling light curves; this noise is highly correlated and it cannot be considered poissonian or gaussian. Detrending non-white noise from light curve data has been an ongoing challenge in modeling eclipsing binary star and exoplanet transit light curves. Here we present an approach using Gaussian Processes (GP) to model noise as part of the overall likelihood function. The likelihood function consists of the eclipsing binary light curve generator PHOEBE, correlated noise model using GP, and a poissonian (shot) noise attributed to the actual stochastic component of the entire noise model. We consider GP parameters and poissonian noise amplitude as free parameters that are being sampled within the likelihood function, so the end result is the posterior probability not only for eclipsing binary model parameters, but for the noise parameters as well. We show that the posteriors of principal parameters are significantly more robust when noise is modeled rigorously compared to modeling detrended data with an eclipsing binary model alone. This work has been funded by NSF grant #1517460.
Zhao, Yuan; Park, Il Memming
2017-05-01
When governed by underlying low-dimensional dynamics, the interdependence of simultaneously recorded populations of neurons can be explained by a small number of shared factors, or a low-dimensional trajectory. Recovering these latent trajectories, particularly from single-trial population recordings, may help us understand the dynamics that drive neural computation. However, due to the biophysical constraints and noise in the spike trains, inferring trajectories from data is a challenging statistical problem in general. Here, we propose a practical and efficient inference method, the variational latent gaussian process (vLGP). The vLGP combines a generative model with a history-dependent point process observation, together with a smoothness prior on the latent trajectories. The vLGP improves on earlier methods for recovering latent trajectories, which assume either observation models inappropriate for point processes or linear dynamics. We compare and validate vLGP on both simulated data sets and population recordings from the primary visual cortex. In the V1 data set, we find that vLGP achieves substantially higher performance than previous methods for predicting omitted spike trains, as well as capturing both the toroidal topology of visual stimuli space and the noise correlation. These results show that vLGP is a robust method with the potential to reveal hidden neural dynamics from large-scale neural recordings.
Tian, Liang; Wilkinson, Richard; Yang, Zhibing; Power, Henry; Fagerlund, Fritjof; Niemi, Auli
2017-08-01
We explore the use of Gaussian process emulators (GPE) in the numerical simulation of CO2 injection into a deep heterogeneous aquifer. The model domain is a two-dimensional, log-normally distributed stochastic permeability field. We first estimate the cumulative distribution functions (CDFs) of the CO2 breakthrough time and the total CO2 mass using a computationally expensive Monte Carlo (MC) simulation. We then show that we can accurately reproduce these CDF estimates with a GPE, using only a small fraction of the computational cost required by traditional MC simulation. In order to build a GPE that can predict the simulator output from a permeability field consisting of 1000s of values, we use a truncated Karhunen-Loève (K-L) expansion of the permeability field, which enables the application of the Bayesian functional regression approach. We perform a cross-validation exercise to give an insight of the optimization of the experiment design for selected scenarios: we find that it is sufficient to use 100s values for the size of training set and that it is adequate to use as few as 15 K-L components. Our work demonstrates that GPE with truncated K-L expansion can be effectively applied to uncertainty analysis associated with modelling of multiphase flow and transport processes in heterogeneous media.
A uniform analysis of HD209458b Spitzer/IRAC lightcurves with Gaussian process models
Evans, Thomas M; Gibson, Neale; Barstow, Joanna K; Amundsen, David S; Tremblin, Pascal; Mourier, Pierre
2015-01-01
We present an analysis of Spitzer/IRAC primary transit and secondary eclipse lightcurves measured for HD209458b, using Gaussian process models to marginalise over the intrapixel sensitivity variations in the 3.6 micron and 4.5 micron channels and the ramp effect in the 5.8 micron and 8.0 micron channels. The main advantage of this approach is that we can account for a broad range of degeneracies between the planet signal and systematics without actually having to specify a deterministic functional form for the latter. Our results do not confirm a previous claim of water absorption in transmission. Instead, our results are more consistent with a featureless transmission spectrum, possibly due to a cloud deck obscuring molecular absorption bands. For the emission data, our values are not consistent with the thermal inversion in the dayside atmosphere that was originally inferred from these data. Instead, we agree with another re-analysis of these same data, which concluded a non-inverted atmosphere provides a b...
Gaussian Processes for Data-Efficient Learning in Robotics and Control.
Deisenroth, Marc Peter; Fox, Dieter; Rasmussen, Carl Edward
2015-02-01
Autonomous learning has been a promising direction in control and robotics for more than a decade since data-driven learning allows to reduce the amount of engineering knowledge, which is otherwise required. However, autonomous reinforcement learning (RL) approaches typically require many interactions with the system to learn controllers, which is a practical limitation in real systems, such as robots, where many interactions can be impractical and time consuming. To address this problem, current learning approaches typically require task-specific knowledge in form of expert demonstrations, realistic simulators, pre-shaped policies, or specific knowledge about the underlying dynamics. In this paper, we follow a different approach and speed up learning by extracting more information from data. In particular, we learn a probabilistic, non-parametric Gaussian process transition model of the system. By explicitly incorporating model uncertainty into long-term planning and controller learning our approach reduces the effects of model errors, a key problem in model-based learning. Compared to state-of-the art RL our model-based policy search method achieves an unprecedented speed of learning. We demonstrate its applicability to autonomous learning in real robot and control tasks.
Measuring the Mass of Kepler-78b Using a Gaussian Process Model
Grunblatt, Samuel K; Haywood, Raphaëlle D
2015-01-01
Kepler-78b is a transiting planet that is 1.2 times the size of Earth and orbits a young K dwarf every 8 hours. Two teams independently reported the mass of Kepler-78b based on radial velocity measurements using the HIRES and HARPS-N spectrographs. We modeled these datasets using a nonparametric Gaussian process (GP) regression. We considered three kernel functions for our GP models to account for the quasi-periodic activity from the young host star. All three kernel functions gave consistent Doppler amplitudes. Based on a likelihood analysis, we selected a quasi-periodic kernel that gives a Doppler amplitude of 1.86 $\\pm$ 0.25 m s$^{-1}$. The mass of 1.87 $^{+0.27}_{-0.26}$ M$_{\\oplus}$ is more precise than can be measured with either data set (a 2.5-{\\sigma} improvement on the HIRES data). Reanalyzing only the HIRES data with a GP model, we reach a Doppler signal uncertainty equivalent with the previous study using slightly more than half of the HIRES measurements. Our GP model is the first analysis of the ...
Directory of Open Access Journals (Sweden)
H. Ru
2016-06-01
Full Text Available Although there have been many studies for change detection, the effective and efficient use of high resolution remote sensing images is still a problem. Conventional supervised methods need lots of annotations to classify the land cover categories and detect their changes. Besides, the training set in supervised methods often has lots of redundant samples without any essential information. In this study, we present a method for interactive change detection using high resolution remote sensing images with active learning to overcome the shortages of existing remote sensing image change detection techniques. In our method, there is no annotation of actual land cover category at the beginning. First, we find a certain number of the most representative objects in unsupervised way. Then, we can detect the change areas from multi-temporal high resolution remote sensing images by active learning with Gaussian processes in an interactive way gradually until the detection results do not change notably. The artificial labelling can be reduced substantially, and a desirable detection result can be obtained in a few iterations. The experiments on Geo-Eye1 and WorldView2 remote sensing images demonstrate the effectiveness and efficiency of our proposed method.
Improved constraints on the dark energy equation of state using Gaussian processes
Wang, Deng; Meng, Xin-He
2017-01-01
We perform a comprehensive study of the dark energy equation of state (EoS) utilizing the model-independent Gaussian processes (GP). Using a combination of the Union 2.1 data set, the 30 newly added H(z) cosmic chronometer data points and Planck's shift parameter, we modify the usual GaPP code and provide a tighter constraint on the dark energy EoS than the previous literature about GP reconstructions. Subsequently, we take the "controlling variable method " to investigate directly the effects of the variable matter density parameter Ωm 0, variable cosmic curvature Ωk 0, and variable Hubble constant H0 on the dark energy EoS. We find that too small or large Ωm 0, Ωk 0, and H0 are all disfavored by our GP reconstructions based on current cosmological observations. Subsequently, we find that variables Ωm 0 and Ωk 0 affect the reconstructions of the dark energy EoS but hardly affect the reconstructions of the normalized comoving distance D (z ) and its derivatives D'(z ) and D''(z ). However, variable H0 affects the reconstructions of the dark energy EoS by affecting obviously those of D (z ) , D'(z ) , and D''(z ). Furthermore, we find that the results of our reconstructions support substantially the recent local measurement of H0 reported by Riess et al.
Sobotta, B; Söhn, M; Alber, M
2012-12-07
In order to provide a consistently high quality treatment, it is of great interest to assess the robustness of a treatment plan under the influence of geometric uncertainties. One possible method to implement this is to run treatment simulations for all scenarios that may arise from these uncertainties. These simulations may be evaluated in terms of the statistical distribution of the outcomes (as given by various dosimetric quality metrics) or statistical moments thereof, e.g. mean and/or variance. This paper introduces a method to compute the outcome distribution and all associated values of interest in a very efficient manner. This is accomplished by substituting the original patient model with a surrogate provided by a machine learning algorithm. This Gaussian process (GP) is trained to mimic the behavior of the patient model based on only very few samples. Once trained, the GP surrogate takes the place of the patient model in all subsequent calculations.The approach is demonstrated on two examples. The achieved computational speedup is more than one order of magnitude.
The method of Gaussian weighted trajectories. V. On the 1GB procedure for polyatomic processes
Bonnet, Laurent
2010-01-01
In recent years, many chemical reactions have been studied by means of the quasi-classical trajectory (QCT) method within the Gaussian binning (GB) procedure. The latter consists in "quantizing" the final vibrational actions in Bohr spirit by putting strong emphasis on the trajectories reaching the products with vibrational actions close to integer values. A major drawback of this procedure is that if N is the number of product vibrational modes, the amount of trajectories necessary to converge the calculations is ~ 10^N larger than with the standard QCT method. Applying it to polyatomic processes is thus problematic. In a recent paper, however, Czako and Bowman propose to quantize the total vibrational energy instead of the vibrational actions [G. Czako and J. M. Bowman, J. Chem. Phys., 131, 244302 (2009)], a procedure called 1GB here. The calculations are then only ~ 10 times more time-consuming than with the standard QCT method, allowing thereby for considerable numerical saving. In this paper, we propose ...
Reddy, K. S.; Somasundharam, S.
2016-09-01
In this work, inverse heat conduction problem (IHCP) involving the simultaneous estimation of principal thermal conductivities (kxx,kyy,kzz ) and specific heat capacity of orthotropic materials is solved by using surrogate forward model. Uniformly distributed random samples for each unknown parameter is generated from the prior knowledge about these parameters and Finite Volume Method (FVM) is employed to solve the forward problem for temperature distribution with space and time. A supervised machine learning technique- Gaussian Process Regression (GPR) is used to construct the surrogate forward model with the available temperature solution and randomly generated unknown parameter data. The statistical and machine learning toolbox available in MATLAB R2015b is used for this purpose. The robustness of the surrogate model constructed using GPR is examined by carrying out the parameter estimation for 100 new randomly generated test samples at a measurement error of ±0.3K. The temperature measurement is obtained by adding random noise with the mean at zero and known standard deviation (σ = 0.1) to the FVM solution of the forward problem. The test results show that Mean Percentage Deviation (MPD) of all test samples for all parameters is < 10%.
Online Model Learning of Buildings Using Stochastic Hybrid Systems Based on Gaussian Processes
Directory of Open Access Journals (Sweden)
Hamzah Abdel-Aziz
2017-01-01
Full Text Available Dynamical models are essential for model-based control methodologies which allow smart buildings to operate autonomously in an energy and cost efficient manner. However, buildings have complex thermal dynamics which are affected externally by the environment and internally by thermal loads such as equipment and occupancy. Moreover, the physical parameters of buildings may change over time as the buildings age or due to changes in the buildings’ configuration or structure. In this paper, we introduce an online model learning methodology to identify a nonparametric dynamical model for buildings when the thermal load is latent (i.e., the thermal load cannot be measured. The proposed model is based on stochastic hybrid systems, where the discrete state describes the level of the thermal load and the continuous dynamics represented by Gaussian processes describe the thermal dynamics of the air temperature. We demonstrate the evaluation of the proposed model using two-zone and five-zone buildings. The data for both experiments are generated using the EnergyPlus software. Experimental results show that the proposed model estimates the thermal load level correctly and predicts the thermal behavior with good performance.
HEp-2 Cell Classification: The Role of Gaussian Scale Space Theory as A Pre-processing Approach
Qi, Xianbiao; Zhao, Guoying; Chen, Jie; Pietikäinen, Matti
2015-01-01
\\textit{Indirect Immunofluorescence Imaging of Human Epithelial Type 2} (HEp-2) cells is an effective way to identify the presence of Anti-Nuclear Antibody (ANA). Most existing works on HEp-2 cell classification mainly focus on feature extraction, feature encoding and classifier design. Very few efforts have been devoted to study the importance of the pre-processing techniques. In this paper, we analyze the importance of the pre-processing, and investigate the role of Gaussian Scale Space (GS...
Human motion tracking by temporal-spatial local gaussian process experts.
Zhao, Xu; Fu, Yun; Liu, Yuncai
2011-04-01
Human pose estimation via motion tracking systems can be considered as a regression problem within a discriminative framework. It is always a challenging task to model the mapping from observation space to state space because of the high-dimensional characteristic in the multimodal conditional distribution. In order to build the mapping, existing techniques usually involve a large set of training samples in the learning process which are limited in their capability to deal with multimodality. We propose, in this work, a novel online sparse Gaussian Process (GP) regression model to recover 3-D human motion in monocular videos. Particularly, we investigate the fact that for a given test input, its output is mainly determined by the training samples potentially residing in its local neighborhood and defined in the unified input-output space. This leads to a local mixture GP experts system composed of different local GP experts, each of which dominates a mapping behavior with the specific covariance function adapting to a local region. To handle the multimodality, we combine both temporal and spatial information therefore to obtain two categories of local experts. The temporal and spatial experts are integrated into a seamless hybrid system, which is automatically self-initialized and robust for visual tracking of nonlinear human motion. Learning and inference are extremely efficient as all the local experts are defined online within very small neighborhoods. Extensive experiments on two real-world databases, HumanEva and PEAR, demonstrate the effectiveness of our proposed model, which significantly improve the performance of existing models.
Spectral band selection for vegetation properties retrieval using Gaussian processes regression
Verrelst, Jochem; Rivera, Juan Pablo; Gitelson, Anatoly; Delegido, Jesus; Moreno, José; Camps-Valls, Gustau
2016-10-01
With current and upcoming imaging spectrometers, automated band analysis techniques are needed to enable efficient identification of most informative bands to facilitate optimized processing of spectral data into estimates of biophysical variables. This paper introduces an automated spectral band analysis tool (BAT) based on Gaussian processes regression (GPR) for the spectral analysis of vegetation properties. The GPR-BAT procedure sequentially backwards removes the least contributing band in the regression model for a given variable until only one band is kept. GPR-BAT is implemented within the framework of the free ARTMO's MLRA (machine learning regression algorithms) toolbox, which is dedicated to the transforming of optical remote sensing images into biophysical products. GPR-BAT allows (1) to identify the most informative bands in relating spectral data to a biophysical variable, and (2) to find the least number of bands that preserve optimized accurate predictions. To illustrate its utility, two hyperspectral datasets were analyzed for most informative bands: (1) a field hyperspectral dataset (400-1100 nm at 2 nm resolution: 301 bands) with leaf chlorophyll content (LCC) and green leaf area index (gLAI) collected for maize and soybean (Nebraska, US); and (2) an airborne HyMap dataset (430-2490 nm: 125 bands) with LAI and canopy water content (CWC) collected for a variety of crops (Barrax, Spain). For each of these biophysical variables, optimized retrieval accuracies can be achieved with just 4 to 9 well-identified bands, and performance was largely improved over using all bands. A PROSAIL global sensitivity analysis was run to interpret the validity of these bands. Cross-validated RCV2 (NRMSECV) accuracies for optimized GPR models were 0.79 (12.9%) for LCC, 0.94 (7.2%) for gLAI, 0.95 (6.5%) for LAI and 0.95 (7.2%) for CWC. This study concludes that a wise band selection of hyperspectral data is strictly required for optimal vegetation properties mapping.
Calculation of Covariance Matrix for Multi-mode Gaussian States in Decoherence Processes
Institute of Scientific and Technical Information of China (English)
XIANG Shao-Hua; SHAO Bin; SONG Ke-Hui
2009-01-01
We investigate the dynamics of n single-mode continuous variable systems in a generic Gaussian state under the influence of the independent and correlated noises making use of the characteristic function method.In two models the bath is assumed to be a squeezed thermal one.We derive an explicit input-output expression between the initial and final covariance matrices.As an example,we study the evolution of entanglement of three-mode Gaussian state embedded in two noisy models.
Energy Technology Data Exchange (ETDEWEB)
Tripathy, Rohit, E-mail: rtripath@purdue.edu; Bilionis, Ilias, E-mail: ibilion@purdue.edu; Gonzalez, Marcial, E-mail: marcial-gonzalez@purdue.edu
2016-09-15
Uncertainty quantification (UQ) tasks, such as model calibration, uncertainty propagation, and optimization under uncertainty, typically require several thousand evaluations of the underlying computer codes. To cope with the cost of simulations, one replaces the real response surface with a cheap surrogate based, e.g., on polynomial chaos expansions, neural networks, support vector machines, or Gaussian processes (GP). However, the number of simulations required to learn a generic multivariate response grows exponentially as the input dimension increases. This curse of dimensionality can only be addressed, if the response exhibits some special structure that can be discovered and exploited. A wide range of physical responses exhibit a special structure known as an active subspace (AS). An AS is a linear manifold of the stochastic space characterized by maximal response variation. The idea is that one should first identify this low dimensional manifold, project the high-dimensional input onto it, and then link the projection to the output. If the dimensionality of the AS is low enough, then learning the link function is a much easier problem than the original problem of learning a high-dimensional function. The classic approach to discovering the AS requires gradient information, a fact that severely limits its applicability. Furthermore, and partly because of its reliance to gradients, it is not able to handle noisy observations. The latter is an essential trait if one wants to be able to propagate uncertainty through stochastic simulators, e.g., through molecular dynamics codes. In this work, we develop a probabilistic version of AS which is gradient-free and robust to observational noise. Our approach relies on a novel Gaussian process regression with built-in dimensionality reduction. In particular, the AS is represented as an orthogonal projection matrix that serves as yet another covariance function hyper-parameter to be estimated from the data. To train the
Tripathy, Rohit; Bilionis, Ilias; Gonzalez, Marcial
2016-09-01
Uncertainty quantification (UQ) tasks, such as model calibration, uncertainty propagation, and optimization under uncertainty, typically require several thousand evaluations of the underlying computer codes. To cope with the cost of simulations, one replaces the real response surface with a cheap surrogate based, e.g., on polynomial chaos expansions, neural networks, support vector machines, or Gaussian processes (GP). However, the number of simulations required to learn a generic multivariate response grows exponentially as the input dimension increases. This curse of dimensionality can only be addressed, if the response exhibits some special structure that can be discovered and exploited. A wide range of physical responses exhibit a special structure known as an active subspace (AS). An AS is a linear manifold of the stochastic space characterized by maximal response variation. The idea is that one should first identify this low dimensional manifold, project the high-dimensional input onto it, and then link the projection to the output. If the dimensionality of the AS is low enough, then learning the link function is a much easier problem than the original problem of learning a high-dimensional function. The classic approach to discovering the AS requires gradient information, a fact that severely limits its applicability. Furthermore, and partly because of its reliance to gradients, it is not able to handle noisy observations. The latter is an essential trait if one wants to be able to propagate uncertainty through stochastic simulators, e.g., through molecular dynamics codes. In this work, we develop a probabilistic version of AS which is gradient-free and robust to observational noise. Our approach relies on a novel Gaussian process regression with built-in dimensionality reduction. In particular, the AS is represented as an orthogonal projection matrix that serves as yet another covariance function hyper-parameter to be estimated from the data. To train the
Determining the Mass of Kepler-78b with Nonparametric Gaussian Process Estimation
Grunblatt, Samuel Kai; Howard, Andrew; Haywood, Raphaëlle
2016-01-01
Kepler-78b is a transiting planet that is 1.2 times the radius of Earth and orbits a young, active K dwarf every 8 hr. The mass of Kepler-78b has been independently reported by two teams based on radial velocity (RV) measurements using the HIRES and HARPS-N spectrographs. Due to the active nature of the host star, a stellar activity model is required to distinguish and isolate the planetary signal in RV data. Whereas previous studies tested parametric stellar activity models, we modeled this system using nonparametric Gaussian process (GP) regression. We produced a GP regression of relevant Kepler photometry. We then use the posterior parameter distribution for our photometric fit as a prior for our simultaneous GP + Keplerian orbit models of the RV data sets. We tested three simple kernel functions for our GP regressions. Based on a Bayesian likelihood analysis, we selected a quasi-periodic kernel model with GP hyperparameters coupled between the two RV data sets, giving a Doppler amplitude of 1.86 ± 0.25 m s-1 and supporting our belief that the correlated noise we are modeling is astrophysical. The corresponding mass of 1.87-0.26+0.27 ME is consistent with that measured in previous studies, and more robust due to our nonparametric signal estimation. Based on our mass and the radius measurement from transit photometry, Kepler-78b has a bulk density of 6.0-1.4+1.9 g cm-3. We estimate that Kepler-78b is 32% ± 26% iron using a two-component rock-iron model. This is consistent with an Earth-like composition, with uncertainty spanning Moon-like to Mercury-like compositions.
Eleftheriadis, Stefanos; Rudovic, Ognjen; Pantic, Maja
2015-01-01
Images of facial expressions are often captured from various views as a result of either head movements or variable camera position. Existing methods for multiview and/or view-invariant facial expression recognition typically perform classification of the observed expression using either classifiers learned separately for each view or a single classifier learned for all views. However, these approaches ignore the fact that different views of a facial expression are just different manifestations of the same facial expression. By accounting for this redundancy, we can design more effective classifiers for the target task. To this end, we propose a discriminative shared Gaussian process latent variable model (DS-GPLVM) for multiview and view-invariant classification of facial expressions from multiple views. In this model, we first learn a discriminative manifold shared by multiple views of a facial expression. Subsequently, we perform facial expression classification in the expression manifold. Finally, classification of an observed facial expression is carried out either in the view-invariant manner (using only a single view of the expression) or in the multiview manner (using multiple views of the expression). The proposed model can also be used to perform fusion of different facial features in a principled manner. We validate the proposed DS-GPLVM on both posed and spontaneously displayed facial expressions from three publicly available datasets (MultiPIE, labeled face parts in the wild, and static facial expressions in the wild). We show that this model outperforms the state-of-the-art methods for multiview and view-invariant facial expression classification, and several state-of-the-art methods for multiview learning and feature fusion.
Gaussian process regression bootstrapping: exploring the effects of uncertainty in time course data.
Kirk, Paul D W; Stumpf, Michael P H
2009-05-15
Although widely accepted that high-throughput biological data are typically highly noisy, the effects that this uncertainty has upon the conclusions we draw from these data are often overlooked. However, in order to assign any degree of confidence to our conclusions, we must quantify these effects. Bootstrap resampling is one method by which this may be achieved. Here, we present a parametric bootstrapping approach for time-course data, in which Gaussian process regression (GPR) is used to fit a probabilistic model from which replicates may then be drawn. This approach implicitly allows the time dependence of the data to be taken into account, and is applicable to a wide range of problems. We apply GPR bootstrapping to two datasets from the literature. In the first example, we show how the approach may be used to investigate the effects of data uncertainty upon the estimation of parameters in an ordinary differential equations (ODE) model of a cell signalling pathway. Although we find that the parameter estimates inferred from the original dataset are relatively robust to data uncertainty, we also identify a distinct second set of estimates. In the second example, we use our method to show that the topology of networks constructed from time-course gene expression data appears to be sensitive to data uncertainty, although there may be individual edges in the network that are robust in light of present data. Matlab code for performing GPR bootstrapping is available from our web site: http://www3.imperial.ac.uk/theoreticalsystemsbiology/data-software/.
Long, Yi; Du, Zhi-Jiang; Chen, Chao-Feng; Dong, Wei; Wang, Wei-Dong
2017-07-01
The most important step for lower extremity exoskeleton is to infer human motion intent (HMI), which contributes to achieve human exoskeleton collaboration. Since the user is in the control loop, the relationship between human robot interaction (HRI) information and HMI is nonlinear and complicated, which is difficult to be modeled by using mathematical approaches. The nonlinear approximation can be learned by using machine learning approaches. Gaussian Process (GP) regression is suitable for high-dimensional and small-sample nonlinear regression problems. GP regression is restrictive for large data sets due to its computation complexity. In this paper, an online sparse GP algorithm is constructed to learn the HMI. The original training dataset is collected when the user wears the exoskeleton system with friction compensation to perform unconstrained movement as far as possible. The dataset has two kinds of data, i.e., (1) physical HRI, which is collected by torque sensors placed at the interaction cuffs for the active joints, i.e., knee joints; (2) joint angular position, which is measured by optical position sensors. To reduce the computation complexity of GP, grey relational analysis (GRA) is utilized to specify the original dataset and provide the final training dataset. Those hyper-parameters are optimized offline by maximizing marginal likelihood and will be applied into online GP regression algorithm. The HMI, i.e., angular position of human joints, will be regarded as the reference trajectory for the mechanical legs. To verify the effectiveness of the proposed algorithm, experiments are performed on a subject at a natural speed. The experimental results show the HMI can be obtained in real time, which can be extended and employed in the similar exoskeleton systems.
Almosallam, Ibrahim A.; Jarvis, Matt J.; Roberts, Stephen J.
2016-10-01
The next generation of cosmology experiments will be required to use photometric redshifts rather than spectroscopic redshifts. Obtaining accurate and well-characterized photometric redshift distributions is therefore critical for Euclid, the Large Synoptic Survey Telescope and the Square Kilometre Array. However, determining accurate variance predictions alongside single point estimates is crucial, as they can be used to optimize the sample of galaxies for the specific experiment (e.g. weak lensing, baryon acoustic oscillations, supernovae), trading off between completeness and reliability in the galaxy sample. The various sources of uncertainty in measurements of the photometry and redshifts put a lower bound on the accuracy that any model can hope to achieve. The intrinsic uncertainty associated with estimates is often non-uniform and input-dependent, commonly known in statistics as heteroscedastic noise. However, existing approaches are susceptible to outliers and do not take into account variance induced by non-uniform data density and in most cases require manual tuning of many parameters. In this paper, we present a Bayesian machine learning approach that jointly optimizes the model with respect to both the predictive mean and variance we refer to as Gaussian processes for photometric redshifts (GPZ). The predictive variance of the model takes into account both the variance due to data density and photometric noise. Using the Sloan Digital Sky Survey (SDSS) DR12 data, we show that our approach substantially outperforms other machine learning methods for photo-z estimation and their associated variance, such as TPZ and ANNZ2. We provide a MATLAB and PYTHON implementations that are available to download at https://github.com/OxfordML/GPz.
Yu, Wenxi; Liu, Yang; Ma, Zongwei; Bi, Jun
2017-08-01
Using satellite-based aerosol optical depth (AOD) measurements and statistical models to estimate ground-level PM2.5 is a promising way to fill the areas that are not covered by ground PM2.5 monitors. The statistical models used in previous studies are primarily Linear Mixed Effects (LME) and Geographically Weighted Regression (GWR) models. In this study, we developed a new regression model between PM2.5 and AOD using Gaussian processes in a Bayesian hierarchical setting. Gaussian processes model the stochastic nature of the spatial random effects, where the mean surface and the covariance function is specified. The spatial stochastic process is incorporated under the Bayesian hierarchical framework to explain the variation of PM2.5 concentrations together with other factors, such as AOD, spatial and non-spatial random effects. We evaluate the results of our model and compare them with those of other, conventional statistical models (GWR and LME) by within-sample model fitting and out-of-sample validation (cross validation, CV). The results show that our model possesses a CV result (R(2) = 0.81) that reflects higher accuracy than that of GWR and LME (0.74 and 0.48, respectively). Our results indicate that Gaussian process models have the potential to improve the accuracy of satellite-based PM2.5 estimates.
Ulmer, Waldemar
2011-01-01
Scatter processes of photons lead to blurring of images. Multiple scatter can usually be described by one Gaussian convolution kernel. This can be a crude approximation and we need a linear combination of 2/3 Gaussian kernels to account for tails.If image structures are recorded by appropriate measurements, these structures are always blurred. The ideal image (source function without any blurring) is subjected to Gaussian convolutions to yield a blurred image, which is recorded by a detector array. The inverse problem of this procedure is the determination of the ideal source image from really determined image. If the scatter parameters are known, we are able to calculate the idealistic source structure by a deconvolution. We shall extend it to linear combinations of two/three Gaussian convolution kernels in order to found applications to aforementioned image processing, where a single Gaussian kernel would be crude. In this communication, we shall derive a new deconvolution method for a linear combination of...
Parrish, R. S.; Carter, M. C.
1974-01-01
This analysis utilizes computer simulation and statistical estimation. Realizations of stationary gaussian stochastic processes with selected autocorrelation functions are computer simulated. Analysis of the simulated data revealed that the mean and the variance of a process were functionally dependent upon the autocorrelation parameter and crossing level. Using predicted values for the mean and standard deviation, by the method of moments, the distribution parameters was estimated. Thus, given the autocorrelation parameter, crossing level, mean, and standard deviation of a process, the probability of exceeding the crossing level for a particular length of time was calculated.
Directory of Open Access Journals (Sweden)
José Luis Gómez-Dans
2016-02-01
Full Text Available There is an increasing need to consistently combine observations from different sensors to monitor the state of the land surface. In order to achieve this, robust methods based on the inversion of radiative transfer (RT models can be used to interpret the satellite observations. This typically results in an inverse problem, but a major drawback of these methods is the computational complexity. We introduce the concept of Gaussian Process (GP emulators: surrogate functions that accurately approximate RT models using a small set of input (e.g., leaf area index, leaf chlorophyll, etc. and output (e.g., top-of-canopy reflectances or at sensor radiances pairs. The emulators quantify the uncertainty of their approximation, and provide a fast and easy route to estimating the Jacobian of the original model, enabling the use of e.g., efficient gradient descent methods. We demonstrate the emulation of widely used RT models (PROSAIL and SEMIDISCRETE and the coupling of vegetation and atmospheric (6S RT models targetting particular sensor bands. A comparison with the full original model outputs shows that the emulators are a viable option to replace the original model, with negligible bias and discrepancies which are much smaller than the typical uncertainty in the observations. We also extend the theory of GP to cope with models with multivariate outputs (e.g., over the full solar reflective domain, and apply this to the emulation of PROSAIL, coupled 6S and PROSAIL and to the emulation of individual spectral components of 6S. In all cases, emulators successfully predict the full model output as well as accurately predict the gradient of the model calculated by finite differences, and produce speed ups between 10,000 and 50,000 times that of the original model. Finally, we use emulators to invert leaf area index ( L A I , leaf chlorophyll content ( C a b and equivalent leaf water thickness ( C w from a time series of observations from Sentinel-2/MSI
A linearly approximated iterative Gaussian decomposition method for waveform LiDAR processing
Mountrakis, Giorgos; Li, Yuguang
2017-07-01
Full-waveform LiDAR (FWL) decomposition results often act as the basis for key LiDAR-derived products, for example canopy height, biomass and carbon pool estimation, leaf area index calculation and under canopy detection. To date, the prevailing method for FWL product creation is the Gaussian Decomposition (GD) based on a non-linear Levenberg-Marquardt (LM) optimization for Gaussian node parameter estimation. GD follows a ;greedy; approach that may leave weak nodes undetected, merge multiple nodes into one or separate a noisy single node into multiple ones. In this manuscript, we propose an alternative decomposition method called Linearly Approximated Iterative Gaussian Decomposition (LAIGD method). The novelty of the LAIGD method is that it follows a multi-step ;slow-and-steady; iterative structure, where new Gaussian nodes are quickly discovered and adjusted using a linear fitting technique before they are forwarded for a non-linear optimization. Two experiments were conducted, one using real full-waveform data from NASA's land, vegetation, and ice sensor (LVIS) and another using synthetic data containing different number of nodes and degrees of overlap to assess performance in variable signal complexity. LVIS data revealed considerable improvements in RMSE (44.8% lower), RSE (56.3% lower) and rRMSE (74.3% lower) values compared to the benchmark GD method. These results were further confirmed with the synthetic data. Furthermore, the proposed multi-step method reduces execution times in half, an important consideration as there are plans for global coverage with the upcoming Global Ecosystem Dynamics Investigation LiDAR sensor on the International Space Station.
First principles interatomic potential for tungsten based on Gaussian process regression
Szlachta, Wojciech Jerzy
2014-01-01
An accurate description of atomic interactions, such as that provided by first principles quantum mechanics, is fundamental to realistic prediction of the properties that govern plasticity, fracture or crack propagation in metals. However, the computational complexity associated with modern schemes explicitly based on quantum mechanics limits their applications to systems of a few hundreds of atoms at most. This thesis investigates the application of the Gaussian Approximation Potential (GAP)...
Directory of Open Access Journals (Sweden)
Ivan D. Lobanov
2016-06-01
Full Text Available In this article, the problem of the number of spikes (level crossings of the stationary narrowband Gaussian process has been considered. The process was specified by an exponentially-cosine autocorrelation function. The problem had been solved earlier by Rice in terms of the joint probabilities’ density of the process and its derivative with respect to time, but in our article we obtained the solution using the functional of probabilities’ density (the functional was obtained by Amiantov, as well as an expansion of the canonical stochastic process. In this article, the optimal canonical expansion of a narrowband stochastic process based on the work of Filimonov and Denisov was also considered to solve the problem. The application of all these resources allowed obtaining an exact analytical solution of the problem on spikes of stationary narrowband Gaussian process. The obtained formulae could be used to solve, for example, some problems about the residual resource of some radiotechnical products, about the breaking sea waves and others.
Kernel-imbedded Gaussian processes for disease classification using microarray gene expression data
Directory of Open Access Journals (Sweden)
Cheung Leo
2007-02-01
Full Text Available Abstract Background Designing appropriate machine learning methods for identifying genes that have a significant discriminating power for disease outcomes has become more and more important for our understanding of diseases at genomic level. Although many machine learning methods have been developed and applied to the area of microarray gene expression data analysis, the majority of them are based on linear models, which however are not necessarily appropriate for the underlying connection between the target disease and its associated explanatory genes. Linear model based methods usually also bring in false positive significant features more easily. Furthermore, linear model based algorithms often involve calculating the inverse of a matrix that is possibly singular when the number of potentially important genes is relatively large. This leads to problems of numerical instability. To overcome these limitations, a few non-linear methods have recently been introduced to the area. Many of the existing non-linear methods have a couple of critical problems, the model selection problem and the model parameter tuning problem, that remain unsolved or even untouched. In general, a unified framework that allows model parameters of both linear and non-linear models to be easily tuned is always preferred in real-world applications. Kernel-induced learning methods form a class of approaches that show promising potentials to achieve this goal. Results A hierarchical statistical model named kernel-imbedded Gaussian process (KIGP is developed under a unified Bayesian framework for binary disease classification problems using microarray gene expression data. In particular, based on a probit regression setting, an adaptive algorithm with a cascading structure is designed to find the appropriate kernel, to discover the potentially significant genes, and to make the optimal class prediction accordingly. A Gibbs sampler is built as the core of the algorithm to make
Igarashi, Yasuhiko; Hori, Takane; Murata, Shin; Sato, Kenichiro; Baba, Toshitaka; Okada, Masato
2016-12-01
We constructed a model to predict the maximum tsunami height by a Gaussian process (GP) that uses pressure gauge data from the Dense Oceanfloor Network System for Earthquakes and Tsunamis (DONET) in the Nankai trough. We found a greatly improved generalization error of the maximum tsunami height by our prediction model. The error is about one third of that by a previous method, which tends to make larger predictions, especially for large tsunami heights (>10 m). These results indicate that GP enables us to get a more accurate prediction of tsunami height by using pressure gauge data.
Fyodorov, Yan V.; Doussal, Pierre Le
2016-07-01
We study three instances of log-correlated processes on the interval: the logarithm of the Gaussian unitary ensemble (GUE) characteristic polynomial, the Gaussian log-correlated potential in presence of edge charges, and the Fractional Brownian motion with Hurst index H → 0 (fBM0). In previous collaborations we obtained the probability distribution function (PDF) of the value of the global minimum (equivalently maximum) for the first two processes, using the freezing-duality conjecture (FDC). Here we study the PDF of the position of the maximum x_m through its moments. Using replica, this requires calculating moments of the density of eigenvalues in the β -Jacobi ensemble. Using Jack polynomials we obtain an exact and explicit expression for both positive and negative integer moments for arbitrary β >0 and positive integer n in terms of sums over partitions. For positive moments, this expression agrees with a very recent independent derivation by Mezzadri and Reynolds. We check our results against a contour integral formula derived recently by Borodin and Gorin (presented in the Appendix 1 from these authors). The duality necessary for the FDC to work is proved, and on our expressions, found to correspond to exchange of partitions with their dual. Performing the limit n → 0 and to negative Dyson index β → -2, we obtain the moments of x_m and give explicit expressions for the lowest ones. Numerical checks for the GUE polynomials, performed independently by N. Simm, indicate encouraging agreement. Some results are also obtained for moments in Laguerre, Hermite-Gaussian, as well as circular and related ensembles. The correlations of the position and the value of the field at the minimum are also analyzed.
A State-Space Approach to Optimal Level-Crossing Prediction for Linear Gaussian Processes
Martin, Rodney Alexander
2009-01-01
In many complex engineered systems, the ability to give an alarm prior to impending critical events is of great importance. These critical events may have varying degrees of severity, and in fact they may occur during normal system operation. In this article, we investigate approximations to theoretically optimal methods of designing alarm systems for the prediction of level-crossings by a zero-mean stationary linear dynamic system driven by Gaussian noise. An optimal alarm system is designed to elicit the fewest false alarms for a fixed detection probability. This work introduces the use of Kalman filtering in tandem with the optimal level-crossing problem. It is shown that there is a negligible loss in overall accuracy when using approximations to the theoretically optimal predictor, at the advantage of greatly reduced computational complexity. I
Arkhipov, Ievgen I.; Peřina, Jan; Peřina, Jan; Miranowicz, Adam
2016-07-01
The behavior of general nonclassical two-mode Gaussian states at a beam splitter is investigated. Single-mode nonclassicality as well as two-mode entanglement of both input and output states are analyzed suggesting their suitable quantifiers. These quantifiers are derived from local and global invariants of linear unitary two-mode transformations such that the sum of input (or output) local nonclassicality measures and entanglement measure gives a global invariant. This invariant quantifies the global nonclassicality resource. Mutual transformations of local nonclassicalities and entanglement induced by the beam splitter are analyzed considering incident noisy twin beams, single-mode noisy squeezed vacuum states, and states encompassing both squeezed states and twin beams. A rich tapestry of interesting nonclassical output states is predicted.
Multivariate stationary non-Gaussian process simulation for wind pressure fields
Sun, Ying; Su, Ning; Wu, Yue
2016-12-01
Stochastic simulation is an important means of acquiring fluctuating wind pressures for wind induced response analyses in structural engineering. The wind pressure acting on a large-span space structure can be characterized as a stationary non-Gaussian field. This paper reviews several simulation algorithms related to the Spectral Representation Method (SRM) and the Static Transformation Method (STM). Polynomial and Exponential transformation functions (PSTM and ESTM) are discussed. Deficiencies in current algorithms, with respect to accuracy, stability and efficiency, are analyzed, and the algorithms are improved for better practical application. In order to verify the improved algorithm, wind pressure fields on a large-span roof are simulated and compared with wind tunnel data. The simulation results fit well with the wind tunnel data, and the algorithm accuracy, stability and efficiency are shown to be better than those of current algorithms.
Hachem, Walid; Roueff, Francois
2009-01-01
This paper addresses the detection of a stochastic process in noise from irregular samples. We consider two hypotheses. The \\emph{noise only} hypothesis amounts to model the observations as a sample of a i.i.d. Gaussian random variables (noise only). The \\emph{signal plus noise} hypothesis models the observations as the samples of a continuous time stationary Gaussian process (the signal) taken at known but random time-instants corrupted with an additive noise. Two binary tests are considered, depending on which assumptions is retained as the null hypothesis. Assuming that the signal is a linear combination of the solution of a multidimensional stochastic differential equation (SDE), it is shown that the minimum Type II error probability decreases exponentially in the number of samples when the False Alarm probability is fixed. This behavior is described by \\emph{error exponents} that are completely characterized. It turns out that they are related with the asymptotic behavior of the Kalman Filter in random s...
Tuzlukov, Vyacheslav
2011-06-01
In this paper, we consider the problem of M-ary signal detection based on the generalized approach to signal processing (GASP) in noise over a single-input multiple-output (SIMO) channel affected by frequency-dispersive Rayleigh distributed fading and corrupted by additive non-Gaussian noise modeled as spherically invariant random process. We derive both the optimum generalized detector (GD) structure based on GASP and a suboptimal reduced-complexity GD applying the low energy coherence approach jointly with the GASP in noise. Both GD structures are independent of the actual noise statistics. We also carry out a performance analysis of both GDs and compare with the conventional receivers. The performance analysis is carried out with reference to the case that the channel is affected by a frequency-selective fading and for a binary frequency-shift keying (BFSK) signaling format. The results obtained through both a Chernoff-bounding technique and Monte Carlo simulations reveal that the adoption of diversity also represents a suitable means to restore performance in the presence of dispersive fading and impulsive non-Gaussian noise. It is also shown that the suboptimal GD incurs a limited loss with respect to the optimum GD and this loss is less in comparison with the conventional receiver.
Sraj, Ihab
2015-10-22
This paper addresses model dimensionality reduction for Bayesian inference based on prior Gaussian fields with uncertainty in the covariance function hyper-parameters. The dimensionality reduction is traditionally achieved using the Karhunen-Loève expansion of a prior Gaussian process assuming covariance function with fixed hyper-parameters, despite the fact that these are uncertain in nature. The posterior distribution of the Karhunen-Loève coordinates is then inferred using available observations. The resulting inferred field is therefore dependent on the assumed hyper-parameters. Here, we seek to efficiently estimate both the field and covariance hyper-parameters using Bayesian inference. To this end, a generalized Karhunen-Loève expansion is derived using a coordinate transformation to account for the dependence with respect to the covariance hyper-parameters. Polynomial Chaos expansions are employed for the acceleration of the Bayesian inference using similar coordinate transformations, enabling us to avoid expanding explicitly the solution dependence on the uncertain hyper-parameters. We demonstrate the feasibility of the proposed method on a transient diffusion equation by inferring spatially-varying log-diffusivity fields from noisy data. The inferred profiles were found closer to the true profiles when including the hyper-parameters’ uncertainty in the inference formulation.
Chen, Xin; Cao, Jianshu; Silbey, Robert J
2013-06-14
The recent experimental discoveries about excitation energy transfer (EET) in light harvesting antenna (LHA) attract a lot of interest. As an open non-equilibrium quantum system, the EET demands more rigorous theoretical framework to understand the interaction between system and environment and therein the evolution of reduced density matrix. A phonon is often used to model the fluctuating environment and convolutes the reduced quantum system temporarily. In this paper, we propose a novel way to construct complex-valued Gaussian processes to describe thermal quantum phonon bath exactly by converting the convolution of influence functional into the time correlation of complex Gaussian random field. Based on the construction, we propose a rigorous and efficient computational method, the covariance decomposition and conditional propagation scheme, to simulate the temporarily entangled reduced system. The new method allows us to study the non-Markovian effect without perturbation under the influence of different spectral densities of the linear system-phonon coupling coefficients. Its application in the study of EET in the Fenna-Matthews-Olson model Hamiltonian under four different spectral densities is discussed. Since the scaling of our algorithm is linear due to its Monte Carlo nature, the future application of the method for large LHA systems is attractive. In addition, this method can be used to study the effect of correlated initial condition on the reduced dynamics in the future.
Hathout, Rania M; Metwally, Abdelkader A
2016-11-01
This study represents one of the series applying computer-oriented processes and tools in digging for information, analysing data and finally extracting correlations and meaningful outcomes. In this context, binding energies could be used to model and predict the mass of loaded drugs in solid lipid nanoparticles after molecular docking of literature-gathered drugs using MOE® software package on molecularly simulated tripalmitin matrices using GROMACS®. Consequently, Gaussian processes as a supervised machine learning artificial intelligence technique were used to correlate the drugs' descriptors (e.g. M.W., xLogP, TPSA and fragment complexity) with their molecular docking binding energies. Lower percentage bias was obtained compared to previous studies which allows the accurate estimation of the loaded mass of any drug in the investigated solid lipid nanoparticles by just projecting its chemical structure to its main features (descriptors). Copyright © 2016 Elsevier B.V. All rights reserved.
Andrade, Xavier
2013-01-01
We discuss the application of graphical processing units (GPUs) to accelerate real-space density functional theory (DFT) calculations. To make our implementation efficient, we have developed a scheme to expose the data parallelism available in the DFT approach; this is applied to the different procedures required for a real-space DFT calculation. We present results for current-generation GPUs from AMD and Nvidia, which show that our scheme, implemented in the free code OCTOPUS, can reach a sustained performance of up to 90 GFlops for a single GPU, representing an important speed-up when compared to the CPU version of the code. Moreover, for some systems our implementation can outperform a GPU Gaussian basis set code, showing that the real-space approach is a competitive alternative for DFT simulations on GPUs.
Andrade, Xavier; Aspuru-Guzik, Alán
2013-10-01
We discuss the application of graphical processing units (GPUs) to accelerate real-space density functional theory (DFT) calculations. To make our implementation efficient, we have developed a scheme to expose the data parallelism available in the DFT approach; this is applied to the different procedures required for a real-space DFT calculation. We present results for current-generation GPUs from AMD and Nvidia, which show that our scheme, implemented in the free code Octopus, can reach a sustained performance of up to 90 GFlops for a single GPU, representing a significant speed-up when compared to the CPU version of the code. Moreover, for some systems, our implementation can outperform a GPU Gaussian basis set code, showing that the real-space approach is a competitive alternative for DFT simulations on GPUs.
Aye, S. A.; Heyns, P. S.
2017-02-01
This paper proposes an optimal Gaussian process regression (GPR) for the prediction of remaining useful life (RUL) of slow speed bearings based on a novel degradation assessment index obtained from acoustic emission signal. The optimal GPR is obtained from an integration or combination of existing simple mean and covariance functions in order to capture the observed trend of the bearing degradation as well the irregularities in the data. The resulting integrated GPR model provides an excellent fit to the data and improves over the simple GPR models that are based on simple mean and covariance functions. In addition, it achieves a low percentage error prediction of the remaining useful life of slow speed bearings. These findings are robust under varying operating conditions such as loading and speed and can be applied to nonlinear and nonstationary machine response signals useful for effective preventive machine maintenance purposes.
Andersson, Jesper L.R.; Sotiropoulos, Stamatios N.
2015-01-01
Diffusion MRI offers great potential in studying the human brain microstructure and connectivity. However, diffusion images are marred by technical problems, such as image distortions and spurious signal loss. Correcting for these problems is non-trivial and relies on having a mechanism that predicts what to expect. In this paper we describe a novel way to represent and make predictions about diffusion MRI data. It is based on a Gaussian process on one or several spheres similar to the Geostatistical method of “Kriging”. We present a choice of covariance function that allows us to accurately predict the signal even from voxels with complex fibre patterns. For multi-shell data (multiple non-zero b-values) the covariance function extends across the shells which means that data from one shell is used when making predictions for another shell. PMID:26236030
Ferreira, P G; Ferreira, Pedro G.; Magueijo, Joao
1997-01-01
Gaussian cosmic microwave background skies are fully specified by the power spectrum. The conventional method of characterizing non-Gaussian skies is to evaluate higher order moments, the n-point functions and their Fourier transforms. We argue that this method is inefficient, due to the redundancy of information existing in the complete set of moments. In this paper we propose a set of new statistics or non-Gaussian spectra to be extracted out of the angular distribution of the Fourier transform of the temperature anisotropies in the small field limit. These statistics complement the power spectrum and act as localization, shape, and connectedness statistics. They quantify generic non-Gaussian structure, and may be used in more general image processing tasks. We concentrate on a subset of these statistics and argue that while they carry no information in Gaussian theories they may be the best arena for making predictions in some non-Gaussian theories. As examples of applications we consider superposed Gaussi...
Ziegler, G; Ridgway, G R; Dahnke, R; Gaser, C
2014-08-15
Structural imaging based on MRI is an integral component of the clinical assessment of patients with potential dementia. We here propose an individualized Gaussian process-based inference scheme for clinical decision support in healthy and pathological aging elderly subjects using MRI. The approach aims at quantitative and transparent support for clinicians who aim to detect structural abnormalities in patients at risk of Alzheimer's disease or other types of dementia. Firstly, we introduce a generative model incorporating our knowledge about normative decline of local and global gray matter volume across the brain in elderly. By supposing smooth structural trajectories the models account for the general course of age-related structural decline as well as late-life accelerated loss. Considering healthy subjects' demography and global brain parameters as informative about normal brain aging variability affords individualized predictions in single cases. Using Gaussian process models as a normative reference, we predict new subjects' brain scans and quantify the local gray matter abnormalities in terms of Normative Probability Maps (NPM) and global z-scores. By integrating the observed expectation error and the predictive uncertainty, the local maps and global scores exploit the advantages of Bayesian inference for clinical decisions and provide a valuable extension of diagnostic information about pathological aging. We validate the approach in simulated data and real MRI data. We train the GP framework using 1238 healthy subjects with ages 18-94 years, and predict in 415 independent test subjects diagnosed as healthy controls, Mild Cognitive Impairment and Alzheimer's disease. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.
基于高斯过程的CLIQUE改进算法%Improved CLIQUE algorithm based on Gaussian processes
Institute of Scientific and Technical Information of China (English)
向柳明; 周渭博; 钟勇
2015-01-01
CLIQUE ( Clustering In QUEst) algorithm finds clusters from any dense grid by Depth-First Search ( DFS) and lacks performance, because a lot of dense grids don't belong to any cluster on the big and noisy data set. Gaussian sampling has a good convergence and can quickly find dense grids of local maximum density, this paper developed an improved CLIQUE algorithm GP-CLIQUE based on Gaussian processes. After locating all dense grids, the algorithm found dense grids of local maximum density by using Gaussian sampling in each dimension. Then it found clusters from these dense grids of local maximum density. Finally it generated minimal cluster descriptions. The experimental results show that: GP-CLIQUE has the same performance with CLIQUE on the small and clean data set, but has a better performance by 6% to 24% on the big and noisy data set.%CLIQUE聚类算法从任意密集网格进行深度优先遍历生成聚类簇时性能不足，因为当聚类数据集大且噪声较多时，大量密集网格不属于任何聚类簇。基于高斯随机采样有较好的收敛性，能快速找到密度局部最大的密集网格，提出了一种基于高斯过程的CLIQUE改进算法GP-CLIQUE。该算法识别密集网格后，先在密集网格空间的每一维上进行高斯随机采样快速找到密度局部最大的密集网格；再分别从这些密度局部最大的密集网格进行深度优先遍历生成聚类簇；最后确定每个聚类簇的最小覆盖。实验结果表明，在数据集小且无噪声时，该算法在性能上与CLIQUE相当，当数据集大噪声较多时，其性能较CLIQUE能提高6%~24%。
Stable non-Gaussian self-similar processes with stationary increments
Pipiras, Vladas
2017-01-01
This book provides a self-contained presentation on the structure of a large class of stable processes, known as self-similar mixed moving averages. The authors present a way to describe and classify these processes by relating them to so-called deterministic flows. The first sections in the book review random variables, stochastic processes, and integrals, moving on to rigidity and flows, and finally ending with mixed moving averages and self-similarity. In-depth appendices are also included. This book is aimed at graduate students and researchers working in probability theory and statistics.
Random Gaussian process effect upon selective system of spectra heterodyne analyzer
Directory of Open Access Journals (Sweden)
N. F. Vollerner
1967-12-01
Full Text Available The formula is obtained that describe mean power changing the selective system output by changing speed tuning of the spectra heterodyne analyzer when searching random stationary processes.
Colkesen, Ismail; Sahin, Emrehan Kutlug; Kavzoglu, Taskin
2016-06-01
Identification of landslide prone areas and production of accurate landslide susceptibility zonation maps have been crucial topics for hazard management studies. Since the prediction of susceptibility is one of the main processing steps in landslide susceptibility analysis, selection of a suitable prediction method plays an important role in the success of the susceptibility zonation process. Although simple statistical algorithms (e.g. logistic regression) have been widely used in the literature, the use of advanced non-parametric algorithms in landslide susceptibility zonation has recently become an active research topic. The main purpose of this study is to investigate the possible application of kernel-based Gaussian process regression (GPR) and support vector regression (SVR) for producing landslide susceptibility map of Tonya district of Trabzon, Turkey. Results of these two regression methods were compared with logistic regression (LR) method that is regarded as a benchmark method. Results showed that while kernel-based GPR and SVR methods generally produced similar results (90.46% and 90.37%, respectively), they outperformed the conventional LR method by about 18%. While confirming the superiority of the GPR method, statistical tests based on ROC statistics, success rate and prediction rate curves revealed the significant improvement in susceptibility map accuracy by applying kernel-based GPR and SVR methods.
Reyes, Adam; Graziani, Carlo; Tzeferacos, Petros
2016-01-01
We introduce an entirely new class of varying high-order methods for computational fluid dynamics based on a stochastic model of Gaussian process (GP). The new approach is based on GP modeling that generalizes Gaussian probability distributions for stochastic data predictions. Our approach is to adapt the idea of the GP prediction technique that utilizes the covariance kernel functions, and use the GP prediction to interpolate/reconstruct high-order approximations for solving hyperbolic PDEs. We present the GP high-order approach as a new class of numerical high-order formulations, alternative to the conventional polynomial-based approaches.
Use Correlation Coefficients in Gaussian Process to Train Stable ELM Models
2015-05-22
Demiris, Y.: The one-hidden layer non-parametric bayesian kernel machine. In: 23rd IEEE International Conference on Tools with Artificial Intelligence , pp...process · Neural network 1 Introduction Extreme learning machine (ELM) is a special single-hidden layer feed-forward neural network (SLFN) [6]. Due to
Extreme Value Estimates for Arbitrary Bandwidth Gaussian Processes Using the Analytic Envelope.
1984-03-01
Dugundji 1.) This envelope is defined by using the Hilbert transform. In a recent paper by Rice15 this envelope is called the analytic envelope. 5 tI...Processes for Envelopes of Normal Noise," IRE Transactions on Information Theory, Vol. IT-3, p. 204 (Sept 1957). 14. Dugundji , J., "Envelopes and Pre
A Novel Method for Generating Non-Stationary Gaussian Processes for Use in Digital Radar Simulators
2007-03-01
penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN...noise generator divided by the simulation bandwidth. Thus, the simulation noise density is ( Dsim − σsim)δt, where the simulation sample time is δt...transient response of the complex system to stochastic processes. Does this hold in general? Since both responses are control by the eigenvalues, a
Bukhari, W; Hong, S-M
2015-01-07
Motion-adaptive radiotherapy aims to deliver a conformal dose to the target tumour with minimal normal tissue exposure by compensating for tumour motion in real time. The prediction as well as the gating of respiratory motion have received much attention over the last two decades for reducing the targeting error of the treatment beam due to respiratory motion. In this article, we present a real-time algorithm for predicting and gating respiratory motion that utilizes a model-based and a model-free Bayesian framework by combining them in a cascade structure. The algorithm, named EKF-GPR(+), implements a gating function without pre-specifying a particular region of the patient's breathing cycle. The algorithm first employs an extended Kalman filter (LCM-EKF) to predict the respiratory motion and then uses a model-free Gaussian process regression (GPR) to correct the error of the LCM-EKF prediction. The GPR is a non-parametric Bayesian algorithm that yields predictive variance under Gaussian assumptions. The EKF-GPR(+) algorithm utilizes the predictive variance from the GPR component to capture the uncertainty in the LCM-EKF prediction error and systematically identify breathing points with a higher probability of large prediction error in advance. This identification allows us to pause the treatment beam over such instances. EKF-GPR(+) implements the gating function by using simple calculations based on the predictive variance with no additional detection mechanism. A sparse approximation of the GPR algorithm is employed to realize EKF-GPR(+) in real time. Extensive numerical experiments are performed based on a large database of 304 respiratory motion traces to evaluate EKF-GPR(+). The experimental results show that the EKF-GPR(+) algorithm effectively reduces the prediction error in a root-mean-square (RMS) sense by employing the gating function, albeit at the cost of a reduced duty cycle. As an example, EKF-GPR(+) reduces the patient-wise RMS error to 37%, 39% and
Directory of Open Access Journals (Sweden)
Douglas A. Fynan
2016-06-01
Full Text Available The Gaussian process model (GPM is a flexible surrogate model that can be used for nonparametric regression for multivariate problems. A unique feature of the GPM is that a prediction variance is automatically provided with the regression function. In this paper, we estimate the safety margin of a nuclear power plant by performing regression on the output of best-estimate simulations of a large-break loss-of-coolant accident with sampling of safety system configuration, sequence timing, technical specifications, and thermal hydraulic parameter uncertainties. The key aspect of our approach is that the GPM regression is only performed on the dominant input variables, the safety injection flow rate and the delay time for AC powered pumps to start representing sequence timing uncertainty, providing a predictive model for the peak clad temperature during a reflood phase. Other uncertainties are interpreted as contributors to the measurement noise of the code output and are implicitly treated in the GPM in the noise variance term, providing local uncertainty bounds for the peak clad temperature. We discuss the applicability of the foregoing method to reduce the use of conservative assumptions in best estimate plus uncertainty (BEPU and Level 1 probabilistic safety assessment (PSA success criteria definitions while dealing with a large number of uncertainties.
Energy Technology Data Exchange (ETDEWEB)
Fynan, Douglas A.; Ahn, Kwang Il [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2016-06-15
The Gaussian process model (GPM) is a flexible surrogate model that can be used for nonparametric regression for multivariate problems. A unique feature of the GPM is that a prediction variance is automatically provided with the regression function. In this paper, we estimate the safety margin of a nuclear power plant by performing regression on the output of best-estimate simulations of a large-break loss-of-coolant accident with sampling of safety system configuration, sequence timing, technical specifications, and thermal hydraulic parameter uncertainties. The key aspect of our approach is that the GPM regression is only performed on the dominant input variables, the safety injection flow rate and the delay time for AC powered pumps to start representing sequence timing uncertainty, providing a predictive model for the peak clad temperature during a reflood phase. Other uncertainties are interpreted as contributors to the measurement noise of the code output and are implicitly treated in the GPM in the noise variance term, providing local uncertainty bounds for the peak clad temperature. We discuss the applicability of the foregoing method to reduce the use of conservative assumptions in best estimate plus uncertainty (BEPU) and Level 1 probabilistic safety assessment (PSA) success criteria definitions while dealing with a large number of uncertainties.
McAllister, M J; Dhillon, V S; Marsh, T R; Ashley, R P; Bours, M C P; Breedt, E; Hardy, L K; Hermes, J J; Kengkriangkrai, S; Kerry, P; Rattanasoon, S; Sahman, D I
2016-01-01
The majority of cataclysmic variable (CV) stars contain a stochastic noise component in their light curves, commonly referred to as flickering. This can significantly affect the morphology of CV eclipses and increases the difficulty in obtaining accurate system parameters with reliable errors through eclipse modelling. Here we introduce a new approach to eclipse modelling, which models CV flickering with the help of Gaussian processes (GPs). A parameterised eclipse model - with an additional GP component - is simultaneously fit to 8 eclipses of the dwarf nova ASASSN-14ag and system parameters determined. We obtain a mass ratio $q$ = 0.149 $\\pm$ 0.016 and inclination $i$ = 83.4 $^{+0.9}_{-0.6}$ $^{\\circ}$. The white dwarf and donor masses were found to be $M_{w}$ = 0.63 $\\pm$ 0.04 $M_{\\odot}$ and $M_{d}$ = 0.093 $^{+0.015}_{-0.012}$ $M_{\\odot}$, respectively. A white dwarf temperature $T_{w}$ = 14000 $^{+2200}_{-2000}$ K and distance $d$ = 146 $^{+24}_{-20}$ pc were determined through multicolour photometry. W...
Aigrain, Suzanne; Pope, Benjamin
2016-01-01
We present K2SC (K2 Systematics Correction), a Python pipeline to model instrumental systematics and astrophysical variability in light curves from the K2 mission. K2SC uses Gaussian process regression to model position-dependent systematics and time-dependent variability simultaneously, enabling the user to remove both (e.g., for transit searches) or to remove systematics while preserving variability (for variability studies). For periodic variables, K2SC automatically computes estimates of the period, amplitude and evolution timescale of the variability. We apply K2SC to publicly available K2 data from campaigns 3--5, showing that we obtain photometric precision approaching that of the original Kepler mission. We compare our results to other publicly available K2 pipelines, showing that we obtain similar or better results, on average. We use transit injection and recovery tests to evaluate the impact of K2SC on planetary transit searches in K2 PDC (Pre-search Data Conditioning) data, for planet-to-star radi...
ChemXSeer Digital Library Gaussian Search
Lahiri, Shibamouli; Nangia, Shikha; Mitra, Prasenjit; Giles, C Lee; Mueller, Karl T
2011-01-01
We report on the Gaussian file search system designed as part of the ChemXSeer digital library. Gaussian files are produced by the Gaussian software [4], a software package used for calculating molecular electronic structure and properties. The output files are semi-structured, allowing relatively easy access to the Gaussian attributes and metadata. Our system is currently capable of searching Gaussian documents using a boolean combination of atoms (chemical elements) and attributes. We have also implemented a faceted browsing feature on three important Gaussian attribute types - Basis Set, Job Type and Method Used. The faceted browsing feature enables a user to view and process a smaller, filtered subset of documents.
Directory of Open Access Journals (Sweden)
Viet Dung Cao
2013-10-01
Full Text Available Background: We extend the "Wedding Ring‟ agent-based model of marriage formation to include some empirical information on the natural population change for the United Kingdom together with behavioural explanations that drive the observed nuptiality trends. Objective: We propose a method to explore statistical properties of agent-based demographic models. By coupling rule-based explanations driving the agent-based model with observed data we wish to bring agent-based modelling and demographic analysis closer together. Methods: We present a Semi-Artificial Model of Population, which aims to bridge demographic micro-simulation and agent-based traditions. We then utilise a Gaussian process emulator - a statistical model of the base model - to analyse the impact of selected model parameters on two key model outputs: population size and share of married agents. A sensitivity analysis is attempted, aiming to assess the relative importance of different inputs. Results: The resulting multi-state model of population dynamics has enhanced predictive capacity as compared to the original specification of the Wedding Ring, but there are some trade-offs between the outputs considered. The sensitivity analysis allows identification of the most important parameters in the modelled marriage formation process. Conclusions: The proposed methods allow for generating coherent, multi-level agent-based scenarios aligned with some aspects of empirical demographic reality. Emulators permit a statistical analysis of their properties and help select plausible parameter values. Comments: Given non-linearities in agent-based models such as the Wedding Ring, and the presence of feedback loops, the uncertainty in the model may not be directly computable by using traditional statistical methods. The use of statistical emulators offers a way forward.
Aigrain, S.; Parviainen, H.; Pope, B. J. S.
2016-07-01
We present K2SC (K2 Systematics Correction), a PYTHON pipeline to model instrumental systematics and astrophysical variability in light curves from the K2 mission. K2SC uses Gaussian Process regression to model position-dependent systematics and time-dependent variability simultaneously, enabling the user to remove both (e.g. for transit searches) or to remove systematics while preserving variability (for variability studies). For periodic variables, K2SC automatically computes estimates of the period, amplitude and evolution time-scale of the variability. We apply K2SC to publicly available K2 data from Campaigns 3-5 showing that we obtain photometric precision approaching that of the original Kepler mission. We compare our results to other publicly available K2 pipelines, showing that we obtain similar or better results, on average. We use transit injection and recovery tests to evaluate the impact of K2SC on planetary transit searches in K2 Pre-search Data Conditioning data, for planet-to-star radius ratios down to Rp/R* = 0.01 and periods up to P = 40 d, and show that K2SC significantly improves the ability to distinguish between true and false detections, particularly for small planets. K2SC can be run automatically on many light curves, or manually tailored for specific objects such as pulsating stars or large amplitude eclipsing binaries. It can be run on ASCII and FITS light-curve files, regardless of their origin. Both the code and the processed light curves are publicly available, and we provide instructions for downloading and using them. The methodology used by K2SC will be applicable to future transit search missions such as TESS and PLATO.
Incremental Gaussian Processes
DEFF Research Database (Denmark)
Quiñonero-Candela, Joaquin; Winther, Ole
2002-01-01
In this paper, we consider Tipping's relevance vector machine (RVM) and formalize an incremental training strategy as a variant of the expectation-maximization (EM) algorithm that we call subspace EM. Working with a subset of active basis functions, the sparsity of the RVM solution will ensure th...
Caywood, Matthew S; Roberts, Daniel M; Colombe, Jeffrey B; Greenwald, Hal S; Weiland, Monica Z
2016-01-01
There is increasing interest in real-time brain-computer interfaces (BCIs) for the passive monitoring of human cognitive state, including cognitive workload. Too often, however, effective BCIs based on machine learning techniques may function as "black boxes" that are difficult to analyze or interpret. In an effort toward more interpretable BCIs, we studied a family of N-back working memory tasks using a machine learning model, Gaussian Process Regression (GPR), which was both powerful and amenable to analysis. Participants performed the N-back task with three stimulus variants, auditory-verbal, visual-spatial, and visual-numeric, each at three working memory loads. GPR models were trained and tested on EEG data from all three task variants combined, in an effort to identify a model that could be predictive of mental workload demand regardless of stimulus modality. To provide a comparison for GPR performance, a model was additionally trained using multiple linear regression (MLR). The GPR model was effective when trained on individual participant EEG data, resulting in an average standardized mean squared error (sMSE) between true and predicted N-back levels of 0.44. In comparison, the MLR model using the same data resulted in an average sMSE of 0.55. We additionally demonstrate how GPR can be used to identify which EEG features are relevant for prediction of cognitive workload in an individual participant. A fraction of EEG features accounted for the majority of the model's predictive power; using only the top 25% of features performed nearly as well as using 100% of features. Subsets of features identified by linear models (ANOVA) were not as efficient as subsets identified by GPR. This raises the possibility of BCIs that require fewer model features while capturing all of the information needed to achieve high predictive accuracy.
Directory of Open Access Journals (Sweden)
David J. Savory
2017-07-01
Full Text Available Sub-Saharan Africa currently has the world’s highest urban population growth rate of any continent at roughly 4.2% annually. A better understanding of the spatiotemporal dynamics of urbanization across the continent is important to a range of fields including public health, economics, and environmental sciences. Nighttime lights imagery (NTL, maintained by the National Oceanic and Atmospheric Administration, offers a unique vantage point for studying trends in urbanization. A well-documented deficiency of this dataset is the lack of intra- and inter-annual calibration between satellites, which makes the imagery unsuitable for temporal analysis in their raw format. Here we have generated an ‘intercalibrated’ time series of annual NTL images for Africa (2000–2013 by building on the widely used invariant region and quadratic regression method (IRQR. Gaussian process methods (GP were used to identify NTL latent functions independent from the temporal noise signals in the annual datasets. The corrected time series was used to explore the positive association of NTL with Gross Domestic Product (GDP and urban population (UP. Additionally, the proportion of change in ‘lit area’ occurring in urban areas was measured by defining urban agglomerations as contiguously lit pixels of >250 km2, with all other pixels being rural. For validation, the IRQR and GP time series were compared as predictors of the invariant region dataset. Root mean square error values for the GP smoothed dataset were substantially lower. Correlation of NTL with GDP and UP using GP smoothing showed significant increases in R2 over the IRQR method on both continental and national scales. Urban growth results suggested that the majority of growth in lit pixels between 2000 and 2013 occurred in rural areas. With this study, we demonstrated the effectiveness of GP to improve conventional intercalibration, used NTL to describe temporal patterns of urbanization in Africa, and
Caywood, Matthew S.; Roberts, Daniel M.; Colombe, Jeffrey B.; Greenwald, Hal S.; Weiland, Monica Z.
2017-01-01
There is increasing interest in real-time brain-computer interfaces (BCIs) for the passive monitoring of human cognitive state, including cognitive workload. Too often, however, effective BCIs based on machine learning techniques may function as “black boxes” that are difficult to analyze or interpret. In an effort toward more interpretable BCIs, we studied a family of N-back working memory tasks using a machine learning model, Gaussian Process Regression (GPR), which was both powerful and amenable to analysis. Participants performed the N-back task with three stimulus variants, auditory-verbal, visual-spatial, and visual-numeric, each at three working memory loads. GPR models were trained and tested on EEG data from all three task variants combined, in an effort to identify a model that could be predictive of mental workload demand regardless of stimulus modality. To provide a comparison for GPR performance, a model was additionally trained using multiple linear regression (MLR). The GPR model was effective when trained on individual participant EEG data, resulting in an average standardized mean squared error (sMSE) between true and predicted N-back levels of 0.44. In comparison, the MLR model using the same data resulted in an average sMSE of 0.55. We additionally demonstrate how GPR can be used to identify which EEG features are relevant for prediction of cognitive workload in an individual participant. A fraction of EEG features accounted for the majority of the model’s predictive power; using only the top 25% of features performed nearly as well as using 100% of features. Subsets of features identified by linear models (ANOVA) were not as efficient as subsets identified by GPR. This raises the possibility of BCIs that require fewer model features while capturing all of the information needed to achieve high predictive accuracy. PMID:28123359
Chen, Sheng; Yao, Liping; Chen, Bao
2016-11-01
The enhancement of lung nodules in chest radiographs (CXRs) plays an important role in the manual as well as computer-aided detection (CADe) lung cancer. In this paper, we proposed a parameterized logarithmic image processing (PLIP) method combined with the Laplacian of a Gaussian (LoG) filter to enhance lung nodules in CXRs. We first applied several LoG filters with varying parameters to an original CXR to enhance the nodule-like structures as well as the edges in the image. We then applied the PLIP model, which can enhance lung nodule images with high contrast and was beneficial in extracting effective features for nodule detection in the CADe scheme. Our method combined the advantages of both the PLIP algorithm and the LoG algorithm, which can enhance lung nodules in chest radiographs with high contrast. To test our nodule enhancement method, we tested a CADe scheme, with a relatively high performance in nodule detection, using a publically available database containing 140 nodules in 140 CXRs enhanced through our nodule enhancement method. The CADe scheme attained a sensitivity of 81 and 70 % with an average of 5.0 frame rate (FP) and 2.0 FP, respectively, in a leave-one-out cross-validation test. By contrast, the CADe scheme based on the original image recorded a sensitivity of 77 and 63 % at 5.0 FP and 2.0 FP, respectively. We introduced the measurement of enhancement by entropy evaluation to objectively assess our method. Experimental results show that the proposed method obtains an effective enhancement of lung nodules in CXRs for both radiologists and CADe schemes.
Chilenski, M. A.; Greenwald, M.; Marzouk, Y.; Howard, N. T.; White, A. E.; Rice, J. E.; Walk, J. R.
2015-02-01
The need to fit smooth temperature and density profiles to discrete observations is ubiquitous in plasma physics, but the prevailing techniques for this have many shortcomings that cast doubt on the statistical validity of the results. This issue is amplified in the context of validation of gyrokinetic transport models (Holland et al 2009 Phys. Plasmas 16 052301), where the strong sensitivity of the code outputs to input gradients means that inadequacies in the profile fitting technique can easily lead to an incorrect assessment of the degree of agreement with experimental measurements. In order to rectify the shortcomings of standard approaches to profile fitting, we have applied Gaussian process regression (GPR), a powerful non-parametric regression technique, to analyse an Alcator C-Mod L-mode discharge used for past gyrokinetic validation work (Howard et al 2012 Nucl. Fusion 52 063002). We show that the GPR techniques can reproduce the previous results while delivering more statistically rigorous fits and uncertainty estimates for both the value and the gradient of plasma profiles with an improved level of automation. We also discuss how the use of GPR can allow for dramatic increases in the rate of convergence of uncertainty propagation for any code that takes experimental profiles as inputs. The new GPR techniques for profile fitting and uncertainty propagation are quite useful and general, and we describe the steps to implementation in detail in this paper. These techniques have the potential to substantially improve the quality of uncertainty estimates on profile fits and the rate of convergence of uncertainty propagation, making them of great interest for wider use in fusion experiments and modelling efforts.
2011-10-01
applications, Spinger -Verlag, 1989. Fig. 7.11. Two dimensional marginal chains for parameters m5,m6,m7,m8. The Gaussian process predictor is obtained after ten...43 (2005), pp. 1306–1315. [48] Radford M. Neal, Bayesian learning for neural networks, Spinger -Verlag, 1996. [49] Ngoc Cuong Nguyen, An uncertainty...J. Santner, Brian J. Williams, and William I. Notz, The Design and Analysis of Computer Experiments, Spinger -Verlag, 2003. [60] Alexandra M. Schmidt
Hierarchy in Sampling Gaussian-correlated Bosons
Huh, Joonsuk
2016-01-01
Boson Sampling represents a class of physical processes potentially intractable for classical devices to simulate. The Gaussian extension of Boson Sampling remains a computationally hard problem, where the input state is a product of uncorrelated Gaussian modes. Besides, motivated by molecular spectroscopy, Vibronic Boson Sampling involves operations that can generate Gaussian correlation among different Boson modes. Therefore, Gaussian Boson Sampling is a special case of Vibronic Boson Sampling. However, this does not necessarily mean that Vibronic Boson Sampling is more complex than Gaussian Boson Sampling. Here we develop a hierarchical structure to show how the initial correlation in Vibronic Boson Sampling can be absorbed in Gaussian Boson Sampling with ancillary modes and in a scattershot fashion. Since every Gaussian state is associated with a thermal state, our result implies that every sampling problem in molecular vibronic transitions, at any temperature, can be simulated by Gaussian Boson Sampling ...
Meyfroidt, Geert; Güiza, Fabian; Cottem, Dominiek; De Becker, Wilfried; Van Loon, Kristien; Aerts, Jean-Marie; Berckmans, Daniël; Ramon, Jan; Bruynooghe, Maurice; Van den Berghe, Greet
2011-10-25
The intensive care unit (ICU) length of stay (LOS) of patients undergoing cardiac surgery may vary considerably, and is often difficult to predict within the first hours after admission. The early clinical evolution of a cardiac surgery patient might be predictive for his LOS. The purpose of the present study was to develop a predictive model for ICU discharge after non-emergency cardiac surgery, by analyzing the first 4 hours of data in the computerized medical record of these patients with Gaussian processes (GP), a machine learning technique. Non-interventional study. Predictive modeling, separate development (n = 461) and validation (n = 499) cohort. GP models were developed to predict the probability of ICU discharge the day after surgery (classification task), and to predict the day of ICU discharge as a discrete variable (regression task). GP predictions were compared with predictions by EuroSCORE, nurses and physicians. The classification task was evaluated using aROC for discrimination, and Brier Score, Brier Score Scaled, and Hosmer-Lemeshow test for calibration. The regression task was evaluated by comparing median actual and predicted discharge, loss penalty function (LPF) ((actual-predicted)/actual) and calculating root mean squared relative errors (RMSRE). Median (P25-P75) ICU length of stay was 3 (2-5) days. For classification, the GP model showed an aROC of 0.758 which was significantly higher than the predictions by nurses, but not better than EuroSCORE and physicians. The GP had the best calibration, with a Brier Score of 0.179 and Hosmer-Lemeshow p-value of 0.382. For regression, GP had the highest proportion of patients with a correctly predicted day of discharge (40%), which was significantly better than the EuroSCORE (p nurses (p = 0.044) but equivalent to physicians. GP had the lowest RMSRE (0.408) of all predictive models. A GP model that uses PDMS data of the first 4 hours after admission in the ICU of scheduled adult cardiac surgery
Chang, Anteng; Li, Huajun; Wang, Shuqing; Du, Junfeng
2017-08-01
Both wave-frequency (WF) and low-frequency (LF) components of mooring tension are in principle non-Gaussian due to nonlinearities in the dynamic system. This paper conducts a comprehensive investigation of applicable probability density functions (PDFs) of mooring tension amplitudes used to assess mooring-line fatigue damage via the spectral method. Short-term statistical characteristics of mooring-line tension responses are firstly investigated, in which the discrepancy arising from Gaussian approximation is revealed by comparing kurtosis and skewness coefficients. Several distribution functions based on present analytical spectral methods are selected to express the statistical distribution of the mooring-line tension amplitudes. Results indicate that the Gamma-type distribution and a linear combination of Dirlik and Tovo-Benasciutti formulas are suitable for separate WF and LF mooring tension components. A novel parametric method based on nonlinear transformations and stochastic optimization is then proposed to increase the effectiveness of mooring-line fatigue assessment due to non-Gaussian bimodal tension responses. Using time domain simulation as a benchmark, its accuracy is further validated using a numerical case study of a moored semi-submersible platform.
Schmidt, Andreas; Lausch, Angela; Vogel, Hans-Jörg
2016-04-01
Diffuse reflectance spectroscopy as a soil analytical tool is spreading more and more. There is a wide range of possible applications ranging from the point scale (e.g. simple soil samples, drill cores, vertical profile scans) through the field scale to the regional and even global scale (UAV, airborne and space borne instruments, soil reflectance databases). The basic idea is that the soil's reflectance spectrum holds information about its properties (like organic matter content or mineral composition). The relation between soil properties and the observable spectrum is usually not exactly know and is typically derived from statistical methods. Nowadays these methods are classified in the term machine learning, which comprises a vast pool of algorithms and methods for learning the relationship between pairs if input - output data (training data set). Within this pool of methods a Gaussian Process Regression (GPR) is newly emerging method (originating from Bayesian statistics) which is increasingly applied to applications in different fields. For example, it was successfully used to predict vegetation parameters from hyperspectral remote sensing data. In this study we apply GPR to predict soil organic carbon from soil spectroscopy data (400 - 2500 nm). We compare it to more traditional and widely used methods such as Partitial Least Squares Regression (PLSR), Random Forest (RF) and Gradient Boosted Regression Trees (GBRT). All these methods have the common ability to calculate a measure for the variable importance (wavelengths importance). The main advantage of GPR is its ability to also predict the variance of the target parameter. This makes it easy to see whether a prediction is reliable or not. The ability to choose from various covariance functions makes GPR a flexible method. This allows for including different assumptions or a priori knowledge about the data. For this study we use samples from three different locations to test the prediction accuracies. One
Energy Technology Data Exchange (ETDEWEB)
Hoejstrup, J. [NEG Micon Project Development A/S, Randers (Denmark); Hansen, K.S. [Denmarks Technical Univ., Dept. of Energy Engineering, Lyngby (Denmark); Pedersen, B.J. [VESTAS Wind Systems A/S, Lem (Denmark); Nielsen, M. [Risoe National Lab., Wind Energy and Atmospheric Physics, Roskilde (Denmark)
1999-03-01
The pdf`s of atmospheric turbulence have somewhat wider tails than a Gaussian, especially regarding accelerations, whereas velocities are close to Gaussian. This behaviour is being investigated using data from a large WEB-database in order to quantify the amount of non-Gaussianity. Models for non-Gaussian turbulence have been developed, by which artificial turbulence can be generated with specified distributions, spectra and cross-correlations. The artificial time series will then be used in load models and the resulting loads in the Gaussian and the non-Gaussian cases will be compared. (au)
Stevenson, M D; Oakley, J; Chilcott, J B
2004-01-01
Individual patient-level models can simulate more complex disease processes than cohort-based approaches. However, large numbers of patients need to be simulated to reduce 1st-order uncertainty, increasing the computational time required and often resulting in the inability to perform extensive sensitivity analyses. A solution, employing Gaussian process techniques, is presented using a case study, evaluating the cost-effectiveness of a sample of treatments for established osteoporosis. The Gaussian process model accurately formulated a statistical relationship between the inputs to the individual patient model and its outputs. This model reduced the time required for future runs from 150 min to virtually-instantaneous, allowing probabilistic sensitivity analyses-to be undertaken. This reduction in computational time was achieved with minimal loss in accuracy. The authors believe that this case study demonstrates the value of this technique in handling 1st- and 2nd-order uncertainty in the context of health economic modeling, particularly when more widely used techniques are computationally expensive or are unable to accurately model patient histories.
Dissipation-induced pure Gaussian state
Koga, Kei
2011-01-01
This paper provides some necessary and sufficient conditions for a general Markovian Gaussian master equation to have a unique pure steady state. The conditions are described by simple matrix equations, thus they can be easily applied to the so-called environment engineering for pure Gaussian state preparation. In particular, it is shown that for any given pure Gaussian state we can actually construct a dissipative process yielding that state as the unique steady state.
Computing an Exact Gaussian Scale-Space
Ives Rey Otero; Mauricio Delbracio
2016-01-01
Gaussian convolution is one of the most important algorithms in image processing. The present work focuses on the computation of the Gaussian scale-space, a family of increasingly blurred images, responsible, among other things, for the scale-invariance of SIFT, a popular image matching algorithm. We discuss and numerically analyze the precision of three different alternatives for defining a discrete counterpart to the continuous Gaussian operator. This study is focused on low blur levels, th...
DEFF Research Database (Denmark)
Højstrup, Jørgen; Hansen, Kurt S.; Pedersen, Bo Juul;
1999-01-01
The pdf's of atmosperic turbulence have somewhat wider tails than a Gaussian, especially regarding accelerations, whereas velocities are close to Gaussian. This behaviour has been investigated using data from a large WEB-database in order to quantify the amount of non-gaussianity. Models for non-...
FPGA design and implementation of Gaussian filter
Yang, Zhihui; Zhou, Gang
2015-12-01
In this paper , we choose four different variances of 1,3,6 and 12 to conduct FPGA design with three kinds of Gaussian filtering algorithm ,they are implementing Gaussian filter with a Gaussian filter template, Gaussian filter approximation with mean filtering and Gaussian filter approximation with IIR filtering. By waveform simulation and synthesis, we get the processing results on the experimental image and the consumption of FPGA resources of the three methods. We set the result of Gaussian filter used in matlab as standard to get the result error. By comparing the FPGA resources and the error of FPGA implementation methods, we get the best FPGA design to achieve a Gaussian filter. Conclusions can be drawn based on the results we have already got. When the variance is small, the FPGA resources is enough for the algorithm to implement Gaussian filter with a Gaussian filter template which is the best choice. But when the variance is so large that there is no more FPGA resources, we can chose the mean to approximate Gaussian filter with IIR filtering.
Energy Technology Data Exchange (ETDEWEB)
Rescigno, Thomas N; Yip, Frank L.; McCurdy, C. William; Rescigno, Thomas N.
2008-08-01
We describe an approach for studying molecular photoionization with a hybrid basis that combines the functionality of analytic basis sets to represent electronic coordinates near the nuclei of a molecule with numerically-defined grid-based functions. We discuss the evaluation of the various classes of two-electron integrals that occur in a hybrid basis consisting of Gaussian type orbitals (GTOs) and discrete variable representation (DVR) functions. This combined basis is applied to calculate single photoionization cross sections for molecular Li_2+, which has a large equilibrium bond distance (R=5.86a_0). The highly non-spherical nature of Li_2+ molecules causes higher angular momentum components to contribute significantly to the cross section even at low photoelectron energies, resulting in angular distributions that appear to be f-wave dominated near the photoionization threshold. At higher energies, where the de Broglie wavelength of the photoelectron becomes comparable with the bond distance, interference effects appear in the photoionization cross section. These interference phenomena appear at much lower energies than would be expected for diatomic targets with shorter internuclear separations.
Wen, Kai; Sakata, Fumihiko; Li, Zhu-Xia; Wu, Xi-Zhen; Zhang, Ying-Xun; Zhou, Shan-Gui
2013-07-05
Macroscopic parameters as well as precise information on the random force characterizing the Langevin-type description of the nuclear fusion process around the Coulomb barrier are extracted from the microscopic dynamics of individual nucleons by exploiting the numerical simulation of the improved quantum molecular dynamics. It turns out that the dissipation dynamics of the relative motion between two fusing nuclei is caused by a non-Gaussian distribution of the random force. We find that the friction coefficient as well as the time correlation function of the random force takes particularly large values in a region a little bit inside of the Coulomb barrier. A clear non-Markovian effect is observed in the time correlation function of the random force. It is further shown that an emergent dynamics of the fusion process can be described by the generalized Langevin equation with memory effects by appropriately incorporating the microscopic information of individual nucleons through the random force and its time correlation function.
Optimality of Gaussian discord.
Pirandola, Stefano; Spedalieri, Gaetana; Braunstein, Samuel L; Cerf, Nicolas J; Lloyd, Seth
2014-10-03
In this Letter we exploit the recently solved conjecture on the bosonic minimum output entropy to show the optimality of Gaussian discord, so that the computation of quantum discord for bipartite Gaussian states can be restricted to local Gaussian measurements. We prove such optimality for a large family of Gaussian states, including all two-mode squeezed thermal states, which are the most typical Gaussian states realized in experiments. Our family also includes other types of Gaussian states and spans their entire set in a suitable limit where they become Choi matrices of Gaussian channels. As a result, we completely characterize the quantum correlations possessed by some of the most important bosonic states in quantum optics and quantum information.
DEFF Research Database (Denmark)
Nielsen, Ulrik Dam
2010-01-01
Mean outcrossing rates can be used as a basis for decision support for ships in severe sea. The article describes a procedure for calculating the mean outcrossing rate of non-Gaussian processes with stochastic input parameters. The procedure is based on the first-order reliability method (FORM......) and stochastic parameters are incorporated by carrying out a number of FORM calculations corresponding to combinations of specific values of the stochastic parameters. Subsequently, the individual FORM calculation is weighted according to the joint probability with which the specific combination of parameter....... The results of the procedure are compared with brute force simulations obtained by Monte Carlo simulation (MCS) and good agreement is observed. Importantly, the procedure requires significantly less CPU time compared to MCS to produce mean outcrossing rates....
Wave Period Distributions in Non-Gaussian Mixed Sea States
Institute of Scientific and Technical Information of China (English)
王迎光
2013-01-01
The wave period probability densities in non-Gaussian mixed sea states are calculated by utilizing a transformed Gaussian process method. The transformation relating the non-Gaussian process and the original Gaussian process is obtained based on the equivalence of the level up-crossing rates of the two processes. A saddle point approximation procedure is applied for calculating the level up-crossing rates in this study. The accuracy and efficiency of the transformed Gaussian process method are validated by comparing the results predicted by using the method with those predicted by the Monte Carlo simulation method.
基于高斯过程的机器人模仿学习研究与实现%Robot Imitation Learning Based on Gaussian Processes
Institute of Scientific and Technical Information of China (English)
于建均; 韩春晓; 阮晓钢; 刘涛
2015-01-01
针对机器人模仿学习控制策略获取的问题，基于高斯过程的方法，建立示教机器人示教行为的样本数据的高斯过程回归模型并加以训练，以求解示教机器人的感知和行为之间的映射关系，并将此映射关系作为模仿机器人的控制策略来实现对示教行为的模仿。以Braitenberg车为仿真对象，研究趋光模仿学习行为。仿真实验表明：基于高斯过程的机器人模仿学习算法具有有效性，模仿机器人在不同任务环境下具有很好的适应性。%To acquire the control strategy in robot imitation learning, a Gaussian processes ( GP ) regression model based on GP is used to construct the mapping relationship between actions of teaching robot and perception by the sample data of the teaching behavior. Then, the mapping relationship is used as control the strategy to imitate the teaching action. The Braitenberg vehicles are used as simulation subject to study phototaxis imitation learning action. Simulation results show that robot imitation learning based on Gaussian processes is effective. Furthermore, the simulation results in various task environments indicate that the method is adaptive.
Shcherbakov, V. P.; Khokhlov, A. V.; Sycheva, N. K.
2015-09-01
The quadrature formula is obtained for the distribution function (DF) of the intensity of the geomagnetic field B and the corresponding virtual axial dipole moment VADM in the model of the Giant Gaussian Process (GGP). The predictions of this model are compared, up to a high degree of detail, with the empirical data for the Brunhes Epoch, which are contained in the global databases (GDB) for paleointensity. With a fixed latitude φ, the DFs f B ( B, φ) and f VADM(VADM, φ) are close to Gaussian within the first approximation. At the same time, the global DF f B ( B) has a high coefficient of asymmetry a = 0.35 since the mean of this function is latitude-dependent. In contrast, the global DF f VADM(VADM) has far lower asymmetry a = 0.16, since its mean barely varies with latitude. The comparison between the distribution histograms of VADM according to the PINT GDB data for the Brunhes Epoch and the results calculated by the BGP model shows that the empirical data and the calculations by the GGP model noticeably differ in the interval of the small VADM. Specifically, the histogram based on PINT GDB data shows a significant predominance of these data compared to the model predictions. At the same time, the same data fairly well agree with the GGP model in directions. This contradiction is probably accounted for by the underestimation of the paleointensity values in the experiments by the Thellier method if the rock carries chemical magnetization instead of thermal remanent magnetization. An alternative explanation suggests a short drop in the geomagnetic dynamo power associated with a simultaneous decrease in both the mean value of the axial dipole and in the variances of all the other terms of the spherical expansion of the geomagnetic field (i.e., quadrupole, octupole, and other components).
Gaussian Intrinsic Entanglement
Mišta, Ladislav; Tatham, Richard
2016-12-01
We introduce a cryptographically motivated quantifier of entanglement in bipartite Gaussian systems called Gaussian intrinsic entanglement (GIE). The GIE is defined as the optimized mutual information of a Gaussian distribution of outcomes of measurements on parts of a system, conditioned on the outcomes of a measurement on a purifying subsystem. We show that GIE vanishes only on separable states and exhibits monotonicity under Gaussian local trace-preserving operations and classical communication. In the two-mode case, we compute GIE for all pure states as well as for several important classes of symmetric and asymmetric mixed states. Surprisingly, in all of these cases, GIE is equal to Gaussian Rényi-2 entanglement. As GIE is operationally associated with the secret-key agreement protocol and can be computed for several important classes of states, it offers a compromise between computable and physically meaningful entanglement quantifiers.
CSIR Research Space (South Africa)
Roux, FS
2009-01-01
Full Text Available . Gaussian beams with vortex dipoles CSIR National Laser Centre – p.2/30 Gaussian beam notation Gaussian beam in normalised coordinates: g(u, v, t) = exp ( −u 2 + v2 1− it ) u = xω0 v = yω0 t = zρ ρ = piω20 λ ω0 — 1/e2 beam waist radius; ρ— Rayleigh range ω ω...(z) 0 x z Rayleigh range Beam waist ρ ρ Rayleigh range CSIR National Laser Centre – p.3/30 Gaussian beam Gaussian beam in terms of amplitude and phase g(u, v, t) = exp ( −u 2 + v2 1 + t2 ) exp ( − it(u 2 + v2) 1 + t2 ) Normalised beam radius: √ 1 + t2...
Conditional and unconditional Gaussian quantum dynamics
Genoni, Marco G.; Lami, Ludovico; Serafini, Alessio
2016-07-01
This article focuses on the general theory of open quantum systems in the Gaussian regime and explores a number of diverse ramifications and consequences of the theory. We shall first introduce the Gaussian framework in its full generality, including a classification of Gaussian (also known as 'general-dyne') quantum measurements. In doing so, we will give a compact proof for the parametrisation of the most general Gaussian completely positive map, which we believe to be missing in the existing literature. We will then move on to consider the linear coupling with a white noise bath, and derive the diffusion equations that describe the evolution of Gaussian states under such circumstances. Starting from these equations, we outline a constructive method to derive general master equations that apply outside the Gaussian regime. Next, we include the general-dyne monitoring of the environmental degrees of freedom and recover the Riccati equation for the conditional evolution of Gaussian states. Our derivation relies exclusively on the standard quantum mechanical update of the system state, through the evaluation of Gaussian overlaps. The parametrisation of the conditional dynamics we obtain is novel and, at variance with existing alternatives, directly ties in to physical detection schemes. We conclude our study with two examples of conditional dynamics that can be dealt with conveniently through our formalism, demonstrating how monitoring can suppress the noise in optical parametric processes as well as stabilise systems subject to diffusive scattering.
Fibers of poly(lactic acid) (PLA) blended with p-toluenesulfonic acid-doped polyaniline, PAni.TSA, were obtained by lectrospinning, following a factorial design which was used mainly to study the effect of four process parameters (PLA solution concentration, PAni solution concentration, applied volt...
Cover: The electrospinning technique was employed to obtain conducting nanofibers based on polyaniline and poly(lactic acid). A statistical model was employed to describe how the process factors (solution concentration, applied voltage, and flow rate) govern the fiber dimensions. Nanofibers down to ...
基于高斯过程元模型的产品设计时间估计方法%Time estimation method for product design based on Gaussian process meta-model
Institute of Scientific and Technical Information of China (English)
张昆仑; 刘新亮; 郭波
2011-01-01
To estimate the product design time more precisely, the modeling methodology of Gaussian process meta-model was applied to estimate the product design time. The modeling principles of Gaussian process meta-model were firstly introduced. Since there were linguistic variables among the factors effecting product design time, Hausdorff distance was applied to assist the construction of relevant matrix in Gaussian Process modeling. The example analysis illustrated that Gaussian Process meta-model was superior to the existing two fuzzy neural network models.%为更精确地预测产品设计时间,将高斯过程元模型建模方法应用于产品设计时间估计中,介绍了高斯过程元模型的建模原理.考虑产品设计时间影响因素中存在语言型变量的问题,利用Hausdorff距离辅助构造高斯过程建模中的相关矩阵,通过算例分析证明高斯过程元模型优于已有的两种模糊神经网络模型.
Peters, Gareth W; Yuan, Jinhong; Collings, Ian
2011-01-01
This paper presents a flexible stochastic model developed for a class of cooperative wireless relay networks, in which the relay processing functionality is not known at the destination. The challenge is then to perform online system identification in this wireless relay network. To address this challenging problem we develop a novel class of statistical models and a computationally efficient algorithm that can be performed in real time processing, to undertake system identification for each relay channel in the presence of partial Channel State Information (CSI). We also develop a lower bound result and several sub-optimal though computationally efficient solutions to the identification problem, for comparison. We provide several examples for different non-linear relay functionalities.
Gaussian expansion approach to Coulomb breakup
Egami, T; Matsumoto, T; Iseri, Y; Kamimura, M; Yahiro, M
2004-01-01
An accurate treatment of Coulomb breakup reactions is presented by using both the Gaussian expansion method and the method of continuum discretized coupled channels. As $L^2$-type basis functions for describing Coulomb breakup processes, we take complex-range Gaussian functions, which form in good approximation a complete set in a large configuration space being important for the processes. Accuracy of the method is tested quantitatively for $^{8}{\\rm B}+^{58}$Ni scattering at 25.8 MeV.
Representation of Gaussian semimartingales with applications to the covariance function
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas
2010-01-01
The present paper is concerned with various aspects of Gaussian semimartingales. Firstly, generalizing a result of Stricker, we provide a convenient representation of Gaussian semimartingales as an -semimartingale plus a process of bounded variation which is independent of M. Secondly, we study...... stationary Gaussian semimartingales and their canonical decomposition. Thirdly, we give a new characterization of the covariance function of Gaussian semimartingales, which enable us to characterize the class of martingales and the processes of bounded variation among the Gaussian semimartingales. We...
Gaussian and Non-Gaussian operations on non-Gaussian state: engineering non-Gaussianity
Directory of Open Access Journals (Sweden)
Olivares Stefano
2014-03-01
Full Text Available Multiple photon subtraction applied to a displaced phase-averaged coherent state, which is a non-Gaussian classical state, produces conditional states with a non trivial (positive Glauber-Sudarshan Prepresentation. We theoretically and experimentally demonstrate that, despite its simplicity, this class of conditional states cannot be fully characterized by direct detection of photon numbers. In particular, the non-Gaussianity of the state is a characteristics that must be assessed by phase-sensitive measurements. We also show that the non-Gaussianity of conditional states can be manipulated by choosing suitable conditioning values and composition of phase-averaged states.
DEFF Research Database (Denmark)
Bennedsen, Mikkel
Using theory on (conditionally) Gaussian processes with stationary increments developed in Barndorff-Nielsen et al. (2009, 2011), this paper presents a general semiparametric approach to conducting inference on the fractal index, α, of a time series. Our setup encompasses a large class of Gaussian...
Computing an Exact Gaussian Scale-Space
Directory of Open Access Journals (Sweden)
Ives Rey Otero
2016-02-01
Full Text Available Gaussian convolution is one of the most important algorithms in image processing. The present work focuses on the computation of the Gaussian scale-space, a family of increasingly blurred images, responsible, among other things, for the scale-invariance of SIFT, a popular image matching algorithm. We discuss and numerically analyze the precision of three different alternatives for defining a discrete counterpart to the continuous Gaussian operator. This study is focused on low blur levels, that are crucial for the scale-space accuracy.
Autonomous Gaussian Decomposition
Lindner, Robert R; Murray, Claire E; Stanimirović, Snežana; Babler, Brian L; Heiles, Carl; Hennebelle, Patrick; Goss, W M; Dickey, John
2014-01-01
We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21cm absorption spectra from the 21cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the HI line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the up...
Broadcasting Correlated Gaussians
Bross, Shraga; Tinguely, Stephan
2007-01-01
We consider the transmission of a bi-variate Gaussian source over a one-to-two power-limited Gaussian broadcast channel. Receiver 1 observes the transmitted signal corrupted by Gaussian noise and wishes to estimate the first component of the source. Receiver 2 observes the transmitted signal in larger Gaussian noise and wishes to estimate the second component. We seek to characterize the pairs of mean squared-error distortions that are simultaneously achievable at the two receivers. Our result is that below a certain SNR-threshold an "uncoded scheme" that sends a linear combination of the source components is optimal. The SNR-theshold can be expressed as a function of the source correlation and the distortion at Receiver 1.
Hammouda, Boualem
2014-01-01
It is common practice to assume that Bragg scattering peaks have Gaussian shape. The Gaussian shape function is used to perform most instrumental smearing corrections. Using Monte Carlo ray tracing simulation, the resolution of a realistic small-angle neutron scattering (SANS) instrument is generated reliably. Including a single-crystal sample with large d-spacing, Bragg peaks are produced. Bragg peaks contain contributions from the resolution function and from spread in the sample structure. Results show that Bragg peaks are Gaussian in the resolution-limited condition (with negligible sample spread) while this is not the case when spread in the sample structure is non-negligible. When sample spread contributes, the exponentially modified Gaussian function is a better account of the Bragg peak shape. This function is characterized by a non-zero third moment (skewness) which makes Bragg peaks asymmetric for broad neutron wavelength spreads. PMID:26601025
Learning conditional Gaussian networks
DEFF Research Database (Denmark)
Bøttcher, Susanne Gammelgaard
This paper considers conditional Gaussian networks. The parameters in the network are learned by using conjugate Bayesian analysis. As conjugate local priors, we apply the Dirichlet distribution for discrete variables and the Gaussian-inverse gamma distribution for continuous variables, given...... independence, parameter modularity and likelihood equivalence. Bayes factors to be used in model search are introduced. Finally the methods derived are illustrated by a simple example....
On Gaussian random supergravity
Bachlechner, Thomas C.
2014-01-01
We study the distribution of metastable vacua and the likelihood of slow roll inflation in high dimensional random landscapes. We consider two examples of landscapes: a Gaussian random potential and an effective supergravity potential defined via a Gaussian random superpotential and a trivial K\\"ahler potential. To examine these landscapes we introduce a random matrix model that describes the correlations between various derivatives and we propose an efficient algorithm that allows for a nume...
Semiparametric Gaussian copula classification
Zhao, Yue; Wegkamp, Marten
2014-01-01
This paper studies the binary classification of two distributions with the same Gaussian copula in high dimensions. Under this semiparametric Gaussian copula setting, we derive an accurate semiparametric estimator of the log density ratio, which leads to our empirical decision rule and a bound on its associated excess risk. Our estimation procedure takes advantage of the potential sparsity as well as the low noise condition in the problem, which allows us to achieve faster convergence rate of...
Gaussian moving averages and semimartingales
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas
2008-01-01
In the present paper we study moving averages (also known as stochastic convolutions) driven by a Wiener process and with a deterministic kernel. Necessary and sufficient conditions on the kernel are provided for the moving average to be a semimartingale in its natural filtration. Our results...... are constructive - meaning that they provide a simple method to obtain kernels for which the moving average is a semimartingale or a Wiener process. Several examples are considered. In the last part of the paper we study general Gaussian processes with stationary increments. We provide necessary and sufficient...
Integrability Estimates for Gaussian Rough Differential Equations
Cass, Thomas; Lyons, Terry
2011-01-01
We derive explicit tail-estimates for the Jacobian of the solution flow of stochastic differential equations driven by Gaussian rough paths. In particular, we deduce that the Jacobian has finite moments of all order for a wide class of Gaussian process including fractional Brownian motion with Hurst parameter H>1/4. We remark on the relevance of such estimates to a number of significant open problems.
Xu, Jian-Wu; Suzuki, Kenji
2011-04-01
A massive-training artificial neural network (MTANN) has been developed for the reduction of false positives (FPs) in computer-aided detection (CADe) of polyps in CT colonography (CTC). A major limitation of the MTANN is the long training time. To address this issue, the authors investigated the feasibility of two state-of-the-art regression models, namely, support vector regression (SVR) and Gaussian process regression (GPR) models, in the massive-training framework and developed massive-training SVR (MTSVR) and massive-training GPR (MTGPR) for the reduction of FPs in CADe of polyps. The authors applied SVR and GPR as volume-processing techniques in the distinction of polyps from FP detections in a CTC CADe scheme. Unlike artificial neural networks (ANNs), both SVR and GPR are memory-based methods that store a part of or the entire training data for testing. Therefore, their training is generally fast and they are able to improve the efficiency of the massive-training methodology. Rooted in a maximum margin property, SVR offers excellent generalization ability and robustness to outliers. On the other hand, GPR approaches nonlinear regression from a Bayesian perspective, which produces both the optimal estimated function and the covariance associated with the estimation. Therefore, both SVR and GPR, as the state-of-the-art nonlinear regression models, are able to offer a performance comparable or potentially superior to that of ANN, with highly efficient training. Both MTSVR and MTGPR were trained directly with voxel values from CTC images. A 3D scoring method based on a 3D Gaussian weighting function was applied to the outputs of MTSVR and MTGPR for distinction between polyps and nonpolyps. To test the performance of the proposed models, the authors compared them to the original MTANN in the distinction between actual polyps and various types of FPs in terms of training time reduction and FP reduction performance. The authors' CTC database consisted of 240 CTC
Short-term Wind Speed Forecasting Based on Gaussian Process Regression Model%基于高斯过程回归的短期风速预测
Institute of Scientific and Technical Information of China (English)
孙斌; 姚海涛; 刘婷
2012-01-01
The short-term wind speed forecasting is very important for the operation of grid-connected wind power generation systems. The accuracy forecasting of the wind speed can also effectively reduces or avoids the adverse effect of wind farm on power grid, meanwhile, strengthens competition ability of wind farm in electricity market. In order to improve the forecasting accuracy, a wind speed forecasting method based on the Gaussian process (GP) was proposed. Firstly, the embedding dimension and the delay time of the wind speed time series were respectively calculated by autocorrelation method and false neighbor method, the phase space reconstruction of the chaotic wind speed time series was received. Then, the reconstructed wind speed time series was predicted by the GP model, at the same time the "super parameter" in the covariance function was determined under the Bayesian framework. Finally, wind speed time series was used to predict by the trained GP, which was compared with support vector machine (SVM), least squares support vector machine (LSSVM) and BP neural network (BPNN). The simulation results show that GP predict model can be used to accurately predict and has stable performance. So it can be widely used in engineering practice.%准确预测风速能有效减轻风电场对整个电网的不利影响,提高风电场在电力市场中的竞争能力.为了提高风速预测的精度,提出一种基于高斯过程(Gaussian processes,GP)的风速预测模型.首先运用自相关法和假近邻法分别求取风速时间序列的延迟时间和嵌入维数,进而对混沌风速时间序列进行相空间重构.其次运用GP模型对重构后的风速时间序列进行训练,同时在贝叶斯框架下,确定协方差函数中的“超参数”.最后利用训练好的GP模型风速时间序列进行预测,并与支持向量机、最小二乘支持向量机和BP神经网络进行比较.仿真结果表明,基于GP的风速预测模型具有很好的稳定性,
The curious nonexistence of Gaussian 2-designs
Blume-Kohout, Robin
2011-01-01
2-designs -- ensembles of quantum pure states whose 2nd moments equal those of the uniform Haar ensemble -- are optimal solutions for several tasks in quantum information science, especially state and process tomography. We show that Gaussian states cannot form a 2-design for the continuous-variable (quantum optical) Hilbert space L2(R). This is surprising because the affine symplectic group HWSp (the natural symmetry group of Gaussian states) is irreducible on the symmetric subspace of two copies. In finite dimensional Hilbert spaces, irreducibility guarantees that HWSp-covariant ensembles (such as mutually unbiased bases in prime dimensions) are always 2-designs. This property is violated by continuous variables, for a subtle reason: the (well-defined) HWSp-invariant ensemble of Gaussian states does not have an average state because the averaging integral does not converge. In fact, no Gaussian ensemble is even close (in a precise sense) to being a 2-design. This surprising difference between discrete and c...
Deblured Gaussian Blurred Images
Al-amri, Salem Saleh; D, Khamitkar S
2010-01-01
This paper attempts to undertake the study of Restored Gaussian Blurred Images. by using four types of techniques of deblurring image as Wiener filter, Regularized filter, Lucy Richardson deconvlutin algorithm and Blind deconvlution algorithm with an information of the Point Spread Function (PSF) corrupted blurred image with Different values of Size and Alfa and then corrupted by Gaussian noise. The same is applied to the remote sensing image and they are compared with one another, So as to choose the base technique for restored or deblurring image.This paper also attempts to undertake the study of restored Gaussian blurred image with no any information about the Point Spread Function (PSF) by using same four techniques after execute the guess of the PSF, the number of iterations and the weight threshold of it. To choose the base guesses for restored or deblurring image of this techniques.
Generalized Gaussian Error Calculus
Grabe, Michael
2010-01-01
For the first time in 200 years Generalized Gaussian Error Calculus addresses a rigorous, complete and self-consistent revision of the Gaussian error calculus. Since experimentalists realized that measurements in general are burdened by unknown systematic errors, the classical, widespread used evaluation procedures scrutinizing the consequences of random errors alone turned out to be obsolete. As a matter of course, the error calculus to-be, treating random and unknown systematic errors side by side, should ensure the consistency and traceability of physical units, physical constants and physical quantities at large. The generalized Gaussian error calculus considers unknown systematic errors to spawn biased estimators. Beyond, random errors are asked to conform to the idea of what the author calls well-defined measuring conditions. The approach features the properties of a building kit: any overall uncertainty turns out to be the sum of a contribution due to random errors, to be taken from a confidence inter...
Institute of Scientific and Technical Information of China (English)
常纯; 李德胜
2016-01-01
A short-term wind speed forecasting method based on phase-space reconstruction and evolutionary Gaussian process model is proposed in this paper .Firstly, the autocorrelation method and false nearest neighbor method are applied to calculate the delay time and embedding dimension of the wind speed time series , which are used to accomplish the phase-space reconstruction of the chaotic wind speed time series .Secondly, the evolutionary Gaussian process model , which combines Gaussian process with evolutionary algorithm , is used to forcast the wind speed .This model uses Gaussian process model to determine the relationship between the input and output variables , and the improved PSO algorithm to optimize the hyper parameters .The prediction results show that the proposed method can improve the prediction accuracy .%提出一种基于相空间重构和进化高斯过程的短期风速预测方法。首先，运用自相关法和假近邻法分别得出原始风速时间序列的延迟时间和嵌入维数，实现混沌风速时间序列的相空间重构；然后，运用进化高斯过程回归模型进行建模，通过高斯过程模型确定输入量和输出量之间的关系，并用改进粒子群算法求取最优超参数。根据某实测风速数据进行了风速预测，结果表明本文所提出的方法能有效提高风速预测精度。
Institute of Scientific and Technical Information of China (English)
李佳; 邱丽荣; 杨佳苗; 刘大礼; 赵维谦
2013-01-01
In order to improve the position precision of the confocal component parameters measurement system, a process data based on Gaussian filtering process is proposed on the disk images collected by the confocal system and confocal axial intensity response signale. The method reduces the optical noise on the disk images, and it weakens the interference of the factors such as environmental perturbations on the confocal axial intensity response signale. The theoretical analyses and preliminary experiments indicate that Gaussian filtering on the disk images and confocal axial intensity response signal can effectively suppress the image noise and reduce the high harmonic interference, thus it improves the system position accuracy.%为进一步提高共焦元件参数测量系统的定焦精度,提出了运用高斯滤波算法对由共焦系统采集的光斑图像和共焦轴向强度响应信号进行滤波处理,以降低系统光学噪声对测量光斑图像的影响,削弱外界环境扰动等因素对共焦轴向强度响应信号的干扰.经理论分析和实验验证,在对测量光斑图像和共焦轴向强度响应信号进行高斯滤波算法处理后,可有效地抑制图像噪声,降低高次谐波干扰,进而提高系统的定焦精度.
Trofimov, M Yu; Kozitskiy, S B
2015-01-01
An adiabatic mode Helmholtz equation for 3D underwater sound propagation is developed. The Gaussian beam tracing in this case is constructed. The test calculations are carried out for the crosswedge benchmark and proved an excellent agreement with the source images method.
AUTONOMOUS GAUSSIAN DECOMPOSITION
Energy Technology Data Exchange (ETDEWEB)
Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian [Department of Astronomy, University of Wisconsin, 475 North Charter Street, Madison, WI 53706 (United States); Heiles, Carl [Radio Astronomy Lab, UC Berkeley, 601 Campbell Hall, Berkeley, CA 94720 (United States); Hennebelle, Patrick [Laboratoire AIM, Paris-Saclay, CEA/IRFU/SAp-CNRS-Université Paris Diderot, F-91191 Gif-sur Yvette Cedex (France); Goss, W. M. [National Radio Astronomy Observatory, P.O. Box O, 1003 Lopezville, Socorro, NM 87801 (United States); Dickey, John, E-mail: rlindner@astro.wisc.edu [University of Tasmania, School of Maths and Physics, Private Bag 37, Hobart, TAS 7001 (Australia)
2015-04-15
We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21 cm absorption spectra from the 21 cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the H i line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the upcoming Square Kilometer Array and pathfinder telescopes.
A Family of Non-Gaussian Martingales with Gaussian Marginals
Directory of Open Access Journals (Sweden)
Kais Hamza
2007-08-01
Full Text Available We construct a family of martingales with Gaussian marginal distributions. We give a weak construction as Markov, inhomogeneous in time processes, and compute their infinitesimal generators. We give the predictable quadratic variation and show that the paths are not continuous. The construction uses distributions GÃÂƒ having a log-convolution semigroup property. Further, we categorize these processes as belonging to one of two classes, one of which is made up of piecewise deterministic pure jump processes. This class includes the case where GÃÂƒ is an inverse log-Poisson distribution. The processes in the second class include the case where GÃÂƒ is an inverse log-gamma distribution. The richness of the family has the potential to allow for the imposition of specifications other than the marginal distributions.
Bukhari, W; Hong, S-M
2016-03-01
The prediction as well as the gating of respiratory motion have received much attention over the last two decades for reducing the targeting error of the radiation treatment beam due to respiratory motion. In this article, we present a real-time algorithm for predicting respiratory motion in 3D space and realizing a gating function without pre-specifying a particular phase of the patient's breathing cycle. The algorithm, named EKF-GPRN(+) , first employs an extended Kalman filter (EKF) independently along each coordinate to predict the respiratory motion and then uses a Gaussian process regression network (GPRN) to correct the prediction error of the EKF in 3D space. The GPRN is a nonparametric Bayesian algorithm for modeling input-dependent correlations between the output variables in multi-output regression. Inference in GPRN is intractable and we employ variational inference with mean field approximation to compute an approximate predictive mean and predictive covariance matrix. The approximate predictive mean is used to correct the prediction error of the EKF. The trace of the approximate predictive covariance matrix is utilized to capture the uncertainty in EKF-GPRN(+) prediction error and systematically identify breathing points with a higher probability of large prediction error in advance. This identification enables us to pause the treatment beam over such instances. EKF-GPRN(+) implements a gating function by using simple calculations based on the trace of the predictive covariance matrix. Extensive numerical experiments are performed based on a large database of 304 respiratory motion traces to evaluate EKF-GPRN(+) . The experimental results show that the EKF-GPRN(+) algorithm reduces the patient-wise prediction error to 38%, 40% and 40% in root-mean-square, compared to no prediction, at lookahead lengths of 192 ms, 384 ms and 576 ms, respectively. The EKF-GPRN(+) algorithm can further reduce the prediction error by employing the gating
Institute of Scientific and Technical Information of China (English)
黄丽平; 孙永雄; 申晨
2013-01-01
针对3G网络中主动监控和对性能指标数据进行预测的需要,提出了基于中值滤波的高斯回归模型的网络性能指标预测方法,将高斯回归模型与中值滤波法相融合,对样本空间中的性能指标数据先进行中值滤波预处理,再对处理过的数据进行高斯回归预测,预测结果作为主动告警机制的预测曲线.仿真实验结果表明,相对于其他预测方法,基于中值滤波的高斯过程预测结果更加有效,生成的预测曲线更精确,为3G及以上网络进行主动监控确定更有效的阈值提供理论依据.%Aiming to the need of proactive monitoring and performance prediction in 3G networks, it proposes a prediction method of the Gaussian regression model based on the median filter, integrates the Gaussian regression model with the median filtering method, pretreats the sample data with median filtering, and then the processed data is done to the Gaussian regression prediction, the prediction results are as the prediction curve of the active alarm mechanism. Simulation results show that compared to other prediction algorithms, the Gaussian process based on median filtering predicts more effectively and generates more accurate prediction curves. It provides a theoretical basis for proactive monitoring in 3G and above network to determine an effective threshold.
Non-Gaussian operations on bosonic modes of light: Photon-added Gaussian channels
Sabapathy, Krishna Kumar; Winter, Andreas
2017-06-01
We present a framework for studying bosonic non-Gaussian channels of continuous-variable systems. Our emphasis is on a class of channels that we call photon-added Gaussian channels, which are experimentally viable with current quantum-optical technologies. A strong motivation for considering these channels is the fact that it is compulsory to go beyond the Gaussian domain for numerous tasks in continuous-variable quantum information processing such as entanglement distillation from Gaussian states and universal quantum computation. The single-mode photon-added channels we consider are obtained by using two-mode beam splitters and squeezing operators with photon addition applied to the ancilla ports giving rise to families of non-Gaussian channels. For each such channel, we derive its operator-sum representation, indispensable in the present context. We observe that these channels are Fock preserving (coherence nongenerating). We then report two examples of activation using our scheme of photon addition, that of quantum-optical nonclassicality at outputs of channels that would otherwise output only classical states and of both the quantum and private communication capacities, hinting at far-reaching applications for quantum-optical communication. Further, we see that noisy Gaussian channels can be expressed as a convex mixture of these non-Gaussian channels. We also present other physical and information-theoretic properties of these channels.
Nonlinearities with Non-Gaussian Inputs.
1978-03-01
possessing a spectral density function . a constant. Then Jet arc tan [G(t)J be the input. By Theorem 3 this input is not bandlimited; and if The rando...such that the absolute ,,~~ovalue of any point in the spectrum is less than N. If the Gaussian process X(t) possesses a H ~ ) spectral density function (i.e...Gaussian process and th. series ii convergent pointvise as veil X(t ) possesses a spectral density function . as in an sense (51. Let z~( ) and g2
Horner, Jonathan S
2013-01-01
The Hamilton-Jacobi (HJ) approach for exploring inflationary trajectories is employed in the generation of generalised inflationary non-Gaussian signals arising from single field inflation. Scale dependent solutions for $f_{NL}$ are determined via the numerical integration of the three--point function in the curvature perturbation. This allows the full exploration of single field inflationary dynamics in the out-of-slow-roll regime and opens up the possibility of using future observations of non-Gaussianity to constraint the inflationary potential using model-independent methods. The distribution of `equilateral' $f_{NL}$ arising from single field inflation with both canonical and non-canonical kinetic terms are show as an example of the application of this procedure.
Gaussian quantum marginal problem
Eisert, J; Sanders, B C; Tyc, T
2007-01-01
The quantum marginal problem asks what local spectra are consistent with a given state of a composite quantum system. This setting, also referred to as the question of the compatibility of local spectra, has several applications in quantum information theory. Here, we introduce the analogue of this statement for Gaussian states for any number of modes, and solve it in generality, for pure and mixed states, both concerning necessary and sufficient conditions. Formally, our result can be viewed as an analogue of the Sing-Thompson Theorem (respectively Horn's Lemma), characterizing the relationship between main diagonal elements and singular values of a complex matrix: We find necessary and sufficient conditions for vectors (d1, ..., dn) and (c1, ..., cn) to be the symplectic eigenvalues and symplectic main diagonal elements of a strictly positive real matrix, respectively. More physically speaking, this result determines what local temperatures or entropies are consistent with a pure or mixed Gaussian state of ...
On Gaussian random supergravity
Energy Technology Data Exchange (ETDEWEB)
Bachlechner, Thomas C. [Department of Physics, Cornell University,Physical Sciences Building 428, Ithaca, NY 14853 (United States)
2014-04-08
We study the distribution of metastable vacua and the likelihood of slow roll inflation in high dimensional random landscapes. We consider two examples of landscapes: a Gaussian random potential and an effective supergravity potential defined via a Gaussian random superpotential and a trivial Kähler potential. To examine these landscapes we introduce a random matrix model that describes the correlations between various derivatives and we propose an efficient algorithm that allows for a numerical study of high dimensional random fields. Using these novel tools, we find that the vast majority of metastable critical points in N dimensional random supergravities are either approximately supersymmetric with |F|≪M{sub susy} or supersymmetric. Such approximately supersymmetric points are dynamical attractors in the landscape and the probability that a randomly chosen critical point is metastable scales as log (P)∝−N. We argue that random supergravities lead to potentially interesting inflationary dynamics.
On Gaussian random supergravity
Bachlechner, Thomas C.
2014-04-01
We study the distribution of metastable vacua and the likelihood of slow roll inflation in high dimensional random landscapes. We consider two examples of landscapes: a Gaussian random potential and an effective supergravity potential defined via a Gaussian random superpotential and a trivial Kähler potential. To examine these landscapes we introduce a random matrix model that describes the correlations between various derivatives and we propose an efficient algorithm that allows for a numerical study of high dimensional random fields. Using these novel tools, we find that the vast majority of metastable critical points in N dimensional random supergravities are either approximately supersymmetric with | F| ≪ M susy or supersymmetric. Such approximately supersymmetric points are dynamical attractors in the landscape and the probability that a randomly chosen critical point is metastable scales as log( P ) ∝ - N. We argue that random supergravities lead to potentially interesting inflationary dynamics.
On Gaussian Random Supergravity
Bachlechner, Thomas C
2014-01-01
We study the distribution of metastable vacua and the likelihood of slow roll inflation in high dimensional random landscapes. We consider two examples of landscapes: a Gaussian random potential and an effective supergravity potential defined via a Gaussian random superpotential and a trivial Kahler potential. To examine these landscapes we introduce a random matrix model that describes the correlations between various derivatives and we propose an efficient algorithm that allows for a numerical study of high dimensional random fields. Using these novel tools, we find that the vast majority of metastable critical points in N dimensional random supergravities are either approximately supersymmetric with |F|<< M_{susy} or supersymmetric. Such approximately supersymmetric points are dynamical attractors in the landscape and the probability that a randomly chosen critical point is metastable scales as log(P)\\propto -N. We argue that random supergravities lead to potentially interesting inflationary dynamics...
Trofimov, M. Yu.; Zakharenko, A. D.; Kozitskiy, S. B.
2016-10-01
A mode parabolic equation in the ray centered coordinates for 3D underwater sound propagation is developed. The Gaussian beam tracing in this case is constructed. The test calculations are carried out for the ASA wedge benchmark and proved an excellent agreement with the source images method in the case of cross-slope propagation. But in the cases of wave propagation at some angles to the cross-slope direction an account of mode interaction becomes necessary.
Bessel-Gaussian entanglement; presentation
CSIR Research Space (South Africa)
Mclaren, M
2013-07-01
Full Text Available GAUSSIAN BEAM LAGUERRE-GAUSSIAN BEAM 15 Page 5 Higher-order Bessel-Gaussian beams carry OAM Page 6 © CSIR 2013 www.csir.co.za Generating Bessel-Gaussian beams using spatial light modulators (SLMs) Blazed axicon Binary axicon... stream_source_info McLaren_2013.pdf.txt stream_content_type text/plain stream_size 2915 Content-Encoding UTF-8 stream_name McLaren_2013.pdf.txt Content-Type text/plain; charset=UTF-8 Bessel-Gaussian entanglement M. Mc...
Eanes, Ritchie C.; Marcus, R. Kenneth
2000-04-01
This article is an electronic publication in Spectrochimica Acta Electronica (SAE), a section of Spectrochimica Acta Part B (SAB). The hardcopy text is accompanied by an electronic archive, stored on the SAE homepage at (http://www.elsevier.nl/locate/sabe). The archive contains program and data files. The main article discusses the scientific spectroscopic and instrumental aspects of the subject and explains the purpose of the program and data files. The work deals with a Microsoft Excel Visual Basic program, Peakfitter, which can process multiple Gaussian-shaped spectral peaks quickly and easily. The program employs Microsoft Excel Solver to process any Gaussian-like spectra that can be opened in Microsoft Excel 97. Up to three peaks in one to 225 spectra, each containing up to 2000 data points can be processed per data file to give background corrected peak areas for both raw data and its associated fit data as calculated by the trapezoidal method or by simple successive addition of channel intensities across each peak. Concurrently output also includes fit peak heights for Gaussian-shaped spectral peaks. Use of other statistical distributions such as the Lorentzian model requires only slight modification to a template file. Hence, Peakfitter was actually written as two application programs, 'Gaussfitter' and 'Lorenfitter' to accommodate spectra of Gaussian or Lorentzian character, respectively. Written initially to process data from a radio frequency glow discharge ion trap mass spectrometer (rf-GD/ITMS), the program is useful for processing sequentially acquired spectra, which have a limited number of data points across each peak. The user may examine and manipulate program variables in cases where the raw data is skewed with respect to the fit data. An assessment of Peakfitter is given using rf-GD/ITMS elemental analysis and ion-molecule reaction data. Peakfitter's (i.e. 'Gaussfitter's) utility in processing rf-GD/ITMS spectra is characterized by a slight
Homodyne estimation of Gaussian quantum discord
Blandino, Rémi; Jean, Etesse; Barbieri, Marco; Paris, Matteo G A; Grangier, Philippe; Tualle-Brouri, Rosa
2012-01-01
We address the experimental estimation of Gaussian quantum discord for two-mode squeezed state, and demonstrate a measurement scheme based on a pair of homodyne detectors assisted by Bayesian analysis. Our scheme provides nearly optimal estimation for small value of discord, where Bayesian analysis allows to greatly improves performances. Besides, though homodyne detection is not optimal for Gaussian discord, the noise ratio to the ultimate quantum limit is limited to about 10 dB. Our results illustrate how suitable data processing can decrease significantly the uncertainty when optimal detection schemes are not available.
Online learning algorithm of Gaussian process based on adaptive nature gradient%基于自适应自然梯度法的在线高斯过程建模
Institute of Scientific and Technical Information of China (English)
申倩倩; 孙宗海
2011-01-01
In order to satisfy the online modeling algorithm' s request of real-time, this paper proposed the adaptive natural gradient method used in online Gaussian process training.The algorithm was named online learning algorithm of Gaussian process based on adaptive nature gradient.The algorithm was applied in Micky-Glass system and continuous stirred tank reactor (CSTR) modeling,and compared with the sparse online Gaussian processes algorithm.Obtained from the simulation results,this algorithm meets the real-time and accuracy requirements of nonlinear system modeling, and overcomes other online algorithms' faults of needing much computation resource and not to accord with the requirement of real-time of online algorithm.%为了满足在线建模算法的实时性要求,提出了在高斯过程的训练中使用自适应自然梯度法(ANG),即基于自适应自然梯度法的在线高斯过程回归建模算法.将此算法运用在Micky-Glass系统和连续搅拌反应釜(CSTR)模型的建立中,并与稀疏在线高斯过程算法进行比较.仿真结果表明此算法满足了非线性系统建模的实时性和精度的要求,同时克服了其他方法计算量很大、不符合在线算法的实时性要求的缺点.
Open problems in Gaussian fluid queueing theory
Dȩbicki, K.; Mandjes, M.
2011-01-01
We present three challenging open problems that originate from the analysis of the asymptotic behavior of Gaussian fluid queueing models. In particular, we address the problem of characterizing the correlation structure of the stationary buffer content process, the speed of convergence to
Oracle Wiener filtering of a Gaussian signal
Babenko, A.; Belitser, E.N.
2011-01-01
We study the problem of filtering a Gaussian process whose trajectories, in some sense, have an unknown smoothness β0 from the white noise of small intensity . If we knew the parameter β0, we would use the Wiener filter which has the meaning of oracle. Our goal is now to mimic the oracle, i.e., cons
Institute of Scientific and Technical Information of China (English)
赵宏旭; 吴甦
2012-01-01
为了提高预测复杂波动过程的能力,结合物理模型和统计方法建立了＂波动方程-Gauss过程＂模型。通过误差分析,波动方程的理论预测与实际数据的差值被分解为3个部分,并拟合为Gauss过程模型：外力和初边值条件偏移带来的误差拟合为正交预测因子的线性叠加;模型假设不成立、数值解收敛性等因素导致的误差拟合为Gauss过程项;测量误差拟合为白噪声。＂波动方程-Gauss过程＂模型的预测因子是波动过程的基函数组,作为波动的本征特性不受外界影响,体现了波动的物理机理。基于实验数据的预测效果检验说明模型的基函数组和Gauss过程项都显著提高了预测波动过程的能力。%A wave equation Gaussian process model was developed to describe complicated wave motion by integrating physical and statistical approaches. The errors between the theoretical solution of the wave equation and the observed data were modeled as the three parts of aGaussian process model. The errors caused by the external interference and the shift boundary and initial conditions were described by a group of orthogonal basis functions. The errors caused by the inadequate model assumptions and limited convergence of the numerical solution were modeled as a Gaussian process term. Measurement errors were modeled as white noise. The basis functions, as the model predictors, are the intrinsic characteristics of the wave motion. The model was validated using experimental data generated i＇rom a vibrating string. The results indicate that both the basis functions and the Gaussian process terms significantly improve the prediction accuracy.
Non-Gaussian entanglement swapping
Dell'Anno, F; Nocerino, G; De Siena, S; Illuminati, F
2016-01-01
We investigate the continuous-variable entanglement swapping protocol in a non-Gaussian setting, with non- Gaussian states employed either as entangled inputs and/or as swapping resources. The quality of the swapping protocol is assessed in terms of the teleportation fidelity achievable when using the swapped states as shared entangled resources in a teleportation protocol. We thus introduce a two-step cascaded quantum communication scheme that includes a swapping protocol followed by a teleportation protocol. The swapping protocol is fed by a general class of tunable non-Gaussian states, the squeezed Bell states, which, by means of controllable free parameters, allows for a continuous morphing from Gaussian twin beams up to maximally non-Gaussian squeezed number states. In the realistic instance, taking into account the effects of losses and imperfections, we show that as the input two-mode squeezing increases, optimized non-Gaussian swapping resources allow for a monotonically increasing enhancement of the ...
Directory of Open Access Journals (Sweden)
Benjamin M. Taylor
2013-01-01
Full Text Available This paper introduces an R package for spatial and spatio-temporal prediction and forecasting for log-Gaussian Cox processes. The main computational tool for these models is Markov chain Monte Carlo (MCMC and the new package, lgcp, therefore also provides an extensible suite of functions for implementing MCMC algorithms for processes of this type. The modeling framework and details of inferential procedures are first presented before a tour of lgcp functionality is given via a walk-through data-analysis. Topics covered include reading in and converting data, estimation of the key components and parameters of the model, specifying output and simulation quantities, computation of Monte Carlo expectations, post-processing and simulation of data sets.
Entangled Bessel-Gaussian beams
CSIR Research Space (South Africa)
McLaren, M
2012-10-01
Full Text Available Orbital angular momentum (OAM) entanglement is investigated in the Bessel-Gaussian (BG) basis. Having a readily adjustable radial scale, BG modes provide an alternative basis for OAM entanglement over Laguerre-Gaussian modes. We show that the OAM...
Gaussian Fibonacci Circulant Type Matrices
Directory of Open Access Journals (Sweden)
Zhaolin Jiang
2014-01-01
Full Text Available Circulant matrices have become important tools in solving integrable system, Hamiltonian structure, and integral equations. In this paper, we prove that Gaussian Fibonacci circulant type matrices are invertible matrices for n>2 and give the explicit determinants and the inverse matrices. Furthermore, the upper bounds for the spread on Gaussian Fibonacci circulant and left circulant matrices are presented, respectively.
Bandwidth of Gaussian weighted Chirp
DEFF Research Database (Denmark)
Wilhjelm, Jens E.
1993-01-01
Four major time duration and bandwidth expressions are calculated for a linearly frequency modulated sinusoid with Gaussian shaped envelope. This includes a Gaussian tone pulse. The bandwidth is found to be a nonlinear function of nominal time duration and nominal frequency excursion of the chirp...
Spectral representation of Gaussian semimartingales
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas
2009-01-01
The aim of the present paper is to characterize the spectral representation of Gaussian semimartingales. That is, we provide necessary and sufficient conditions on the kernel K for X t =∫ K t (s) dN s to be a semimartingale. Here, N denotes an independently scattered Gaussian random measure...
Structural first failure times under non-Gaussian stochastic behavior
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
An analytical moment-based method for calculating structural first failure times under non-Gaussian stochastic behavior is proposed. In the method, a power series that constants can be obtained from response moments (skewness, kurtosis, etc.) is used firstly to map a non-Gaussian structural response into a standard Gaussian process, then mean up-crossing rates, mean clump size and the initial passage probability of a critical barrier level by the original structural response are estimated, and finally, the formula for calculating first failure times is established on the assumption that corrected up-crossing rates are independent. An analysis of a nonlinear single-degree-of-freedom dynamical system excited by a Gaussian model of load not only demonstrates the usage of the proposed method but also shows the accuracy and efficiency of the proposed method by comparisons between the present method and other methods such as Monte Carlo simulation and the traditional Gaussian model.
Shandarin, S F; Xu, Y; Tegmark, M; Shandarin, Sergei F.; Feldman, Hume A.; Xu, Yongzhong; Tegmark, Max
2001-01-01
We test degree-scale cosmic microwave background (CMB) anisotropy for Gaussianity by studying the \\qmask map that was obtained from combining the QMAP and Saskatoon data. We compute seven morphological functions $M_i(\\dt)$, $i=1,...,7$: six \\mf and the number of regions $N_c$ at a hundred $\\dt$ levels. We also introduce a new parameterization of the morphological functions $M_i(A)$ in terms of the total area $A$ of the excursion set. We show that the latter considerably decorrelates the morphological statistics. We compare these results with those from 1000 Gaussian Monte Carlo maps with the same power spectrum, and conclude that the \\qmask map is neither a very typical nor a very exceptional realization of a Gaussian field. Roughly 20% of the 1000 Gaussian Monte Carlo maps differ more than the \\qmask map from the mean morphological parameters of the Gaussian fields.
Nonlinear Approximation Using Gaussian Kernels
Hangelbroek, Thomas
2009-01-01
It is well-known that non-linear approximation has an advantage over linear schemes in the sense that it provides comparable approximation rates to those of the linear schemes, but to a larger class of approximands. This was established for spline approximations and for wavelet approximations, and more recently for homogeneous radial basis function (surface spline) approximations. However, no such results are known for the Gaussian function. The crux of the difficulty lies in the necessity to vary the tension parameter in the Gaussian function spatially according to local information about the approximand: error analysis of Gaussian approximation schemes with varying tension are, by and large, an elusive target for approximators. We introduce and analyze in this paper a new algorithm for approximating functions using translates of Gaussian functions with varying tension parameters. Our scheme is sophisticated to a degree that it employs even locally Gaussians with varying tensions, and that it resolves local ...
Normal form decomposition for Gaussian-to-Gaussian superoperators
Energy Technology Data Exchange (ETDEWEB)
De Palma, Giacomo [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa (Italy); INFN, Pisa (Italy); Mari, Andrea; Giovannetti, Vittorio [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa (Italy); Holevo, Alexander S. [Steklov Mathematical Institute, 119991 Moscow, Russia and National Research University Higher School of Economics (HSE), 101000 Moscow (Russian Federation)
2015-05-15
In this paper, we explore the set of linear maps sending the set of quantum Gaussian states into itself. These maps are in general not positive, a feature which can be exploited as a test to check whether a given quantum state belongs to the convex hull of Gaussian states (if one of the considered maps sends it into a non-positive operator, the above state is certified not to belong to the set). Generalizing a result known to be valid under the assumption of complete positivity, we provide a characterization of these Gaussian-to-Gaussian (not necessarily positive) superoperators in terms of their action on the characteristic function of the inputs. For the special case of one-mode mappings, we also show that any Gaussian-to-Gaussian superoperator can be expressed as a concatenation of a phase-space dilatation, followed by the action of a completely positive Gaussian channel, possibly composed with a transposition. While a similar decomposition is shown to fail in the multi-mode scenario, we prove that it still holds at least under the further hypothesis of homogeneous action on the covariance matrix.
Reza, Syed Azer; Qasim, Muhammad
2016-01-10
This paper presents a novel approach to simultaneously measuring the thickness and refractive index of a sample. The design uses an electronically controlled tunable lens (ECTL) and a microelectromechanical-system-based digital micromirror device (DMD). The method achieves the desired results by using the DMD to characterize the spatial profile of a Gaussian laser beam at different focal length settings of the ECTL. The ECTL achieves tunable lensing through minimal motion of liquid inside a transparent casing, whereas the DMD contains an array of movable micromirrors, which make it a reflective spatial light modulator. As the proposed system uses an ECTL, a DMD, and other fixed optical components, it measures the thickness and refractive index without requiring any motion of bulk components such as translational and rotational stages. A motion-free system improves measurement repeatability and reliability. Moreover, the measurement of sample thickness and refractive index can be completely automated because the ECTL and DMD are controlled through digital signals. We develop and discuss the theory in detail to explain the measurement methodology of the proposed system and present results from experiments performed to verify the working principle of the method. Refractive index measurement accuracies of 0.22% and 0.2% were achieved for two BK-7 glass samples used, and the thicknesses of the two samples were measured with a 0.1 mm accuracy for each sample, corresponding to a 0.39% and 0.78% measurement error, respectively, for the aforementioned samples.
Baura, Alendu; Sen, Monoj Kumar; Goswami, Gurupada; Bag, Bidhan Chandra
2011-01-28
In this paper we have calculated escape rate from a meta stable state in the presence of both colored internal thermal and external nonthermal noises. For the internal noise we have considered usual gaussian distribution but the external noise may be gaussian or non-gaussian in characteristic. The calculated rate is valid for low noise strength of non-gaussian noise such that an effective gaussian approximation of non-gaussian noise wherein the higher order even cumulants of order "4" and higher are neglected. The rate expression we derived here reduces to the known results of the literature, as well as for purely external noise driven activated rate process. The latter exhibits how the rate changes if one switches from non-gaussian to gaussian character of the external noise.
Power Spectrum of Generalized Fractional Gaussian Noise
Directory of Open Access Journals (Sweden)
Ming Li
2013-01-01
Full Text Available Recently, we introduced a type of autocorrelation function (ACF to describe a long-range dependent (LRD process indexed with two parameters, which takes standard fractional Gaussian noise (fGn for short as a special case. For simplicity, we call it the generalized fGn (GfGn. This short paper gives the power spectrum density function (PSD of GfGn.
Institute of Scientific and Technical Information of China (English)
李纪真; 孟相如; 温祥西; 康巧燕
2015-01-01
A prediction method based on the Gaussian process optimized by glowworm swarm optimization (GSO)is proposed to solve the problems of difficult determination of iteration steps and less accuracy of predic-tion which are caused by searching the hyperparameters of the Gaussian process with the conj ugate gradient al-gorithm.And it is applied to the research of network security situation prediction.The hyperparameters of the Gaussian process are intelligently searched by the GSO algorithm for establishing the network security situation prediction model based on Gaussian process regression.The analysis results of the experiment show that the av-erage relative prediction error of this new method is reduced by about 29.46%,10.37% and 4.22% compared with the conjugate gradient algorithm,the particle swarm optimization (PSO)algorithm and the artificial bee colony (ABC)algorithm separately,and the new method has a better convergence.In addition,the impact of the prediction results are analyzed and compared by three single type covariance functions and two composite type covariance functions,and the analysis results of the experiment show that the average relative prediction error with neural network and rational quadratic composite covariance function (NN-RQ)is reduced by 1 .6 5%to 7.51% compared with other four covariance functions.%针对共轭梯度法获取高斯过程超参数存在迭代次数难以确定及预测不精准等问题，提出一种萤火虫群算法优化高斯过程的预测方法，并将其应用于网络安全态势预测研究。采用萤火虫群优化算法对高斯过程超参数进行智能寻优，建立基于高斯过程回归的网络安全态势预测模型。实验结果表明新方法的平均相对预测误差较共轭梯度法、粒子群优化算法和人工蜂群优化算法分别降低了近29．46％、10．37％和4．22％，且新方法收敛较快。另外，分析对比了3种单一类型和2种复合类型的协方差函数对
Quantification of Gaussian quantum steering
Kogias, Ioannis; Ragy, Sammy; Adesso, Gerardo
2014-01-01
Einstein-Podolsky-Rosen steering incarnates a useful nonclassical correlation which sits in-between entanglement and Bell nonlocality. While a number of qualitative steering criteria exist, very little has been achieved for what concerns quantifying steerability. We introduce a computable measure of steering for arbitrary bipartite Gaussian states of continuous variable systems. For two-mode Gaussian states, the measure reduces to a form of coherent information, which is proven never to exceed entanglement, and to reduce to it on pure states. We provide an operational connection between our measure and the key rate in one-sided device-independent quantum key distribution. We further prove that steering bound entangled Gaussian states by Gaussian measurements is impossible.
Gaussian maximally multipartite entangled states
Facchi, Paolo; Lupo, Cosmo; Mancini, Stefano; Pascazio, Saverio
2009-01-01
We introduce the notion of maximally multipartite entangled states (MMES) in the context of Gaussian continuous variable quantum systems. These are bosonic multipartite states that are maximally entangled over all possible bipartitions of the system. By considering multimode Gaussian states with constrained energy, we show that perfect MMESs, which exhibit the maximum amount of bipartite entanglement for all bipartitions, only exist for systems containing n=2 or 3 modes. We further numerically investigate the structure of MMESs and their frustration for n <= 7.
Gaussian-mixture umbrella sampling
Maragakis, Paul; van der Vaart, Arjan; Karplus, Martin
2009-01-01
We introduce the Gaussian-mixture umbrella sampling method (GAMUS), a biased molecular dynamics technique based on adaptive umbrella sampling that efficiently escapes free energy minima in multi-dimensional problems. The prior simulation data are reweighted with a maximum likelihood formulation, and the new approximate probability density is fit to a Gaussian-mixture model, augmented by information about the unsampled areas. The method can be used to identify free energy minima in multi-dimen...
Edge Detection By Differences Of Gaussians
Marthon, Ph.; Thiesse, B.; Bruel, A.
1986-06-01
The Differences of Gaussians (DOGs) are of fundamental importance in edge detection. They belong to the human vision system as shown by Enroth-Cugell and Robson [ENR66]. The zero-crossings of their outputs mark the loci of the intensity changes. The set of descriptions from different operator sizes forms the input for later visual processes, such as stereopsis and motion analysis. We show that DOGs uniformly converge to the Laplacian of a Gaussian (ΔG2,σ) when both the inhibitory and excitatory variables converge to σ. Spatial and spectral properties of DOGs and ΔGs are compared: width and height of their central positive regions, bandiwidths... Finally, DOGs' responses to some features such as ideal edge, right angle corner, general corner..., are presented and magnitudes of error on edge position are given.
Multipole invariants and non-Gaussianity
Land, K; Land, Kate; Magueijo, Joao
2004-01-01
We propose a framework for separating the information contained in the CMB multipoles, $a_{\\ell m}$, into its algebraically independent components. Thus we cleanly separate information pertaining to the power spectrum, non-Gaussianity and preferred axis effects. The formalism builds upon the recently proposed multipole vectors (Copi, Huterer & Starkman 2003; Schwarz & al 2004; Katz & Weeks 2004), and we elucidate a few features regarding these vectors, namely their lack of statistical independence for a Gaussian random process. In a few cases we explicitly relate our proposed invariants to components of the $n$-point correlation function (power spectrum, bispectrum). We find the invariants' distributions using a mixture of analytical and numerical methods. We also evaluate them for the co-added WMAP first year map.
Distributed Kalman Filter via Gaussian Belief Propagation
Bickson, Danny; Dolev, Danny
2008-01-01
Recent result shows how to compute distributively and efficiently the linear MMSE for the multiuser detection problem, using the Gaussian BP algorithm. In the current work, we extend this construction, and show that operating this algorithm twice on the matching inputs, has several interesting interpretations. First, we show equivalence to computing one iteration of the Kalman filter. Second, we show that the Kalman filter is a special case of the Gaussian information bottleneck algorithm, when the weight parameter $\\beta = 1$. Third, we discuss the relation to the Affine-scaling interior-point method and show it is a special case of Kalman filter. Besides of the theoretical interest of this linking estimation, compression/clustering and optimization, we allow a single distributed implementation of those algorithms, which is a highly practical and important task in sensor and mobile ad-hoc networks. Application to numerous problem domains includes collaborative signal processing and distributed allocation of ...
Properties of Orthogonal Gaussian-Hermite Moments and Their Applications
Directory of Open Access Journals (Sweden)
Jun Shen
2005-03-01
Full Text Available Moments are widely used in pattern recognition, image processing, and computer vision and multiresolution analysis. In this paper, we first point out some properties of the orthogonal Gaussian-Hermite moments, and propose a new method to detect the moving objects by using the orthogonal Gaussian-Hermite moments. The experiment results are reported, which show the good performance of our method.
Space-time correlations of a Gaussian interface
Dunlop, Francois M
2010-01-01
The serial harness introduced by Hammersley is equivalent, in the Gaussian case, to the Gaussian Solid-On-Solid interface model with parallel heat bath dynamics. Here we consider sub-lattice parallel dynamics, and give exact results about relaxation dynamics, based on the equivalence to the infinite time limit of a time periodic random field. We also give a numerical comparison to the harness process in continuous time studied by Hsiao and by Ferrari, Niederhauser and Pechersky.
Gaussian semiparametric estimation of non-stationary time series
Velasco, Carlos
1998-01-01
Generalizing the definition of the memory parameter d in terms of the differentiated series, we showed in Velasco (Non-stationary log-periodogram regression, Forthcoming J. Economet., 1997) that it is possible to estimate consistently the memory of non-stationary processes using methods designed for stationary long-range-dependent time series. In this paper we consider the Gaussian semiparametric estimate analysed by Robinson (Gaussian semiparametric estimation of long range dependence. Ann. ...
Least-squares Gaussian beam migration
Yuan, Maolin; Huang, Jianping; Liao, Wenyuan; Jiang, Fuyou
2017-02-01
A theory of least-squares Gaussian beam migration (LSGBM) is presented to optimally estimate a subsurface reflectivity. In the iterative inversion scheme, a Gaussian beam (GB) propagator is used as the kernel of linearized forward modeling (demigration) and its adjoint (migration). Born approximation based GB demigration relies on the calculation of Green’s function by a Gaussian-beam summation for the downward and upward wavefields. The adjoint operator of GB demigration accounts for GB prestack depth migration under the cross-correlation imaging condition, where seismic traces are processed one by one for each shot. A numerical test on the point diffractors model suggests that GB demigration can successfully simulate primary scattered data, while migration (adjoint) can yield a corresponding image. The GB demigration/migration algorithms are used for the least-squares migration scheme to deblur conventional migrated images. The proposed LSGBM is illustrated with two synthetic data for a four-layer model and the Marmousi2 model. Numerical results show that LSGBM, compared to migration (adjoint) with GBs, produces images with more balanced amplitude, higher resolution and even fewer artifacts. Additionally, the LSGBM shows a robust convergence rate.
Multiscale Entropy under the Inverse Gaussian Distribution: Analytical Results
Institute of Scientific and Technical Information of China (English)
TANG Ying; PEI Wen-Jiang; XIA Hai-Shan; HE Zhen-Ya
2007-01-01
The multiscale entropy (MSE) reveals the intrinsic multiple scales in the complexity of physical and physiological signals, which are usually featured by heavy-tailed distributions. However, most research results are pure experimental search. Recently, Costa et al. have made the first attempt to present the theoretical basis of MSE, but it only supports the Gaussian distribution [Phys Rev. E 71 (2005) 021906]. We present the theoretical basis of MSE under the inverse Gaussian distribution, a typical model for physiological, physical and financial data sets. The analysis allows for uncorrelated inverse Gaussian process and 1/f noise with the multivariate inverse Gaussian distribution, and then provides a reliable foundation for the potential applications of MSE to explore complex physical and physical time series.
Imaginary time Gaussian dynamics of the Ar_3 cluster
Cartarius, Holger
2010-01-01
Semiclassical Gaussian approximations to the Boltzmann operator have become an important tool for the investigation of thermodynamic properties of clusters of atoms at low temperatures. Usually, numerically expensive thawed Gaussian variants are applied. In this article, we introduce a numerically much cheaper frozen Gaussian approximation to the imaginary time propagator with a width matrix especially suited for the dynamics of clusters. The quality of the results is comparable to that of thawed Gaussian methods based on the single-particle ansatz. We apply the method to the argon trimer and investigate the dissociation process of the cluster. The results clearly show a classical-like transition from a bounded moiety to three free particles at a temperature T ~ 20 K, whereas previous studies of the system were not able to resolve this transition. Quantum effects, i.e., differences with the purely classical case manifest themselves in the low-temperature behavior of the mean energy and specific heat as well a...
Gaussian mixture models as flux prediction method for central receivers
Grobler, Annemarie; Gauché, Paul; Smit, Willie
2016-05-01
Flux prediction methods are crucial to the design and operation of central receiver systems. Current methods such as the circular and elliptical (bivariate) Gaussian prediction methods are often used in field layout design and aiming strategies. For experimental or small central receiver systems, the flux profile of a single heliostat often deviates significantly from the circular and elliptical Gaussian models. Therefore a novel method of flux prediction was developed by incorporating the fitting of Gaussian mixture models onto flux profiles produced by flux measurement or ray tracing. A method was also developed to predict the Gaussian mixture model parameters of a single heliostat for a given time using image processing. Recording the predicted parameters in a database ensures that more accurate predictions are made in a shorter time frame.
Some error bounds for K-iterated Gaussian recursive filters
Cuomo, Salvatore; Galletti, Ardelio; Giunta, Giulio; Marcellino, Livia
2016-10-01
Recursive filters (RFs) have achieved a central role in several research fields over the last few years. For example, they are used in image processing, in data assimilation and in electrocardiogram denoising. More in particular, among RFs, the Gaussian RFs are an efficient computational tool for approximating Gaussian-based convolutions and are suitable for digital image processing and applications of the scale-space theory. As is a common knowledge, the Gaussian RFs, applied to signals with support in a finite domain, generate distortions and artifacts, mostly localized at the boundaries. Heuristic and theoretical improvements have been proposed in literature to deal with this issue (namely boundary conditions). They include the case in which a Gaussian RF is applied more than once, i.e. the so called K-iterated Gaussian RFs. In this paper, starting from a summary of the comprehensive mathematical background, we consider the case of the K-iterated first-order Gaussian RF and provide the study of its numerical stability and some component-wise theoretical error bounds.
Gaussian Entanglement Distribution via Satellite
Hosseinidehaj, Nedasadat
2014-01-01
In this work we analyse three quantum communication schemes for the generation of Gaussian entanglement between two ground stations. Communication occurs via a satellite over two independent atmospheric fading channels dominated by turbulence-induced beam wander. In our first scheme the engineering complexity remains largely on the ground transceivers, with the satellite acting simply as a reflector. Although the channel state information of the two atmospheric channels remains unknown in this scheme, the Gaussian entanglement generation between the ground stations can still be determined. On the ground, distillation and Gaussification procedures can be applied, leading to a refined Gaussian entanglement generation rate between the ground stations. We compare the rates produced by this first scheme with two competing schemes in which quantum complexity is added to the satellite, thereby illustrating the trade-off between space-based engineering complexity and the rate of ground-station entanglement generation...
Equi-Gaussian Curvature Folding
Indian Academy of Sciences (India)
E M El-Kholy; El-Said R Lashin; Salama N Daoud
2007-08-01
In this paper we introduce a new type of folding called equi-Gaussian curvature folding of connected Riemannian 2-manifolds. We prove that the composition and the cartesian product of such foldings is again an equi-Gaussian curvature folding. In case of equi-Gaussian curvature foldings, $f:M→ P_n$, of an orientable surface onto a polygon $P_n$ we prove that (i) $f\\in\\mathcal{F}_{EG}(S^2)\\Leftrightarrow n=3$ (ii) $f\\in\\mathcal{F}_{EG}(T^2)\\Rightarrow n=4$ (iii) $f\\in\\mathcal{F}_{EG}(\\# 2T^2)\\Rightarrow n=5, 6$ and we generalize (iii) for $\\# nT^2$.
National Research Council Canada - National Science Library
黒田, 義弘; 藤原, 靖弘; 斉藤, 雅子; 新宮, 徹朗
1988-01-01
Advantages and disadvantages of a Lorentzian to Gaussian trans formation function, which has been commonly employed in enhancing the resolution of two-timensional nuclear magnetic resonance (2D NMR...
On Minimax Robust Detection of Stationary Gaussian Signals in White Gaussian Noise
Zhang, Wenyi
2010-01-01
The problem of detecting a wide-sense stationary Gaussian signal process embedded in white Gaussian noise, where the power spectral density of the signal process exhibits uncertainty, is investigated. The performance of minimax robust detection is characterized by the exponential decay rate of the miss probability under a Neyman-Pearson criterion with a fixed false alarm probability, as the length of the observation interval grows without bound. A dominance condition is identified for the uncertainty set of spectral density functions, and it is established that, under the dominance condition, the resulting minimax problem possesses a saddle point, which is achievable by the likelihood ratio tests matched to a so-called dominated power spectral density in the uncertainty set. No convexity condition on the uncertainty set is required to establish this result.
Ballistic diffusion induced by non-Gaussian noise
Institute of Scientific and Technical Information of China (English)
Qin Li; Li Qiang
2013-01-01
In this letter,we have analyzed the diffusive behavior of a Brownian particle subject to both internal Gaussian thermal and external non-Gaussian noise sources.We discuss two time correlation functions C(t) of the non-Gaussian stochastic process,and find that they depend on the parameter q,indicating the departure of the non-Gaussian noise from Gaussian behavior:for q ≤ 1,C(t) is fitted very well by the first-order exponentially decaying curve and approaches zero in the longtime limit,whereas for q ＞ 1,C(t) can be approximated by a second-order exponentially decaying function and converges to a non-zero constant.Due to the properties of C(t),the particle exhibits a normal diffusion for q ≤ 1,while for q ＞ 1 the non-Gaussian noise induces a ballistic diffusion,i.e.,the long-time mean square displacement of the free particle reads ]2) ∝ t2.
Gaussian Analytic Centroiding method of star image of star tracker
Wang, Haiyong; Xu, Ershuai; Li, Zhifeng; Li, Jingjin; Qin, Tianmu
2015-11-01
The energy distribution of an actual star image coincides with the Gaussian law statistically in most cases, so the optimized processing algorithm about star image centroiding should be constructed also by following Gaussian law. For a star image spot covering a certain number of pixels, the marginal distribution of the gray accumulation on rows and columns are shown and analyzed, based on which the formulas of Gaussian Analytic Centroiding method (GAC) are deduced, and the robustness is also promoted due to the inherited filtering effect of gray accumulation. Ideal reference star images are simulated by the PSF (point spread function) with integral form. Precision and speed tests for the Gaussian Analytic formulas are conducted under three scenarios of Gaussian radius (0.5, 0.671, 0.8 pixel), The simulation results show that the precision of GAC method is better than that of the other given algorithms when the Gaussian radius is not bigger than 5 × 5 pixel window, a widely used parameter. Above all, the algorithm which consumes the least time is still the novel GAC method. GAC method helps to promote the comprehensive performance in the attitude determination of a star tracker.
Scaled unscented transform Gaussian sum filter: theory and application
Luo, Xiaodong; Hoteit, Ibrahim
2010-01-01
In this work we consider the state estimation problem in nonlinear/non-Gaussian systems. We introduce a framework, called the scaled unscented transform Gaussian sum filter (SUT-GSF), which combines two ideas: the scaled unscented Kalman filter (SUKF) based on the concept of scaled unscented transform (SUT), and the Gaussian mixture model (GMM). The SUT is used to approximate the mean and covariance of a Gaussian random variable which is transformed by a nonlinear function, while the GMM is adopted to approximate the probability density function (pdf) of a random variable through a set of Gaussian distributions. With these two tools, a framework can be set up to assimilate nonlinear systems in a recursive way. Within this framework, one can treat a nonlinear stochastic system as a mixture model of a set of sub-systems, each of which takes the form of a nonlinear system driven by a known Gaussian random process. Then, for each sub-system, one applies the SUKF to estimate the mean and covariance of the underlyi...
Betti Numbers of Gaussian Fields
Park, Changbom; Pranav, Pratyush; Chingangbam, Pravabati; van de Weygaert, Rien; Jones, Bernard; Vegter, Gert; Kim, Inkang; Hidding, Johan; Hellwing, Wojciech A.
2013-01-01
We present the relation between the genus in cosmology and the Betti numbers for excursion sets of three- and two-dimensional smooth Gaussian random fields, and numerically investigate the Betti numbers as a function of threshold level. Betti numbers are topological invariants of figures that can be
The Multivariate Gaussian Probability Distribution
DEFF Research Database (Denmark)
Ahrendt, Peter
2005-01-01
This technical report intends to gather information about the multivariate gaussian distribution, that was previously not (at least to my knowledge) to be found in one place and written as a reference manual. Additionally, some useful tips and tricks are collected that may be useful in practical...
Institute of Scientific and Technical Information of China (English)
徐琛; 尹燕燕; 刘飞
2016-01-01
Based on Gaussian Process (GP),a wavelength selection algorithm named Synergy Interval Gaussian Process (siGP) model is proposed in this paper by using near infrared spectroscopy technology.Full spectrum is divided into a series of unique and equal spacing intervals,before selecting optimal several intervals to establish GP model.Due to the GP model with nonlinear processing ability,the method reduces the disadvantages of nonlinear factor.Taking the near infrared spectrum data of moisture content and pH in solid-state fermentation of monascus as performance verification object of this new algorithm,the prediction correlation coefficient (R p )of moisture content and pH are 0.956 4 and 0.977 3,respectively.The root mean square errors for prediction set (RMSEP)are 0.012 7 and 0.1 61 0,respectively.Data points participating in modeling decrease respectively from the original 1 500 to 225 and 375.In the prediction for independent samples,it shows good accuracy.Comparing with traditional synergy interval partial least squares (siPLS)algorithm,the results show that the siGP achieves the best prediction result.The prediction correlation coefficient of moisture content and pH in new algorithm has increased respectively by 3.37% and 3.5 1%under the model of Gaussian Process,with increases of 29.4% and 34.8% in the root mean square errors for prediction set. This study shows that the combination of siGP and GP model can select wavelength effectively and improves the prediction accu-racy of the NIR model.This method is reference for realizing the online detection and optimization control.%针对近红外光谱应用,提出了一种基于高斯过程(GP)模型的波长选择算法,即联合区间高斯过程(synergy interval gaussian process,siGP)算法。首先将全光谱区域划分为一系列无重复且间距相等的区间,再选取最优的若干个区间联合建立 GP 模型,由于 GP 模型具有非线性处理能力,因此该方法可以减少非线性的影响。
Institute of Scientific and Technical Information of China (English)
陈勇; 杨雪; 刘焕淋; 杨凯; 张玉兰
2016-01-01
detecting algorithm is the key technology of the system demodu-lation.The current peak detecting algorithms has a precondition for peak detection on FBG reflective spectrum,that the FBG reflective spectrum was a standard Gaussian model.But FBG reflective spectrum is not a standard Gaussian spectrum owing to the practical manufacture process and the individual environment;actually,it is an asymmetrical Gaussian spectrum.The experi-ment would achieve a lower accuracy because of this asymmetric property during peak-seeking.Based on the defect of the exist-ing algorithm,an Exponent Modified Gaussian (EMG)Curve Fitting peak detecting algorithm is proposed in this paper.In the proposed algorithm,the coarse location was first determined by three times j udgments and it can remove the false peak and peak invalid at the same time.Based on this,as the center of the coarse localization point to reconstruct the spectrum,and using the integral to j udge the peak bias;then according to different peak bias,it revised the peak by the prepared exponential modified function.Simulation results show that at normal temperature or under variable temperature conditions,by comparing with direct peak searching algorithm,Gaussian fitting algorithm and the algorithm proposed by literature,the error of EMG peak detection algorithm is the minimum and high peak detecting precision.The algorithm proposed in this paper considers the FBG reflection spectrum characteristic of asymmetric effect.From its spectrum character,the EMG algorithm solves the problem of the limits of traditional peak detecting algorithm,meanwhile also guarantees a high-precision peak search results.
Selvendran, S.; Sivanantharaja, A.; Arivazhagan, S.; Kannan, M.
2016-09-01
We propose an index profiled, highly nonlinear ultraflattened dispersion fibre (HN-UFF) with appreciable values of fibre parameters such as dispersion, dispersion slope, effective area, nonlinearity, bending loss and splice loss. The designed fibre has normal zero flattened dispersion over S, C, L, U bands and extends up to 1.9857 μm. The maximum dispersion variation observed for this fibre is as low as 1.61 ps km-1 nm-1 over the 500-nm optical fibre transmission spectrum. This fibre also has two zero dispersion wavelengths at 1.487 and 1.9857 μm and the respective dispersion slopes are 0.02476 and 0.0068 ps nm-2 km-1. The fibre has a very low ITU-T cutoff wavelength of 1.2613 μm and a virtuous nonlinear coefficient of 9.43 W-1 km-1. The wide spectrum of zero flattened dispersion and a good nonlinear coefficient make the designed fibre very promising for different nonlinear optical signal processing applications.
Laguerre Gaussian beam multiplexing through turbulence
CSIR Research Space (South Africa)
Trichili, A
2014-08-17
Full Text Available We analyze the effect of atmospheric turbulence on the propagation of multiplexed Laguerre Gaussian modes. We present a method to multiplex Laguerre Gaussian modes using digital holograms and decompose the resulting field after encountering a...
Analytic matrix elements with shifted correlated Gaussians
DEFF Research Database (Denmark)
Fedorov, D. V.
2017-01-01
Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are calculated analytically. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics.......Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are calculated analytically. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics....
Stable Lévy motion with inverse Gaussian subordinator
Kumar, A.; Wyłomańska, A.; Gajda, J.
2017-09-01
In this paper we study the stable Lévy motion subordinated by the so-called inverse Gaussian process. This process extends the well known normal inverse Gaussian (NIG) process introduced by Barndorff-Nielsen, which arises by subordinating ordinary Brownian motion (with drift) with inverse Gaussian process. The NIG process found many interesting applications, especially in financial data description. We discuss here the main features of the introduced subordinated process, such as distributional properties, existence of fractional order moments and asymptotic tail behavior. We show the connection of the process with continuous time random walk. Further, the governing fractional partial differential equations for the probability density function is also obtained. Moreover, we discuss the asymptotic distribution of sample mean square displacement, the main tool in detection of anomalous diffusion phenomena (Metzler et al., 2014). In order to apply the stable Lévy motion time-changed by inverse Gaussian subordinator we propose a step-by-step procedure of parameters estimation. At the end, we show how the examined process can be useful to model financial time series.
Optical trapping with Super-Gaussian beams
CSIR Research Space (South Africa)
McLaren, M
2013-04-01
Full Text Available We outline the possibility of optical trapping and tweezing with Super-Gaussian beam profiles. We show that the trapping strength can be tuned continuously by adjusting the order of a Super-Gaussian beam, approaching that of a perfect Gaussian...
Minimum output entropy of Gaussian channels
Lloyd, S; Maccone, L; Pirandola, S; Garcia-Patron, R
2009-01-01
We show that the minimum output entropy for all single-mode Gaussian channels is additive and is attained for Gaussian inputs. This allows the derivation of the channel capacity for a number of Gaussian channels, including that of the channel with linear loss, thermal noise, and linear amplification.
Performing edge detection by Difference of Gaussians using q-Gaussian kernels
Assirati, Lucas; Berton, Lilian; Lopes, Alneu de A; Bruno, Odemir M
2013-01-01
In image processing, edge detection is a valuable tool to perform the extraction of features from an image. This detection reduces the amount of information to be processed, since the redundant information (considered less relevant) can be unconsidered. The technique of edge detection consists of determining the points of a digital image whose intensity changes sharply. This changes are due to the discontinuities of the orientation on a surface for example. A well known method of edge detection is the Difference of Gaussians (DoG). The method consists of subtracting two Gaussians, where a kernel has a standard deviation smaller than the previous one. The convolution between the subtraction of kernels and the input image results in the edge detection of this image. This paper introduces a method of extracting edges using DoG with kernels based on the q-Gaussian probability distribution, derived from the q-statistic proposed by Constantino Tsallis. To demonstrate the method's potential, we compare the introduce...
Institute of Scientific and Technical Information of China (English)
姚伏天; 钱沄涛
2009-01-01
高光谱遥感图像分类是遥感图像处理的一项重要内容.高光谱遥感图像具有非线性属性.图像中不同方位光谱特征的变化将使得仅从标记训练样本得到的分类器分类精度不会太高.为了提高分类的精度,一方面应对光谱信息的合理利用;另一方面,对空间信息的利用也非常重要.高斯过程(Gaussion process,GP)是一种贝叶斯统计学习方法,能够建立概率模型,并且使得分类结果更易于解释.传统GP分类方法中核函数的构造仅利用光谱信息.本文提出了一种加入空间关系的新分类方法.利用遥感图像空间相关性,在GP分类方法中通过构造新的核函数(spatial Gauss kernel,SGK)来实现空间约束,部分消除了同物异谱和同谱异物造成的分类错误.实验结果表明,该方法对于提高高光谱遥感图像的分类精度具有积极意义.%Classification of hyperspectral remote sensing imagery is an important issue of remote sensing images processing. Hyperspectral remote sensing images have nonlinear property. A classifier derived from labeled samples may not perform well for a specific sub-region if the spectral signatures of classes vary across the image. In order to improve accuracy of classification, not only spectral information of images should be utilized, but spatial information is necessary for classification as well. Gaussian process (GP) is a Bayesian statistics learning method. GP bears a full Bayesian formulation, thus enable explicitly probabilistic modeling and makes results easily interpretable. Usually, only spectral information is used for kernel construction in the traditional GP. In this paper, we explore the effectiveness of the Bayesian Gaussian process approach for classifying Hyperspectral remote sensing images. Furthermore, a new GP based classification method is proposed in which spatial information is considered. The method is a Bayesian kernel-based nonlinear method, so it is suitable for
Information geometry of Gaussian channels
Monras, Alex
2009-01-01
We define a local Riemannian metric tensor in the manifold of Gaussian channels and the distance that it induces. We adopt an information-geometric approach and define a metric derived from the Bures-Fisher metric for quantum states. The resulting metric inherits several desirable properties from the Bures-Fisher metric and is operationally motivated from distinguishability considerations: It serves as an upper bound to the attainable quantum Fisher information for the channel parameters using Gaussian states, under some restriction on the available resources. We prove that optimal states are always pure and bounded in the number of ancillary modes that are needed. This has experimental and computational advantages: It limits the complexity of optimal experimental setups for channel estimation and reduces the computational requirements for the evaluation of the metric. Indeed, we construct a converging algorithm for computing the metric. We provide explicit formulae for computing the multiparametric quantum F...
Event Seismic Classification using Gaussian Processes
Alvarez López, Mauricio Alexander; Henao, Ricardo; Duque Cardona, Edison
2007-01-01
La clasificación de señales sísmicas es de crucial importancia para el descubrimiento de posibles interacciones entre movimientos telúricos volcánicos y procesos volcánicos per se. En este artículo, se presenta la aplicación de procesos gaussianos para la clasificación de eventos sísmicos registrados en el volcán Nevado del Ruíz. Las señales se caracterizan usando los coeficientes de un modelo autoregresivo, empleado para estimar la densidad espectral de potencia. La función de distribución p...
Making Predictions using Large Scale Gaussian Processes
National Aeronautics and Space Administration — One of the key problems that arises in many areas is to estimate a potentially nonlinear function [tex] G(x, theta)[/tex] given input and output samples tex [/tex]...
Non-Gaussian Stochastic Gravity
Bates, Jason D.
2013-01-01
This paper presents a new, non-Gaussian formulation of stochastic gravity by incorporating the higher moments of the fluctuations of the quantum stress energy tensor for a free quantum scalar field in a consistent way. A scheme is developed for obtaining realizations of these fluctuations in terms of the Wightman function, and the behavior of the fluctuations is investigated. The resulting probability distribution for fluctuations of the energy density in Minkowski spacetime is found to be si...
Scaled unscented transform Gaussian sum filter: Theory and application
Luo, Xiaodong
2010-05-01
In this work we consider the state estimation problem in nonlinear/non-Gaussian systems. We introduce a framework, called the scaled unscented transform Gaussian sum filter (SUT-GSF), which combines two ideas: the scaled unscented Kalman filter (SUKF) based on the concept of scaled unscented transform (SUT) (Julier and Uhlmann (2004) [16]), and the Gaussian mixture model (GMM). The SUT is used to approximate the mean and covariance of a Gaussian random variable which is transformed by a nonlinear function, while the GMM is adopted to approximate the probability density function (pdf) of a random variable through a set of Gaussian distributions. With these two tools, a framework can be set up to assimilate nonlinear systems in a recursive way. Within this framework, one can treat a nonlinear stochastic system as a mixture model of a set of sub-systems, each of which takes the form of a nonlinear system driven by a known Gaussian random process. Then, for each sub-system, one applies the SUKF to estimate the mean and covariance of the underlying Gaussian random variable transformed by the nonlinear governing equations of the sub-system. Incorporating the estimations of the sub-systems into the GMM gives an explicit (approximate) form of the pdf, which can be regarded as a "complete" solution to the state estimation problem, as all of the statistical information of interest can be obtained from the explicit form of the pdf (Arulampalam et al. (2002) [7]). In applications, a potential problem of a Gaussian sum filter is that the number of Gaussian distributions may increase very rapidly. To this end, we also propose an auxiliary algorithm to conduct pdf re-approximation so that the number of Gaussian distributions can be reduced. With the auxiliary algorithm, in principle the SUT-GSF can achieve almost the same computational speed as the SUKF if the SUT-GSF is implemented in parallel. As an example, we will use the SUT-GSF to assimilate a 40-dimensional system due to
Image reconstruction under non-Gaussian noise
DEFF Research Database (Denmark)
Sciacchitano, Federica
During acquisition and transmission, images are often blurred and corrupted by noise. One of the fundamental tasks of image processing is to reconstruct the clean image from a degraded version. The process of recovering the original image from the data is an example of inverse problem. Due......D thesis intends to solve some of the many open questions for image restoration under non-Gaussian noise. The two main kinds of noise studied in this PhD project are the impulse noise and the Cauchy noise. Impulse noise is due to for instance the malfunctioning pixel elements in the camera sensors, errors...... that the CM estimate outperforms the MAP estimate, when the error depends on Bregman distances. This PhD project can have many applications in the modern society, in fact the reconstruction of high quality images with less noise and more details enhances the image processing operations, such as edge detection...
Gaussian Functions, Γ-Functions and Wavelets
Institute of Scientific and Technical Information of China (English)
蔡涛; 许天周
2003-01-01
The relations between Gaussian function and Γ-function is revealed first at one-dimensional situation. Then, the Fourier transformation of n-dimensional Gaussian function is deduced by a lemma. Following the train of thought in one-dimensional situation, the relation between n-dimensional Gaussian function and Γ-function is given. By these, the possibility of arbitrary derivative of an n-dimensional Gaussian function being a mother wavelet is indicated. The result will take some enlightening role in exploring the internal relations between Gaussian function and Γ-function as well as in finding high-dimensional mother wavelets.
One-mode quantum-limited Gaussian channels have Gaussian maximizers
2016-01-01
We prove that Gaussian states saturate the p->q norms of the one-mode quantum-limited attenuator and amplifier. The proof starts from the majorization result of De Palma et al., IEEE Trans. Inf. Theory 62, 2895 (2016), and is based on a new logarithmic Sobolev inequality. Our result extends to noncommutative probability the seminal theorem "Gaussian kernels have only Gaussian maximizers" (Lieb, Invent. Math. 102, 179 (1990)), stating that Gaussian operators saturate the p->q norms of Gaussian...
A new statistic for picking out Non-Gaussianity in the CMB
Lewin, A; Magueijo, J; Lewin, Alex; Albrecht, Andreas; Magueijo, Joao
1999-01-01
In this paper we propose a new statistic capable of detecting non-Gaussianity in the CMB. The statistic is defined in Fourier space, and therefore naturally separates angular scales. It consists of taking another Fourier transform, in angle, over the Fourier modes within a given ring of scales. Like other Fourier space statistics, our statistic outdoes more conventional methods when faced with combinations of Gaussian processes (be they noise or signal) and a non-Gaussian signal which dominates only on some scales. However, unlike previous efforts along these lines, our statistic is successful in recognizing multiple non-Gaussian patterns in a single field. We discuss various applications, in which the Gaussian component may be noise or primordial signal, and the non-Gaussian component may be a cosmic string map, or some geometrical construction mimicking, say, small scale dust maps.
Analytic model of the effect of poly-Gaussian roughness on rarefied gas flow near the surface
Aksenova, Olga A.; Khalidov, Iskander A.
2016-11-01
The dependence of the macro-parameters of the flow on surface roughness of the walls and on geometrical shape of the surface is investigated asymptotically and numerically in a rarefied gas molecular flow at high Knudsen numbers. Surface roughness is approximated in statistical simulation by the model of poly-Gaussian (with probability density as the mixture of Gaussian densities [1]) random process. Substantial difference is detected for considered models of the roughness (Gaussian, poly-Gaussian and simple models applied by other researchers), as well in asymptotical expressions [3], as in numerical results. For instance, the influence of surface roughness on momentum and energy exchange coefficients increases noticeably for poly-Gaussian model compared to Gaussian one (although the main properties of poly-Gaussian random processes and fields are similar to corresponding properties of Gaussian processes and fields). Main advantage of the model is based on relative simple relations between the parameters of the model and the basic statistical characteristics of random field. Considered statistical approach permits to apply not only diffuse-specular model of the local scattering function V0 of reflected gas atoms, but also Cercignani-Lampis scattering kernel or phenomenological models of scattering function. Thus, the comparison between poly-Gaussian and Gaussian models shows more significant effect of roughness in aerodynamic values for poly-Gaussian model.
Permutation entropy of fractional Brownian motion and fractional Gaussian noise
Energy Technology Data Exchange (ETDEWEB)
Zunino, L. [Centro de Investigaciones Opticas, C.C. 124 Correo Central, 1900 La Plata (Argentina); Departamento de Ciencias Basicas, Facultad de Ingenieria, Universidad Nacional de La Plata (UNLP), 1900 La Plata (Argentina); Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, 1900 La Plata (Argentina)], E-mail: lucianoz@ciop.unlp.edu.ar; Perez, D.G. [Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso (PUCV), 23-40025 Valparaiso (Chile)], E-mail: dario.perez@ucv.cl; Martin, M.T. [Instituto de Fisica (IFLP), Facultad de Ciencias Exactas, Universidad Nacional de La Plata and Argentina' s National Council (CCT-CONICET), C.C. 727, 1900 La Plata (Argentina)], E-mail: mtmartin@fisica.unlp.edu.ar; Garavaglia, M. [Centro de Investigaciones Opticas, C.C. 124 Correo Central, 1900 La Plata (Argentina); Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, 1900 La Plata (Argentina)], E-mail: garavagliam@ciop.unlp.edu.ar; Plastino, A. [Instituto de Fisica (IFLP), Facultad de Ciencias Exactas, Universidad Nacional de La Plata and Argentina' s National Council (CCT-CONICET), C.C. 727, 1900 La Plata (Argentina)], E-mail: plastino@fisica.unlp.edu.ar; Rosso, O.A. [Centre for Bioinformatics, Biomarker Discovery and Information-Based Medicine, School of Electrical Engineering and Computer Science, The University of Newcastle, University Drive, Callaghan NSW 2308 (Australia); Chaos and Biology Group, Instituto de Calculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellon II, Ciudad Universitaria, 1428 Ciudad de Buenos Aires (Argentina)], E-mail: oarosso@fibertel.com.ar
2008-06-30
We have worked out theoretical curves for the permutation entropy of the fractional Brownian motion and fractional Gaussian noise by using the Bandt and Shiha [C. Bandt, F. Shiha, J. Time Ser. Anal. 28 (2007) 646] theoretical predictions for their corresponding relative frequencies. Comparisons with numerical simulations show an excellent agreement. Furthermore, the entropy-gap in the transition between these processes, observed previously via numerical results, has been here theoretically validated. Also, we have analyzed the behaviour of the permutation entropy of the fractional Gaussian noise for different time delays.
Improved Gaussian Mixture Models for Adaptive Foreground Segmentation
DEFF Research Database (Denmark)
Katsarakis, Nikolaos; Pnevmatikakis, Aristodemos; Tan, Zheng-Hua
2016-01-01
Adaptive foreground segmentation is traditionally performed using Stauffer & Grimson’s algorithm that models every pixel of the frame by a mixture of Gaussian distributions with continuously adapted parameters. In this paper we provide an enhancement of the algorithm by adding two important dynamic...... elements to the baseline algorithm: The learning rate can change across space and time, while the Gaussian distributions can be merged together if they become similar due to their adaptation process. We quantify the importance of our enhancements and the effect of parameter tuning using an annotated...
Gaussian entanglement generation from coherence using beam-splitters
Wang, Zhong-Xiao; Wang, Shuhao; Ma, Teng; Wang, Tie-Jun; Wang, Chuan
2016-01-01
The generation and quantification of quantum entanglement is crucial for quantum information processing. Here we study the transition of Gaussian correlation under the effect of linear optical beam-splitters. We find the single-mode Gaussian coherence acts as the resource in generating Gaussian entanglement for two squeezed states as the input states. With the help of consecutive beam-splitters, single-mode coherence and quantum entanglement can be converted to each other. Our results reveal that by using finite number of beam-splitters, it is possible to extract all the entanglement from the single-mode coherence even if the entanglement is wiped out before each beam-splitter. PMID:27892537
Generation of correlated finite alphabet waveforms using gaussian random variables
Ahmed, Sajid
2016-01-13
Various examples of methods and systems are provided for generation of correlated finite alphabet waveforms using Gaussian random variables in, e.g., radar and communication applications. In one example, a method includes mapping an input signal comprising Gaussian random variables (RVs) onto finite-alphabet non-constant-envelope (FANCE) symbols using a predetermined mapping function, and transmitting FANCE waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern. The FANCE waveforms can be based upon the mapping of the Gaussian RVs onto the FANCE symbols. In another example, a system includes a memory unit that can store a plurality of digital bit streams corresponding to FANCE symbols and a front end unit that can transmit FANCE waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern. The system can include a processing unit that can encode the input signal and/or determine the mapping function.
Identification of the distribution parameters of additive and multiplicative non-Gaussian noise
Artyushenko, V. M.; Volovach, V. I.
2017-05-01
This paper considers issues related to the identification of the parameters and form of the probability density function of generally non-Gaussian additive and multiplicative noise affecting the signal. The results of numerical simulation of methods for estimating the information parameters of random processes with a non-Gaussian probability density function for a finite sample.
Gaussian free fields for mathematicians
Sheffield, Scott
2003-01-01
The d-dimensional Gaussian free field (GFF), also called the (Euclidean bosonic) massless free field, is a d-dimensional-time analog of Brownian motion. Just as Brownian motion is the limit of the simple random walk (when time and space are appropriately scaled), the GFF is the limit of many incrementally varying random functions on d-dimensional grids. We present an overview of the GFF and some of the properties that are useful in light of recent connections between the GFF and the Schramm-L...
Bipartite and Multipartite Entanglement of Gaussian States
Adesso, G; Adesso, Gerardo; Illuminati, Fabrizio
2005-01-01
In this chapter we review the characterization of entanglement in Gaussian states of continuous variable systems. For two-mode Gaussian states, we discuss how their bipartite entanglement can be accurately quantified in terms of the global and local amounts of mixedness, and efficiently estimated by direct measurements of the associated purities. For multimode Gaussian states endowed with local symmetry with respect to a given bipartition, we show how the multimode block entanglement can be completely and reversibly localized onto a single pair of modes by local, unitary operations. We then analyze the distribution of entanglement among multiple parties in multimode Gaussian states. We introduce the continuous-variable tangle to quantify entanglement sharing in Gaussian states and we prove that it satisfies the Coffman-Kundu-Wootters monogamy inequality. Nevertheless, we show that pure, symmetric three-mode Gaussian states, at variance with their discrete-variable counterparts, allow a promiscuous sharing of ...
Monogamy inequality for distributed gaussian entanglement.
Hiroshima, Tohya; Adesso, Gerardo; Illuminati, Fabrizio
2007-02-02
We show that for all n-mode Gaussian states of continuous variable systems, the entanglement shared among n parties exhibits the fundamental monogamy property. The monogamy inequality is proven by introducing the Gaussian tangle, an entanglement monotone under Gaussian local operations and classical communication, which is defined in terms of the squared negativity in complete analogy with the case of n-qubit systems. Our results elucidate the structure of quantum correlations in many-body harmonic lattice systems.
D'Amico, Guido
2014-01-01
We analyze primordial non-Gaussianity in single field inflationary models when the tensor/scalar ratio is large, $r \\sim 0.2$. Our results show that detectable levels of non-Gaussianity $f_{NL} \\sim 50$ are still possible in the simplest class of models described by the effective theory of inflation. However, the \\emph{shape} is very tightly constrained, making a sharp prediction that could be confirmed or falsified by a future detection of non-Gaussianity.
Strongly Scale-dependent Non-Gaussianity
Riotto, Antonio
2011-01-01
We discuss models of primordial density perturbations where the non-Gaussianity is strongly scale-dependent. In particular, the non-Gaussianity may have a sharp cut-off and be very suppressed on large cosmological scales, but sizeable on small scales. This may have an impact on probes of non-Gaussianity in the large-scale structure and in the cosmic microwave background radiation anisotropies.
Gaussian Networks Generated by Random Walks
Javarone, Marco Alberto
2014-01-01
We propose a random walks based model to generate complex networks. Many authors studied and developed different methods and tools to analyze complex networks by random walk processes. Just to cite a few, random walks have been adopted to perform community detection, exploration tasks and to study temporal networks. Moreover, they have been used also to generate scale-free networks. In this work, we define a random walker that plays the role of "edges-generator". In particular, the random walker generates new connections and uses these ones to visit each node of a network. As result, the proposed model allows to achieve networks provided with a Gaussian degree distribution, and moreover, some features as the clustering coefficient and the assortativity show a critical behavior. Finally, we performed numerical simulations to study the behavior and the properties of the cited model.
Institute of Scientific and Technical Information of China (English)
曹鸿钧; 朱玉强; 张功
2012-01-01
Bayesian reliability method is one of the efficient approaches tor rehabfllty analysis ior struc tures with incomplete probability information. The computational cost of the Bayesian reliability estima tion is often prohibitive for real applications. It is necessary to use surrogate models to replace actual models in order to reduce the computational burden. Commonly used surrogate modeling approaches, which construct approximation models for response functions rather than limit state surfaces, are indirect and not easy to take model uncertainties into account. Furthermore, these methods are difficult to be used for problems exhibiting discontinuous responses and disjoint failure domains. In order to handle these dif ficulties,this paper presents a method to identify the limit state surface by using Gaussian process classi fication. The variances of distribution parameters of failure probability due to the model uncertainty are derived. An adaptive sampling criterion for updating the surrogate model is proposed. An example is presented to demonstrate the efficiency and effectiveness of the proposed method.%贝叶斯可靠性方法是处理不完备信息条件下结构可靠性问题的有效途径之一。在实际应用中，由于可靠性分析的计算量较大，常须采用各种近似替代模型以提高计算效率。传统的替代模型方法是对结构的功能函数予以近似建模。这种方法不易定量考虑模型误差对可靠性分析的影响，且难以应用于诸如功能函数不连续和失效域不连通等情况。为此，本文提出一种基于高斯过程分类的替代模型，直接辨识结构的极限状态曲面，并将其应用于结构贝叶斯可靠性分析之中。分析了替代模型不确定性对可靠性预测结果的影响，给出了失效概率分布参数的方差算式，进而提出了改善模型精度的补充采样准则。通过算例验证了方法的适用性和有被性．
Breaking Gaussian incompatibility on continuous variable quantum systems
Energy Technology Data Exchange (ETDEWEB)
Heinosaari, Teiko, E-mail: teiko.heinosaari@utu.fi [Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turku (Finland); Kiukas, Jukka, E-mail: jukka.kiukas@aber.ac.uk [Department of Mathematics, Aberystwyth University, Penglais, Aberystwyth, SY23 3BZ (United Kingdom); Schultz, Jussi, E-mail: jussi.schultz@gmail.com [Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turku (Finland); Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano (Italy)
2015-08-15
We characterise Gaussian quantum channels that are Gaussian incompatibility breaking, that is, transform every set of Gaussian measurements into a set obtainable from a joint Gaussian observable via Gaussian postprocessing. Such channels represent local noise which renders measurements useless for Gaussian EPR-steering, providing the appropriate generalisation of entanglement breaking channels for this scenario. Understanding the structure of Gaussian incompatibility breaking channels contributes to the resource theory of noisy continuous variable quantum information protocols.
Gaussian measures of entanglement versus negativities and the ordering of two-mode Gaussian states
Adesso, G; Adesso, Gerardo; Illuminati, Fabrizio
2005-01-01
In this work we focus on entanglement of two--mode Gaussian states of continuous variable systems. We introduce the formalism of Gaussian entanglement measures, adopting the framework developed in [M. M. Wolf {\\em et al.}, Phys. Rev. A {\\bf 69}, 052320 (2004)], where the Gaussian entanglement of formation was defined. We compute Gaussian measures explicitely for two important families of nonsymmetric two--mode Gaussian states, namely the states of extremal (maximal and minimal) negativities at fixed global and local purities, introduced in [G. Adesso {\\em et al.}, Phys. Rev. Lett. {\\bf 92}, 087901 (2004)]. This allows us to compare the {\\em orderings} induced on the set of entangled two--mode Gaussian states by the negativities and by the Gaussian entanglement measures. We find that in a certain range of global and local purities (characterizing the covariance matrix of the corresponding extremal states), states of minimum negativity can have more Gaussian entanglement than states of maximum negativity. Thus ...
Gaussian fluctuations in chaotic eigenstates
Srednicki, M A; Srednicki, Mark; Stiernelof, Frank
1996-01-01
We study the fluctuations that are predicted in the autocorrelation function of an energy eigenstate of a chaotic, two-dimensional billiard by the conjecture (due to Berry) that the eigenfunction is a gaussian random variable. We find an explicit formula for the root-mean-square amplitude of the expected fluctuations in the autocorrelation function. These fluctuations turn out to be O(\\hbar^{1/2}) in the small \\hbar (high energy) limit. For comparison, any corrections due to scars from isolated periodic orbits would also be O(\\hbar^{1/2}). The fluctuations take on a particularly simple form if the autocorrelation function is averaged over the direction of the separation vector. We compare our various predictions with recent numerical computations of Li and Robnik for the Robnik billiard, and find good agreement. We indicate how our results generalize to higher dimensions.
Gaussian diffusion interrupted by Lévy walk
Weber, Piotr; Pepłowski, Piotr
2016-10-01
We investigate a stochastic process that links two processes in one model: Gaussian diffusion and one-sided Levy walks leading to anomalous diffusion. The motivation for our study is an observation of ‘heavy-tailed’ momentum probability density in a standard map and its modifications when accelerated modes emerge in the phase space. In this stochastic model, we derive a fractional differential equation for its probability density function. Numerical and analytical solutions for certain values of parameters are presented.
Strongly Scale-dependent Non-Gaussianity
DEFF Research Database (Denmark)
Riotto, Antonio; Sloth, Martin Snoager
2010-01-01
We discuss models of primordial density perturbations where the non-Gaussianity is strongly scale-dependent. In particular, the non-Gaussianity may have a sharp cut-off and be very suppressed on large cosmological scales, but sizeable on small scales. This may have an impact on probes of non...
Helical apodizers for tunable hyper Gaussian masks
Ojeda-Castañeda, J.; Ledesma, Sergio; Gómez-Sarabia, Cristina M.
2013-09-01
We discuss an optical method for controlling the half-width of Gaussian like transmittance windows, by using a pair of absorption masks that have both radial and helical amplitude variations. For describing the radial part of the proposed masks, we employ amplitude transmittance profiles of the form T(ρ) = exp(- ρ s ). For s = 2, one has an amplitude transmittance that is proportional to a Gaussian function. A sub Gaussian mask is defined by a value of s 2, one has super Gaussian masks. Our discussion considers that any of these radially varying masks has also helical modulations. We show that by using a suitable pair of this type of masks, one can control the halfwidth of Gaussian like windows.
Time between plastic displacements of elasto-plastic oscillators subject to Gaussian white noise
DEFF Research Database (Denmark)
Tarp-Johansen, Niels Jacob; Ditlevsen, Ove Dalager
2001-01-01
A one degree of freedom elasto-plastic oscillator subject to stationary Gaussian white noise has a plastic displacement response process of intermittent character. During shorter or longer time intervals the oscillator vibrates within the elastic domain without undergoing any plastic displacements....... These pieces of elastic response cannot be distinguished from conditional Gaussian response samples given that they are within the elasticity limits. Therefore, suitable Gaussian process theory can be applied to these pieces. Typically the plastic displacements occur in clumps of random plastic displacements...
Gaussian Sum PHD Filtering Algorithm for Nonlinear Non-Gaussian Models
Institute of Scientific and Technical Information of China (English)
Yin Jianjun; Zhang Jianqiu; Zhuang Zesen
2008-01-01
A new multi-target filtering algorithm, termed as the Gaussian sum probability hypothesis density (GSPHD) filter, is proposed for nonlinear non-Gaussian tracking models. Provided that the initial prior intensity of the states is Gaussian or can be identified as a Gaussiaa sum, the analytical results of the algorithm show that the posterior intensity at any subsequent time step remains a Gaussian sum under the assumption that the state noise, the measurement noise, target spawn intensity, new target birth intensity, target survival probability, and detection probability are all Gaussian sums. The analysis also shows that the existing Gaassian mixture probability hypothesis density (GMPHD) filter, which is unsuitable for handling the non-Gaussian noise cases, is no more than a special ease of the proposed algorithm, which fills the shortage of incapability of treating non-Gaussian noise. The multi-target tracking simulation results verify the effectiveness of the proposed GSPHD.
An approach to the stochastic calculus in the non-Gaussian case
Directory of Open Access Journals (Sweden)
Andrey A. Dorogovtsev
1995-01-01
Full Text Available We introduce and study a class of operators of stochastic differentiation and integration for non-Gaussian processes. As an application, we establish an analog of the Itô formula.
Increasing Entanglement between Gaussian States by Coherent Photon Subtraction
DEFF Research Database (Denmark)
Ourjoumtsev, Alexei; Dantan, Aurelien Romain; Tualle Brouri, Rosa
2007-01-01
We experimentally demonstrate that the entanglement between Gaussian entangled states can be increased by non-Gaussian operations. Coherent subtraction of single photons from Gaussian quadrature-entangled light pulses, created by a nondegenerate parametric amplifier, produces delocalized states w...
Betti numbers of Gaussian fields
Park, Changbom; Chingangbam, Pravabati; van de Weygaert, Rien; Jones, Bernard; Vegter, Gert; Kim, Inkang; Hidding, Johan; Hellwing, Wojciech A
2013-01-01
We present the relation between the genus in cosmology and the Betti numbers for excursion sets of three- and two-dimensional smooth Gaussian random fields, and numerically investigate the Betti numbers as a function of threshold level. Betti numbers are topological invariants of figures that can be used to distinguish topological spaces. In the case of the excursion sets of a three-dimensional field there are three possibly non-zero Betti numbers; $\\beta_0$ is the number of connected regions, $\\beta_1$ is the number of circular holes, and $\\beta_2$ is the number of three-dimensional voids. Their sum with alternating signs is the genus of the surface of excursion regions. It is found that each Betti number has a dominant contribution to the genus in a specific threshold range. $\\beta_0$ dominates the high-threshold part of the genus curve measuring the abundance of high density regions (clusters). $\\beta_1$ dominates the genus near the median thresholds which measures the topology of negatively curved iso-den...
Asymmetric Laguerre-Gaussian beams
Kovalev, A. A.; Kotlyar, V. V.; Porfirev, A. P.
2016-06-01
We introduce a family of asymmetric Laguerre-Gaussian (aLG) laser beams. The beams have been derived via a complex-valued shift of conventional LG beams in the Cartesian plane. While propagating in a uniform medium, the first bright ring of the aLG beam becomes less asymmetric and the energy is redistributed toward peripheral diffraction rings. The projection of the orbital angular momentum (OAM) onto the optical axis is calculated. The OAM is shown to grow quadratically with increasing asymmetry parameter of the aLG beam, which equals the ratio of the shift to the waist radius. Conditions for the OAM becoming equal to the topological charge have been derived. For aLG beams with zero radial index, we have deduced an expression to define the intensity maximum coordinates and shown the crescent-shaped intensity pattern to rotate during propagation. Results of the experimental generation and rotation of aLG beams agree well with theoretical predictions.
On Gaussian Beams Described by Jacobi's Equation
Smith, Steven Thomas
2013-01-01
Gaussian beams describe the amplitude and phase of rays and are widely used to model acoustic propagation. This paper describes four new results in the theory of Gaussian beams. (1) It is shown that the \\v{C}erven\\'y equations for the amplitude and phase are equivalent to the classical Jacobi Equation of differential geometry. The \\v{C}erven\\'y equations describe Gaussian beams using Hamilton-Jacobi theory, whereas the Jacobi Equation expresses how Gaussian and Riemannian curvature determine geodesic flow on a Riemannian manifold. Thus the paper makes a fundamental connection between Gaussian beams and an acoustic channel's so-called intrinsic Gaussian curvature from differential geometry. (2) A new formula $\\pi(c/c")^{1/2}$ for the distance between convergence zones is derived and applied to several well-known profiles. (3) A class of "model spaces" are introduced that connect the acoustics of ducting/divergence zones with the channel's Gaussian curvature $K=cc"-(c')^2$. The "model" SSPs yield constant Gauss...
Optical coherence tomography image denoising using Gaussianization transform
Amini, Zahra; Rabbani, Hossein
2017-08-01
We demonstrate the power of the Gaussianization transform (GT) for modeling image content by applying GT for optical coherence tomography (OCT) denoising. The proposed method is a developed version of the spatially constrained Gaussian mixture model (SC-GMM) method, which assumes that each cluster of similar patches in an image has a Gaussian distribution. SC-GMM tries to find some clusters of similar patches in the image using a spatially constrained patch clustering and then denoise each cluster by the Wiener filter. Although in this method GMM distribution is assumed for the noisy image, holding this assumption on a dataset is not investigated. We illustrate that making a Gaussian assumption on a noisy dataset has a significant effect on denoising results. For this purpose, a suitable distribution for OCT images is first obtained and then GT is employed to map this original distribution of OCT images to a GMM distribution. Then, this Gaussianized image is used as the input of the SC-GMM algorithm. This method, which is a combination of GT and SC-GMM, remarkably improves the results of OCT denoising compared with earlier version of SC-GMM and even produces better visual and numerical results than the state-of-the art works in this field. Indeed, the main advantage of the proposed OCT despeckling method is texture preservation, which is important for main image processing tasks like OCT inter- and intraretinal layer analysis. Thus, to prove the efficacy of the proposed method for this analysis, an improvement in the segmentation of intraretinal layers using the proposed method as a preprocessing step is investigated. Furthermore, the proposed method can achieve the best expert ranking between other contending methods, and the results show the helpfulness and usefulness of the proposed method in clinical applications.
Institute of Scientific and Technical Information of China (English)
李中伟; 龙新华; 孟光
2009-01-01
机床铣削系统的动力学可以通过一微分差分方程组来描述.对该动力学模型进行稳定性分析,可以确定稳定的铣削参数域及稳定性图.半离散法作为一种有效的半解析稳定性分析法,在对铣削系统动力学模型进行零阶半离散化时的误差级数较大,往往需要进行多步长的运算才能获得比较精确的稳定性分析结果.通过引入Magnus-Gaussian 截断法,推导出了基于Magnus-Gaussian 截断的零阶半离散稳定性分析法.用该方法对铣床切削稳定性进行了分析,并获得了各种工况下的铣床稳定性图.结果表明该方法比原来的零阶半离散稳定性分析法能够更快的收敛于稳定解,从而节省了稳定性分析的运算时间.
Gaussian mixture model of heart rate variability.
Directory of Open Access Journals (Sweden)
Tommaso Costa
Full Text Available Heart rate variability (HRV is an important measure of sympathetic and parasympathetic functions of the autonomic nervous system and a key indicator of cardiovascular condition. This paper proposes a novel method to investigate HRV, namely by modelling it as a linear combination of Gaussians. Results show that three Gaussians are enough to describe the stationary statistics of heart variability and to provide a straightforward interpretation of the HRV power spectrum. Comparisons have been made also with synthetic data generated from different physiologically based models showing the plausibility of the Gaussian mixture parameters.
Non-Gaussian signatures of tachyacoustic cosmology
Energy Technology Data Exchange (ETDEWEB)
Bessada, Dennis, E-mail: dennis.bessada@unifesp.br [UNIFESP — Universidade Federal de São Paulo, Laboratório de Física Teórica e Computação Científica, Rua São Nicolau, 210, 09913-030, Diadema, SP (Brazil)
2012-09-01
I investigate non-Gaussian signatures in the context of tachyacoustic cosmology, that is, a noninflationary model with superluminal speed of sound. I calculate the full non-Gaussian amplitude A, its size f{sub NL}, and corresponding shapes for a red-tilted spectrum of primordial scalar perturbations. Specifically, for cuscuton-like models I show that f{sub NL} ∼ O(1), and the shape of its non-Gaussian amplitude peaks for both equilateral and local configurations, the latter being dominant. These results, albeit similar, are quantitatively distinct from the corresponding ones obtained by Magueijo et al. in the context of superluminal bimetric models.
Differential Evolution with Gaussian Mutation for Economic Dispatch
Basu, Mousumi; Jena, Chitralekha; Panigrahi, Chinmoy Kumar
2016-12-01
This paper presents differential evolution with Gaussian mutation (DEGM) to solve economic dispatch problem of thermal generating units with non-smooth/non-convex cost functions due to valve-point loading, taking into account transmission losses and nonlinear generator constraints such as prohibited operating zones. Differential evolution (DE) is a simple yet powerful global optimization technique. It exploits the differences of randomly sampled pairs of objective vectors for its mutation process. This mutation process is not suitable for complex multimodal optimization. This paper proposes Gaussian mutation in DE which improves search efficiency and guarantees a high probability of obtaining the global optimum without significantly impairing the simplicity of the structure of DE. The effectiveness of the proposed method has been verified on three different test systems. From the comparison with other evolutionary methods, it is found that DEGM based approach is able to provide better solution.
Gaussian weighting of ocular wave-front measurements.
Schwiegerling, Jim
2004-11-01
The measurement of ocular wave-front error gives insight into the optical performance of the eye and possibly a means for assessing visual performance. The visual system responds not only to the quality of the optical image formed on the retina but also to the processing that occurs in the retina and the brain. To develop a metric of visual performance based on wave-front error measurements, these latter processes must somehow be incorporated. In representing the wave-front error in terms of Zernike polynomials, it appears that terms with lower angular frequency have a greater deleterious effect on visual performance than higher-angular-frequency terms. A technique for weighting the pupil function of the eye with a Gaussian filter is demonstrated. It is further demonstrated that the variance of the Gaussian-weighted wave-front error is well correlated with visual performance.
Array processors based on Gaussian fraction-free method
Energy Technology Data Exchange (ETDEWEB)
Peng, S.; Sedukhin, S. [Aizu Univ., Aizuwakamatsu, Fukushima (Japan); Sedukhin, I.
1998-03-01
The design of algorithmic array processors for solving linear systems of equations using fraction-free Gaussian elimination method is presented. The design is based on a formal approach which constructs a family of planar array processors systematically. These array processors are synthesized and analyzed. It is shown that some array processors are optimal in the framework of linear allocation of computations and in terms of number of processing elements and computing time. (author)
The Impact of Non-Gaussian Distribution Trafiic on Network Performance
Institute of Scientific and Technical Information of China (English)
JIN Zhigang(金志刚); SHU Yantai(舒炎泰); Oliver W.W.Yang
2002-01-01
Recent extensive measurements of real-life traffic demonstrate that the probability density function of the traffic is non-Gaussian. If a traffic model does not capture this characteristics, any analytical or simulation results will not be accurate. In this work, we study the impact of non-Gaussian traffic on network performance, and present an approach that can accurately model the marginal distribution of real-life traffic. Both the long- and short-range autocorrelations are also accounted. We show that the removal of non-Gaussian components of the process does not change its correlation structure, and we validate our promising procedure by simulations.
Non-Gaussianity of quantum states: an experimental test on single-photon added coherent states
Barbieri, Marco; Genoni, Marco G; Ferreyrol, Franck; Blandino, Rémi; Paris, Matteo G A; Grangier, Philippe; Tualle-Brouri, Rosa
2010-01-01
Non Gaussian states and processes are useful resources in quantum information with continuous variables. An experimentally accessible criterion has been proposed to measure the degree of non Gaussianity of quantum states, based on the conditional entropy of the state with a Gaussian reference. Here we adopt such criterion to characterise an important class of non classical states, single-photon added coherent states. Our studies demonstrate the reliability and sensitivity of this measure, and use it to quantify how detrimental is the role of experimental imperfections in our realisation.
Phase Correlations in Non-Gaussian Fields
Matsubara, T
2003-01-01
A breakthrough in understanding the phase information of Fourier modes in non-Gaussian fields is presented, discovering the general relation between phase correlations and the hierarchy of polyspectra. Although the exact relations involve the expansions of infinite series, one can truncate these expansions in weakly non-Gaussian fields. The phase sum, $\\theta_{\\sbfm{k}_1} + >... + \\theta_{\\sbfm{k}_N}$, satisfying $\\bfm{k}_1 + ... + \\bfm{k}_N = 0$, is found to be non-uniformly distributed in non-Gaussian fields, and the non-uniformness is represented by the polyspectra. A numerical demonstration proves that the distribution of the phase sum is the robust estimator of the non-Gaussianity.
Statistical Compressed Sensing of Gaussian Mixture Models
Yu, Guoshen
2011-01-01
A novel framework of compressed sensing, namely statistical compressed sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution, and achieving accurate reconstruction on average, is introduced. SCS based on Gaussian models is investigated in depth. For signals that follow a single Gaussian model, with Gaussian or Bernoulli sensing matrices of O(k) measurements, considerably smaller than the O(k log(N/k)) required by conventional CS based on sparse models, where N is the signal dimension, and with an optimal decoder implemented via linear filtering, significantly faster than the pursuit decoders applied in conventional CS, the error of SCS is shown tightly upper bounded by a constant times the best k-term approximation error, with overwhelming probability. The failure probability is also significantly smaller than that of conventional sparsity-oriented CS. Stronger yet simpler results further show that for any sensing matrix, the error of Gaussian SCS is u...
Parity Violation in Graviton Non-gaussianity
Soda, Jiro; Nozawa, Masato
2011-01-01
We study parity violation in graviton non-gaussianity generated during inflation. We develop a useful formalism to calculate graviton non-gaussianity. Using this formalism, we explicitly calculate the parity violating part of the bispectrum for primordial gravitational waves in the exact de Sitter spacetime and prove that no parity violation appears in the non-gaussianity. We also extend the analysis to slow-roll inflation and find that the parity violation of the bispectrum is proportional to the slow-roll parameter. We argue that parity violating non-gaussianity can be tested by the CMB. Our results are also useful for calculating three-point function of the stress tensor in the non-conformal field theory through the gravity/field theory correspondence.
Lecture notes on non-Gaussianity
Byrnes, Christian T
2014-01-01
We discuss how primordial non-Gaussianity of the curvature perturbation helps to constrain models of the early universe. Observations are consistent with Gaussian initial conditions, compatible with the predictions of the simplest models of inflation. Deviations are constrained to be at the sub percent level, constraining alternative models such as those with multiple fields, non-canonical kinetic terms or breaking the slow-roll conditions. We introduce some of the most important models of inflation which generate non-Gaussian perturbations and provide practical tools on how to calculate the three-point correlation function for a popular class of non-Gaussian models. The current state of the field is summarised and an outlook is given.
Uniform dimension results for Gaussian random fields
Institute of Scientific and Technical Information of China (English)
2009-01-01
Let X = {X(t),t ∈ RN} be a Gaussian random field with values in Rd defined by X(t) =(X1(t),...,Xd(t)), t ∈ RN.(1) The properties of space and time anisotropy of X and their connections to uniform Hausdorff dimension results are discussed.It is shown that in general the uniform Hausdorff dimension result does not hold for the image sets of a space-anisotropic Gaussian random field X.When X is an(N,d)-Gaussian random field as in(1),where X1,...,Xd are independent copies of a real valued,centered Gaussian random field X0 which is anisotropic in the time variable.We establish uniform Hausdorff dimension results for the image sets of X.These results extend the corresponding results on one-dimensional Brownian motion,fractional Brownian motion and the Brownian sheet.
A non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related families
Dutta, Subhajit
2014-07-28
Several fascinating examples of non-Gaussian bivariate distributions which have marginal distribution functions to be Gaussian have been proposed in the literature. These examples often clarify several properties associated with the normal distribution. In this paper, we generalize this result in the sense that we construct a pp-dimensional distribution for which any proper subset of its components has the Gaussian distribution. However, the jointpp-dimensional distribution is inconsistent with the distribution of these subsets because it is not Gaussian. We study the probabilistic properties of this non-Gaussian multivariate distribution in detail. Interestingly, several popular tests of multivariate normality fail to identify this pp-dimensional distribution as non-Gaussian. We further extend our construction to a class of elliptically contoured distributions as well as skewed distributions arising from selections, for instance the multivariate skew-normal distribution.
Gas distribution, metal enrichment, and baryon fraction in Gaussian and non-Gaussian universes
Maio, Umberto
2011-01-01
We study the cosmological evolution of baryons in universes with and without primordial non-Gaussianities via (large scale) N-body/hydrodynamical simulations, including gas cooling, star formation, stellar evolution, chemical enrichment from both population III and population II regimes, and feedback effects. We find that large fnl values for non-Gaussianities can alter the gas probability distribution functions, the metal pollution history, the halo baryon, gas and stellar fractions, mostly at early times. More precisely: (i) non-Gaussianities lead to an earlier evolution of primordial gas, structures, and star formation; (ii) metal enrichment starts earlier (with respect to the Gaussian scenario) in non-Gaussian models with larger fnl; (iii) gas fractions within the haloes are not significantly affected by the different values of fnl, with deviations of ~1-10%; (iv) the stellar fraction is quite sensitive to non-Gaussianities at early times, with discrepancies reaching up to a factor of ~10 at very high z, ...
Path properties of lp-valued Gaussian random fields
Institute of Scientific and Technical Information of China (English)
Yong-Kab; CHOI
2007-01-01
[1]Csáki E,Cs(o)rg(o) M.Inequalities for increments of stochastic processes and moduli of continuity.Ann Probab,20:1031-1052 (1992)[2]Csáki E,Cs(o)rg(o) M,Shao Q M.Fernique type inequalities and moduli of continuity for l2-valued Ornstein-Uhlenbeck Processes.Ann In st Henri Poincare Probabilities et Statistiques,28:479-517 (1992)[3]Csáki E,Cs(o)rg(o) M,Shao Q M.Moduli of continuity for lp-valued Gaussian processes.Acta Sci Math,60:149-175 (1995)[4]Cs(o)rg(o) M,Shao Q M.Strong limit theorems for large and small increments of lp-valued Gaussian Processes.Ann Probab,21:1958-1990 (1993)[5]Cs(o)rg(o) M,Shao Q M.On almost sure limit inferior for B-valued stochastic processes and applications.Probab Theory & Rel Fields,99:29-54 (1994)[6]Lin Z Y,Quin Y C.On the increments of l∞-valued Gaussian processes.In:Szyszkowicz B,ed.Asymptotic Methods in Probability and Statistics.Elsevier Science B V,1998,293-302[7]Choi Y K.Erd(o)s-Rényi-type laws applied to Gaussian processes.J Math Kyoto Univ,31(3):191-217(1991)[8]Csáki E,Cs(o)rg(o) M,Lin Z Y,et al.On infinite series of independent Ornstein-uhlenbeck processes.Stoch Proc & their Appl,39:25-44 (1991)[9]Cs(o)rg(o) M,Révész P.How big are the increments of a Wiener process? Ann Probab,7(4):731-737 (1979)[10]Cs(o)rg(o) M,Révész P.Strong Approximations in Probability and Statistics.New York:Academic Press,1981[11]Lin Z Y,Lu C R.Strong Limit Theorems.Hong Kong:Kluwer Academic Publ,1992[12]Ortega J.On the size of the increments of non-stationary Gaussian processes.Stoch Proc & Their Appl,18:47-56 (1984)[13]Zhang L X.A note on liminfs for increments of a fractional Brownian motion.Acta Math Hungar,76:145-154 (1997)[14]K(o)no N.The exact modulus of continuity for Gaussian processes taking values of finite dimensional normed space.Trends in Probab & Related Analysis,SAP'96.Singapore:World Scientific,1996.pp.219-232[15]Lin Z Y,Hwang K S.On the increments of a d-dimensional Gaussian process.J Korean Math Soc,42(6):1215-1230 (2005
Homodyne estimation of Gaussian quantum discord.
Blandino, Rémi; Genoni, Marco G; Etesse, Jean; Barbieri, Marco; Paris, Matteo G A; Grangier, Philippe; Tualle-Brouri, Rosa
2012-11-02
We address the experimental estimation of Gaussian quantum discord for a two-mode squeezed thermal state, and demonstrate a measurement scheme based on a pair of homodyne detectors assisted by Bayesian analysis, which provides nearly optimal estimation for small value of discord. In addition, though homodyne detection is not optimal for Gaussian discord, the noise ratio to the ultimate quantum limit, as dictated by the quantum Cramer-Rao bound, is limited to about 10 dB.
GAUSSIAN WHITE NOISE CALCULUS OF GENERALIZED EXPANSION
Institute of Scientific and Technical Information of China (English)
陈泽乾
2002-01-01
A new framework of Gaussian white noise calculus is established, in line with generalized expansion in [3, 4, 7]. A suitable frame of Fock expansion is presented on Gaussian generalized expansion functionals being introduced here, which provides the integral kernel operator decomposition of the second quantization of Koopman operators for chaotic dynamical systems, in terms of annihilation operators (e)t and its dual, creation operators (e)*t.
TURBO EQUALIZATION WITH JOINTLY GAUSSIAN EQUALIZER
Institute of Scientific and Technical Information of China (English)
Jiang Sen; Sun Hong; Li Ping
2005-01-01
A Jointly Gaussian (JG) equalizer is derived for turbo equalization based on an augmented real matrix representation of channel model and a Gaussian approximation of the received symbol sequence. Using matrix inversion lemma and Cholesky decomposition, a lowcomplexity implementation of JG equalizer is also presented. The simulation results and complexity comparison confirm that turbo equalization with JG equalizer has a better performance and a lower complexity than the existing turbo equalization with linear minimum mean squared error equalizer.
Approximate Capacity of Gaussian Relay Networks
Avestimehr, Amir Salman; Tse, David N C
2008-01-01
We present an achievable rate for general Gaussian relay networks. We show that the achievable rate is within a constant number of bits from the information-theoretic cut-set upper bound on the capacity of these networks. This constant depends on the topology of the network, but not the values of the channel gains. Therefore, we uniformly characterize the capacity of Gaussian relay networks within a constant number of bits, for all channel parameters.
Nonparaxial Propagation of Vectorial Elliptical Gaussian Beams
Directory of Open Access Journals (Sweden)
Wang Xun
2016-01-01
Full Text Available Based on the vectorial Rayleigh-Sommerfeld diffraction integral formulae, analytical expressions for a vectorial elliptical Gaussian beam’s nonparaxial propagating in free space are derived and used to investigate target beam’s propagation properties. As a special case of nonparaxial propagation, the target beam’s paraxial propagation has also been examined. The relationship of vectorial elliptical Gaussian beam’s intensity distribution and nonparaxial effect with elliptic coefficient α and waist width related parameter fω has been analyzed. Results show that no matter what value of elliptic coefficient α is, when parameter fω is large, nonparaxial conclusions of elliptical Gaussian beam should be adopted; while parameter fω is small, the paraxial approximation of elliptical Gaussian beam is effective. In addition, the peak intensity value of elliptical Gaussian beam decreases with increasing the propagation distance whether parameter fω is large or small, and the larger the elliptic coefficient α is, the faster the peak intensity value decreases. These characteristics of vectorial elliptical Gaussian beam might find applications in modern optics.
Gaussian vs non-Gaussian turbulence: impact on wind turbine loads
DEFF Research Database (Denmark)
Berg, Jacob; Natarajan, Anand; Mann, Jakob;
2016-01-01
From large-eddy simulations of atmospheric turbulence, a representation of Gaussian turbulence is constructed by randomizing the phases of the individual modes of variability. Time series of Gaussian turbulence are constructed and compared with its non-Gaussian counterpart. Time series from the two...... types of turbulence are then used as input to wind turbine load simulations under normal operations with the HAWC2 software package. A slight increase in the extreme loads of the tower base fore-aft moment is observed for high wind speeds when using non-Gaussian turbulence but is insignificant when...
Multiplicativity of maximal output purities of Gaussian channels under Gaussian inputs
Serafini, A; Wolf, M M
2005-01-01
We address the question of the multiplicativity of the maximal p-norm output purities of bosonic Gaussian channels under Gaussian inputs. We focus on general Gaussian channels resulting from the reduction of unitary dynamics in larger Hilbert spaces. It is shown that the maximal output purity of tensor products of single-mode channels under Gaussian inputs is multiplicative for any p>1 for products of arbitrary identical channels as well as for a large class of products of different channels. In the case of p=2 multiplicativity is shown to be true for arbitrary products of generic channels acting on any number of modes.
Convergence rates for the full Gaussian rough paths
Friz, Peter
2011-01-01
Under the key assumption of finite $\\rho $-variation, $\\rho \\in \\lbrack 1,2)$, of the covariance of the underlying Gaussian process, sharp a.s. convergence rates for approximations of Gaussian rough paths are established. When applied to Brownian resp. fractional Brownian motion, $\\rho =1$ resp. $\\rho =1/(2H) $, we recover and extend the respective results of [Hu--Nualart; Rough path analysis via fractional calculus; TAMS 361 (2009) 2689-2718] and [Deya--Neuenkirch--Tindel; A Milstein-type scheme without L\\'{e}vy area terms for SDEs driven by fractional Brownian motion; AIHP (2011)]. In particular, we establish an a.s. rate $n^{-(1/\\rho -1/2-\\epsilon)}$, any $\\epsilon >0 $, for Wong-Zakai and Milstein-type approximations with mesh-size $1/n$. When applied to fBM this answers a conjecture in the afore-mentioned references.
Tail Approximations of Integrals of Gaussian Random Fields
Liu, Jingchen
2010-01-01
This paper develops asymptotic approximations of $P(\\int_T e^{f(t)}dt > b)$ as $b\\rightarrow \\infty$ for homogeneous smooth Gaussian random field, $f$, living on a compact $d$-dimensional Jordan measurable set $T$. The integral of exponent of Gaussian random field is an important random variable for many generic models in spatial point processes, portfolio risk analysis, asset pricing and so forth. The analysis technique consists of two steps: 1. evaluate the tail probability $P(\\int_\\Delta e^{f(t)}dt > b)$ over a small domain $\\Delta$ depending on $b$, where $mes(\\Delta) \\rightarrow 0$ as $b\\rightarrow \\infty$ and $mes(\\cdot)$ is the Lebesgue measure; 2. with $\\Delta$ appropriately chosen, we show that $P(\\int_T e^{f(t)}dt > b) =(1+o(1)) mes(T) mes^{-1}(\\Delta) P(\\int_\\Delta e^{f(t)}dt > b)$.
Maximum Entropy Production and Non-Gaussian Climate Variability
Sura, Philip
2016-01-01
Earth's atmosphere is in a state far from thermodynamic equilibrium. For example, the large scale equator-to-pole temperature gradient is maintained by tropical heating, polar cooling, and a midlatitude meridional eddy heat flux predominantly driven by baroclinically unstable weather systems. Based on basic thermodynamic principles, it can be shown that the meridional heat flux, in combination with the meridional temperature gradient, acts to maximize entropy production of the atmosphere. In fact, maximum entropy production (MEP) has been successfully used to explain the observed mean state of the atmosphere and other components of the climate system. However, one important feature of the large scale atmospheric circulation is its often non-Gaussian variability about the mean. This paper presents theoretical and observational evidence that some processes in the midlatitude atmosphere are significantly non-Gaussian to maximize entropy production. First, after introducing the basic theory, it is shown that the ...
DEFF Research Database (Denmark)
Li, Chunjian; Andersen, Søren Vang
2007-01-01
We propose two blind system identification methods that exploit the underlying dynamics of non-Gaussian signals. The two signal models to be identified are: an Auto-Regressive (AR) model driven by a discrete-state Hidden Markov process, and the same model whose output is perturbed by white Gaussian...
The optimal pure Gaussian state canonically associated to a Gaussian quantum state
Energy Technology Data Exchange (ETDEWEB)
Gosson, Maurice de [Blekinge Institute of Technology, Karlskrona 371 79 (Sweden)]. E-mail: mdg@bth.se
2004-09-20
We show, using the symplectically invariant notion of 'quantum blob', that it is possible to attach a canonical optimal Gaussian pure state to an arbitrary quantum state. When at least one pair of conjugate variables satisfies the minimum uncertainty condition, then the associated Gaussian is uniquely determined up to an overall phase factor.
Generation of coherence via Gaussian measurements
Albarelli, Francesco; Genoni, Marco G.; Paris, Matteo G. A.
2017-07-01
We address measurement-based generation of quantum coherence in continuous variable systems. We consider Gaussian measurements performed on Gaussian states and focus on two scenarios: In the first one, we assume an initially correlated bipartite state shared by two parties and study how correlations may be exploited to remotely create quantum coherence via measurement back action. In particular, we focus on conditional states with zero first moments, so as to address coherence due to properties of the covariance matrix. We consider different classes of bipartite states with incoherent marginals and show that the larger the measurement squeezing, the larger the conditional coherence. Homodyne detection is thus the optimal Gaussian measurement to remotely generate coherence. We also show that for squeezed thermal states there exists a threshold value for the generated coherence which separates entangled and separable states at a fixed energy. Finally, we briefly discuss the tripartite case and the relationship between tripartite correlations and the conditional two-mode coherence. In the second scenario, we address the steady-state coherence of a system interacting with an environment which is continuously monitored. In particular, we discuss the dynamics of an optical parametric oscillator in order to investigate how the coherence of a Gaussian state may be increased by means of time-continuous Gaussian measurement on the interacting environment.
Trap split with Laguerre-Gaussian beams
Hamideh Kazemi, Seyedeh; Ghanbari, Saeed; Mahmoudi, Mohammad
2017-08-01
We present a convenient and effective way to generate a novel phenomenon of trapping, named ‘trap split’, in a conventional four-level double-Λ atomic system, driven by four femtosecond Laguerre-Gaussian laser pulses. We find that trap split can always be achieved when atoms are trapped by such laser pulses, as compared to Gaussian ones. This feature is enabled by the interaction of the atomic system and the Laguerre-Gaussian laser pulses with zero intensity in the center. A further advantage of using Laguerre-Gaussian laser pulses is the insensitivity to fluctuation in the intensity of the lasers in such a way that the separation between the traps remains constant. Moreover, it is demonstrated that the suggested scheme with Laguerre-Gaussian laser pulses can form optical traps with spatial sizes that are not limited by the wavelength of the laser, and can, in principle, become smaller than the wavelength of light. This work would greatly facilitate the trapping and manipulating of particles and the generation of trap split. It may also suggest the possibility of extension into new research fields, such as micro-machining and biophysics.
Induced focusing and conversion of a Gaussian beam into an elliptic Gaussian beam
Indian Academy of Sciences (India)
Manoj Mishra; Swapan Konar
2005-09-01
We have presented an investigation of the induced focusing in Kerr media of two laser beams, the pump beam and the probe beam, which could be either Gaussian or elliptic Gaussian or a combination of the two. We have used variational formalism to derive relevant beam-width equations. Among several important findings, the finding that a very week probe beam can be guided and focused when power of both beams are well below their individual threshold for self-focusing, is a noteworthy one. It has been found that induced focusing is not possible for laser beams of any wavelength and beam radius. In case both beams are elliptic Gaussian, we have shown that when power of both beams is above a certain threshold value then the effective radius of both beams collapses and collapse distance depends on power. Moreover, it has been found that induced focusing can be employed to convert a circular Gaussian beam into an elliptic Gaussian beam.
Energy Efficient Estimation of Gaussian Sources Over Inhomogeneous Gaussian MAC Channels
Wei, Shuangqing; Iyengar, Sitharama; Rao, Nageswara S
2007-01-01
It has been shown lately the optimality of uncoded transmission in estimating Gaussian sources over homogeneous/symmetric Gaussian multiple access channels (MAC) using multiple sensors. It remains, however, unclear whether it still holds for any arbitrary networks and/or with high channel signal-to-noise ratio (SNR) and high signal-to-measurement-noise ratio (SMNR). In this paper, we first provide a joint source and channel coding approach in estimating Gaussian sources over Gaussian MAC channels, as well as its sufficient and necessary condition in restoring Gaussian sources with a prescribed distortion value. An interesting relationship between our proposed joint approach with a more straightforward separate source and channel coding scheme is then established. We then formulate constrained power minimization problems and transform them to relaxed convex geometric programming problems, whose numerical results exhibit that either separate or uncoded scheme becomes dominant over a linear topology network. In ...
On O(1) Gaussian filtering using box splines
Chauhdury, Kunal N
2011-01-01
It is well-known that box filters can be efficiently computed using pre-integrations and local finite-differences [Crow1984,Heckbert1986,Viola2001]. Several image processing algorithms based on this idea have been proposed in the literature. By generalizing this idea and by combining it with a non-standard variant of the Central Limit Theorem, a constant-time or O(1) algorithm was proposed in [Chaudhury2010] that allowed one to perform space-variant filtering using Gaussian-like kernels . The algorithm was based on the observation that both isotropic and anisotropic Gaussians could be approximated using certain bivariate splines called box splines. The attractive feature of the algorithm was that it allowed one to continuously control the shape and size of the filter, and that it had a fixed computational cost per pixel, irrespective of the size of the filter. The algorithm, however, had the drawback that it offered only a limited control on the covariance and accuracy of the Gaussian approximation. In this w...
FPGA implementation of filtered image using 2D Gaussian filter
Directory of Open Access Journals (Sweden)
Leila kabbai
2016-07-01
Full Text Available Image filtering is one of the very useful techniques in image processing and computer vision. It is used to eliminate useless details and noise from an image. In this paper, a hardware implementation of image filtered using 2D Gaussian Filter will be present. The Gaussian filter architecture will be described using a different way to implement convolution module. Thus, multiplication is in the heart of convolution module, for this reason, three different ways to implement multiplication operations will be presented. The first way is done using the standard method. The second way uses Field Programmable Gate Array (FPGA features Digital Signal Processor (DSP to ensure and make fast the scalability of the effective FPGA resource and then to speed up calculation. The third way uses real multiplier for more precision and a the maximum uses of FPGA resources. In this paper, we compare the image quality of hardware (VHDL and software (MATLAB implementation using the Peak Signal-to-Noise Ratio (PSNR. Also, the FPGA resource usage for different sizes of Gaussian kernel will be presented in order to provide a comparison between fixed-point and floating point implementations.
Influence of Initial Chirp on Propagation of Super-Gaussian Pulse inside Fiber
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Under the condition of combined effects of group-velocity dispersion and self-phase modulation, the step Fourier method is used to simulate the propagation of initial chirped super-Gaussian pulses inside fiber. The initial chirp influences the shapes of super-Gaussian pulses in propagation process, and positive and negative chirps have different effects. For the existing of initial chirp, the splits of pulses and the spreading speed move ahead and increase. When the amplitude of super-Gaussian pulses increases by 1.4 times, in the range of |C|<1.5, pulses can keep good shapes along their propagation distance. Even if |C| increases to 3.5, their shapes are also good. Most energy of pulse is still at the middle parts. These results show that, for the initial chirped super-Gaussian pulses, the influence of initial chirp will be decreased by increasing the intensity of pulses. This will be of benefit to optical communication.
Quantitative comparison of self-healing ability between Bessel–Gaussian beam and Airy beam
Energy Technology Data Exchange (ETDEWEB)
Wen, Wei [Department of Physics and Information Engineering, Huaihua University, Huaihua 418008 (China); Chu, Xiuxiang, E-mail: xiuxiangchu@yahoo.com [School of Sciences, Zhejiang Agriculture and Forestry University, Lin’an 311300 (China)
2015-09-15
The self-healing ability during propagation process is one of the most important properties of non-diffracting beams. This ability has crucial advantages to light sheet-based microscopy to reduce scattering artefacts, increase the quality of the image and enhance the resolution of microscopy. Based on similarity between two infinite-dimensional complex vectors in Hilbert space, the ability to a Bessel–Gaussian beam and an Airy beam have been studied and compared. Comparing the evolution of the similarity of Bessel–Gaussian beam with Airy beam under the same conditions, we find that Bessel–Gaussian beam has stronger self-healing ability and is more stable than that of Airy beam. To confirm this result, the intensity profiles of Bessel–Gaussian beam and Airy beam with different similarities are numerically calculated and compared.
Generation and propagation of a sine-azimuthal wavefront modulated Gaussian beam.
Lao, Guanming; Zhang, Zhaohui; Luo, Meilan; Zhao, Daomu
2016-07-21
We introduce a method for modulating the Gaussian beam by means of sine-azimuthal wavefront and carry out the experimental generation. The analytical propagation formula of such a beam passing through a paraxial ABCD optical system is derived, by which the intensity properties of the sine-azimuthal wavefront modulated Gaussian (SWMG) beam are examined both theoretically and experimentally. Both of the experimental and theoretical results show that the SWMG beam goes through the process from beam splitting to a Gaussian-like profile, which is closely determined by the phase factor and the propagation distance. Appropriate phase factor and short distance are helpful for the splitting of beam. However, in the cases of large phase factor and focal plane, the intensity distributions tend to take a Gaussian form. Such unique features may be of importance in particle trapping and medical applications.
Khan, Tariq Mahmood; Bailey, Donald G; Khan, Mohammad A U; Kong, Yinan
2017-05-01
A real-time image filtering technique is proposed which could result in faster implementation for fingerprint image enhancement. One major hurdle associated with fingerprint filtering techniques is the expensive nature of their hardware implementations. To circumvent this, a modified anisotropic Gaussian filter is efficiently adopted in hardware by decomposing the filter into two orthogonal Gaussians and an oriented line Gaussian. An architecture is developed for dynamically controlling the orientation of the line Gaussian filter. To further improve the performance of the filter, the input image is homogenized by a local image normalization. In the proposed structure, for a middle-range reconfigurable FPGA, both parallel compute-intensive and real-time demands were achieved. We manage to efficiently speed up the image-processing time and improve the resource utilization of the FPGA. Test results show an improved speed for its hardware architecture while maintaining reasonable enhancement benchmarks.
Novel blind source separation algorithm using Gaussian mixture density function
Institute of Scientific and Technical Information of China (English)
孔薇; 杨杰; 周越
2004-01-01
The blind source separation (BSS) is an important task for numerous applications in signal processing, communications and array processing. But for many complex sources blind separation algorithms are not efficient because the probability distribution of the sources cannot be estimated accurately. So in this paper, to justify the ME(maximum enteropy) approach, the relation between the ME and the MMI(minimum mutual information) is elucidated first. Then a novel algorithm that uses Gaussian mixture density to approximate the probability distribution of the sources is presented based on the ME approach. The experiment of the BSS of ship-radiated noise demonstrates that the proposed algorithm is valid and efficient.
Improved estimation in a non-Gaussian parametric regression
Pchelintsev, Evgeny
2011-01-01
The paper considers the problem of estimating the parameters in a continuous time regression model with a non-Gaussian noise of pulse type. The noise is specified by the Ornstein-Uhlenbeck process driven by the mixture of a Brownian motion and a compound Poisson process. Improved estimates for the unknown regression parameters, based on a special modification of the James-Stein procedure with smaller quadratic risk than the usual least squares estimates, are proposed. The developed estimation scheme is applied for the improved parameter estimation in the discrete time regression with the autoregressive noise depending on unknown nuisance parameters.
Institute of Scientific and Technical Information of China (English)
Li Wang(王丽); Jianhua Xue(薛建华)
2003-01-01
The conversion efficiency of THG on the flattened Gaussian and Gaussian beams is obtained in detail numerical stimulation for CsLiB6O10. The conversion efficiencies of 86.7% and 96% of the flattened Gaussian are larger than those of Gaussian beams of 72.6% and 88% under type I and type Ⅱ(1) phase matching. The efficiencies affected by the pump intensity, polarization rate, crystal lengths and orders of the flattened Gaussian beams were presented.
Bridging asymptotic independence and dependence in spatial exbtremes using Gaussian scale mixtures
Huser, Raphaël
2017-06-23
Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect dependence. In this paper, we study the extremal dependence properties of Gaussian scale mixtures and we unify and extend general results on their joint tail decay rates in both asymptotic dependence and independence cases. Motivated by the analysis of spatial extremes, we propose flexible yet parsimonious parametric copula models that smoothly interpolate from asymptotic dependence to independence and include the Gaussian dependence as a special case. We show how these new models can be fitted to high threshold exceedances using a censored likelihood approach, and we demonstrate that they provide valuable information about tail characteristics. In particular, by borrowing strength across locations, our parametric model-based approach can also be used to provide evidence for or against either asymptotic dependence class, hence complementing information given at an exploratory stage by the widely used nonparametric or parametric estimates of the χ and χ̄ coefficients. We demonstrate the capacity of our methodology by adequately capturing the extremal properties of wind speed data collected in the Pacific Northwest, US.
Spectra for the product of Gaussian noises
Kish, L B; Gingl, Z; Granqvist, C G
2012-01-01
Products of Gaussian noises often emerge as the result of non-linear detection techniques or as a parasitic effect, and their proper handling is important in many practical applications, including in fluctuation-enhanced sensing, indoor air or environmental quality monitoring, etc. We use Rice's random phase oscillator formalism to calculate the power density spectra variance for the product of two Gaussian band-limited white noises with zero-mean and the same bandwidth W. The ensuing noise spectrum is found to decrease linearly from zero frequency to 2W, and it is zero for frequencies greater than 2W. Analogous calculations performed for the square of a single Gaussian noise confirm earlier results. The spectrum at non-zero frequencies, and the variance of the square of a noise, is amplified by a factor two as a consequence of correlation effects between frequency products. Our analytic results is corroborated by computer simulations.
Gaussian entanglement in the turbulent atmosphere
Bohmann, M.; Semenov, A. A.; Sperling, J.; Vogel, W.
2016-07-01
We provide a rigorous treatment of the entanglement properties of two-mode Gaussian states in atmospheric channels by deriving and analyzing the input-output relations for the corresponding entanglement test. A key feature of such turbulent channels is a nontrivial dependence of the transmitted continuous-variable entanglement on coherent displacements of the quantum state of the input field. Remarkably, this allows one to optimize the entanglement certification by modifying local coherent amplitudes using a finite, but optimal amount of squeezing. In addition, we propose a protocol which, in principle, renders it possible to transfer the Gaussian entanglement through any turbulent channel over arbitrary distances. Therefore, our approach provides the theoretical foundation for advanced applications of Gaussian entanglement in free-space quantum communication.
Statistical Compressive Sensing of Gaussian Mixture Models
Yu, Guoshen
2010-01-01
A new framework of compressive sensing (CS), namely statistical compressive sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution and achieving accurate reconstruction on average, is introduced. For signals following a Gaussian distribution, with Gaussian or Bernoulli sensing matrices of O(k) measurements, considerably smaller than the O(k log(N/k)) required by conventional CS, where N is the signal dimension, and with an optimal decoder implemented with linear filtering, significantly faster than the pursuit decoders applied in conventional CS, the error of SCS is shown tightly upper bounded by a constant times the k-best term approximation error, with overwhelming probability. The failure probability is also significantly smaller than that of conventional CS. Stronger yet simpler results further show that for any sensing matrix, the error of Gaussian SCS is upper bounded by a constant times the k-best term approximation with probability one, and the ...
Number Counts and Non-Gaussianity
Shandera, Sarah; Scott, Pat; Galarza, Jhon Yana
2013-01-01
We describe a general procedure for using number counts of any object to constrain the probability distribution of the primordial fluctuations, allowing for generic weak non-Gaussianity. We apply this procedure to use limits on the abundance of primordial black holes and dark matter ultracompact minihalos (UCMHs) to characterize the allowed statistics of primordial fluctuations on very small scales. We present constraints on the power spectrum and the amplitude of the skewness for two different families of non-Gaussian distributions, distinguished by the relative importance of higher moments. Although primordial black holes probe the smallest scales, ultracompact minihalos provide significantly stronger constraints on the power spectrum and so are more likely to eventually provide small-scale constraints on non-Gaussianity.
Rough interfaces beyond the Gaussian approximation
Caselle, M; Gliozzi, F; Hasenbusch, M; Pinn, K; Vinti, S; Caselle, M; Gliozzi, F; Fiore, R; Hasenbusch, M; Pinn, K; Vinti, S
1994-01-01
We compare predictions of the Capillary Wave Model beyond its Gaussian approximation with Monte Carlo results for the energy gap and the surface energy of the 3D Ising model in the scaling region. Our study reveals that the finite size effects of these quantities are well described by the Capillary Wave Model, expanded to two--loop order ( one order beyond the Gaussian approximation). We compare predictions of the Capillary Wave Model with Monte Carlo results for the energy gap and the interface energy of the 3D Ising model in the scaling region. Our study reveals that the finite size effects of these quantities are well described by the Capillary Wave Model, expanded to two-loop order (one order beyond the Gaussian approximation).
Non-Gaussianity of Racetrack Inflation Models
Institute of Scientific and Technical Information of China (English)
SUN Cheng-Yi; ZHANG De-Hai
2007-01-01
In this paper, we use the result in [C.Y. Sun and D.H. Zhang, arXiv:astro-ph/0510709] to calculate the non-Gaussianity of the racetrack models in[J.J. Blanco-Pillado, et al., JHEP 0411 (2004) 063; arXiv:hep-th/0406230]and [J.J. Blanco-Pillado, et al., arXiv:hep-th/0603129]. The two models give different non-Gaussianities. Both of them are reasonable. However, we find that, for multi-field inflationary models with the non-trivial metric of the field space,the condition of the slow-roll cannot guarantee small non-Gaussianities.
Majorization preservation of Gaussian bosonic channels
Jabbour, Michael G.; García-Patrón, Raúl; Cerf, Nicolas J.
2016-07-01
It is shown that phase-insensitive Gaussian bosonic channels are majorization-preserving over the set of passive states of the harmonic oscillator. This means that comparable passive states under majorization are transformed into equally comparable passive states by any phase-insensitive Gaussian bosonic channel. Our proof relies on a new preorder relation called Fock-majorization, which coincides with regular majorization for passive states but also induces another order relation in terms of mean boson number, thereby connecting the concepts of energy and disorder of a quantum state. The consequences of majorization preservation are discussed in the context of the broadcast communication capacity of Gaussian bosonic channels. Because most of our results are independent of the specific nature of the system under investigation, they could be generalized to other quantum systems and Hamiltonians, providing a new tool that may prove useful in quantum information theory and especially quantum thermodynamics.
Integration of non-Gaussian fields
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager; Mohr, Gunnar; Hoffmeyer, Pernille
1996-01-01
enough to justify that it is sufficiently accurate for the applications to shortcut the problem and just assume that the distribution of the relevant stochastic integral is Gaussian. An earlier published example exhibiting this problem concerns silo pressure fields. [Ditlevsen, O., Christensen, C......The limitations of the validity of the central limit theorem argument as applied to definite integrals of non-Gaussian random fields are empirically explored by way of examples. The purpose is to investigate in specific cases whether the asymptotic convergence to the Gaussian distribution is fast....... and Randrup-Thomsen, S. Reliability of silo ring under lognormal stochastic pressure using stochastic interpolation. Proc. IUTAM Symp., Probabilistic Structural Mechanics: Advances in Structural Reliability Methods, San Antonio, TX, USA, June 1993 (eds.: P. D. Spanos & Y.-T. Wu) pp. 134-162. Springer, Berlin...
Cross-correlations and joint gaussianity in multivariate level crossing models.
Di Bernardino, Elena; León, José; Tchumatchenko, Tatjana
2014-04-17
A variety of phenomena in physical and biological sciences can be mathematically understood by considering the statistical properties of level crossings of random Gaussian processes. Notably, a growing number of these phenomena demand a consideration of correlated level crossings emerging from multiple correlated processes. While many theoretical results have been obtained in the last decades for individual Gaussian level-crossing processes, few results are available for multivariate, jointly correlated threshold crossings. Here, we address bivariate upward crossing processes and derive the corresponding bivariate Central Limit Theorem as well as provide closed-form expressions for their joint level-crossing correlations.
Donor Centers in a Gaussian Potential
Institute of Scientific and Technical Information of China (English)
XIE Wen-Fang
2007-01-01
We study a neutral donor center (D0) and a negatively charged donor center (D-) trapped by a quantum dot, which is subjected to a Gaussian potential confinement. Calculations are made by using the method of numerical diagonalization of Hamiltonian within the effective-mass approximation. The dependence of the ground state of the neutral shallow donor and the negatively charged donor on the dot size and the potential depth is investigated. The same calculations performed with the parabolic approximation of the Gaussian potential lead to the results that are qualitatively and quantitatively different from each other.
Invariant measures on multimode quantum Gaussian states
Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.
2012-12-01
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom—the symplectic eigenvalues—which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.
Invariant measures on multimode quantum Gaussian states
Lupo, C; De Pasquale, A; Facchi, P; Florio, G; Pascazio, S
2012-01-01
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom -- the symplectic eigenvalues -- which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest or applications in quantum optics and quantum information.
Invariant measures on multimode quantum Gaussian states
Energy Technology Data Exchange (ETDEWEB)
Lupo, C. [School of Science and Technology, Universita di Camerino, I-62032 Camerino (Italy); Mancini, S. [School of Science and Technology, Universita di Camerino, I-62032 Camerino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, I-06123 Perugia (Italy); De Pasquale, A. [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa (Italy); Facchi, P. [Dipartimento di Matematica and MECENAS, Universita di Bari, I-70125 Bari (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Florio, G. [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi, Piazza del Viminale 1, I-00184 Roma (Italy); Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy); Pascazio, S. [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy)
2012-12-15
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom-the symplectic eigenvalues-which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.
Model selection for Gaussian kernel PCA denoising
DEFF Research Database (Denmark)
Jørgensen, Kasper Winther; Hansen, Lars Kai
2012-01-01
We propose kernel Parallel Analysis (kPA) for automatic kernel scale and model order selection in Gaussian kernel PCA. Parallel Analysis [1] is based on a permutation test for covariance and has previously been applied for model order selection in linear PCA, we here augment the procedure to also...... tune the Gaussian kernel scale of radial basis function based kernel PCA.We evaluate kPA for denoising of simulated data and the US Postal data set of handwritten digits. We find that kPA outperforms other heuristics to choose the model order and kernel scale in terms of signal-to-noise ratio (SNR...
Cosine-Gaussian Schell-model sources.
Mei, Zhangrong; Korotkova, Olga
2013-07-15
We introduce a new class of partially coherent sources of Schell type with cosine-Gaussian spectral degree of coherence and confirm that such sources are physically genuine. Further, we derive the expression for the cross-spectral density function of a beam generated by the novel source propagating in free space and analyze the evolution of the spectral density and the spectral degree of coherence. It is shown that at sufficiently large distances from the source the degree of coherence of the propagating beam assumes Gaussian shape while the spectral density takes on the dark-hollow profile.
Ergodicity and Gaussianity for Spherical Random Fields
Marinucci, Domenico
2009-01-01
We investigate the relationship between ergodicity and asymptotic Gaussianity of isotropic spherical random fields, in the high-resolution (or high-frequency) limit. In particular, our results suggest that under a wide variety of circumstances the two conditions are equivalent, i.e. the sample angular power spectrum may converge to the population value if and only if the underlying field is asymptotically Gaussian, in the high frequency sense. These findings may shed some light on the role of Cosmic Variance in Cosmic Microwave Background (CMB) radiation data analysis.
Construction of Capacity Achieving Lattice Gaussian Codes
Alghamdi, Wael
2016-04-01
We propose a new approach to proving results regarding channel coding schemes based on construction-A lattices for the Additive White Gaussian Noise (AWGN) channel that yields new characterizations of the code construction parameters, i.e., the primes and dimensions of the codes, as functions of the block-length. The approach we take introduces an averaging argument that explicitly involves the considered parameters. This averaging argument is applied to a generalized Loeliger ensemble [1] to provide a more practical proof of the existence of AWGN-good lattices, and to characterize suitable parameters for the lattice Gaussian coding scheme proposed by Ling and Belfiore [3].
Quantum information theory with Gaussian systems
Energy Technology Data Exchange (ETDEWEB)
Krueger, O.
2006-04-06
This thesis applies ideas and concepts from quantum information theory to systems of continuous-variables such as the quantum harmonic oscillator. The focus is on three topics: the cloning of coherent states, Gaussian quantum cellular automata and Gaussian private channels. Cloning was investigated both for finite-dimensional and for continuous-variable systems. We construct a private quantum channel for the sequential encryption of coherent states with a classical key, where the key elements have finite precision. For the case of independent one-mode input states, we explicitly estimate this precision, i.e. the number of key bits needed per input state, in terms of these parameters. (orig.)
Measurement-induced disturbances and nonclassical correlations of Gaussian states
Mišta, Ladislav; Tatham, Richard; Girolami, Davide; Korolkova, Natalia; Adesso, Gerardo
2010-01-01
We study quantum correlations beyond entanglement in two--mode Gaussian states of continuous variable systems, by means of the measurement-induced disturbance (MID) and its ameliorated version (AMID). In analogy with the recent studies of the Gaussian quantum discord, we define a Gaussian AMID by constraining the optimization to all bi-local Gaussian positive operator valued measurements. We solve the optimization explicitly for relevant families of states, including squeezed thermal states. Remarkably, we find that there is a finite subset of two--mode Gaussian states, comprising pure states, where non-Gaussian measurements such as photon counting are globally optimal for the AMID and realize a strictly smaller state disturbance compared to the best Gaussian measurements. However, for the majority of two--mode Gaussian states the unoptimized MID provides a loose overestimation of the actual content of quantum correlations, as evidenced by its comparison with Gaussian discord. This feature displays strong sim...
A Gaussian-product stochastic Gent-McWilliams parameterization
Grooms, Ian
2016-10-01
The locally-averaged horizontal buoyancy flux by mesoscale eddies is computed from eddy-resolving quasigeostrophic simulations of ocean-mesoscale eddy dynamics. This flux has a very non-Gaussian distribution peaked at zero, not at the mean value. This non-Gaussian flux distribution arises because the flux is a product of zero-mean random variables: the eddy velocity and buoyancy. A framework for stochastic Gent-McWilliams (GM) parameterization is presented. Gaussian random field models for subgrid-scale velocity and buoyancy are developed. The product of these Gaussian random fields is used to construct a non-Gaussian stochastic parameterization of the horizontal subgrid-scale density flux, which leads to a non-Gaussian stochastic GM parameterization. This new non-Gaussian stochastic GM parameterization is tested in an idealized box ocean model, and compared to a Gaussian approach that simply multiplies the deterministic GM parameterization by a Gaussian random field. The non-Gaussian approach has a significant impact on both the mean and variability of the simulations, more so than the Gaussian approach; for example, the non-Gaussian simulation has a much larger net kinetic energy and a stronger overturning circulation than a comparable Gaussian simulation. Future directions for development of the stochastic GM parameterization and extensions of the Gaussian-product approach are discussed.
Directory of Open Access Journals (Sweden)
Sergey Haitun
2015-06-01
Full Text Available Statistical criteria used today in the analysis of radio signals suspected on reasonable extraterrestrial origin, are based on the assumption that all the radio signals of natural origin are described by a Gaussian distribution, which is traditionally understood as the Gauss distribution. Usually the normal (Gauss distribution is opposed to all the others. However, this is difficult to recognize the reasonable, because in nature there are many different distributions. The article offers a more realistic dichotomy: the Gaussian distributions, obeying the central limiting theorem, dominate in nature, while non-Gaussian ones, obeying the Gnedenko-Doeblin limiting theorem, are generated by intelligent beings. When identifying objects belonging to an extraterrestrial civilization described by a non-Gaussian distribution is preferable to use the rank form distributions. Using this criterion is associated with certain difficulties: (1 in nature there are also non-Gaussian distributions; (2 in their activities animals generate non-Gaussian distributions like humans; (3 the identification of non-Gaussian distributions in the rank form is hampered sometimes by the rank distortion effect of mathematical nature.
Comparison of the Sachs-Wolfe Effect for Gaussian and Non-Gaussian Fluctuations
Kung, J H
1993-01-01
A consequence of non-Gaussian perturbations on the Sachs-Wolfe effect is studied. For a particular power spectrum, predicted Sachs-Wolfe effects are calculated for two cases: Gaussian (random phase) configuration, and a specific kind of non-Gaussian configuration. We obtain a result that the Sachs-Wolfe effect for the latter case is smaller when each temperature fluctuation is properly normalized with respect to the corresponding mass fluctuation ${\\delta M\\over M}(R)$. The physical explanation and the generality of the result are discussed.
Non-Gaussian spectra and the search for cosmic strings
Magueijo, Joao; Lewin, Alex
1997-01-01
We present a new tool for relating theory and experiment suited for non-Gaussian theories: non-Gaussian spectra. It does for non-Gaussian theories what the angular power spectrum $C_\\ell$ does for Gaussian theories. We then show how previous studies of cosmic strings have over rated their non-Gaussian signature. More realistic maps are not visually stringy. However non-Gaussian spectra will accuse their stringiness. We finally summarise the steps of an undergoing experimental project aiming a...
Institute of Scientific and Technical Information of China (English)
Yang-Xiu Jiao; Huan-Yuan Shan; Zu-Hui Fan
2011-01-01
Taking into account the noise from intrinsic ellipticities of source galaxies,we study the efficiency and completeness of halo detections from weak lensing convergence maps. Particularly, with numerical simulations, we compare the Gaussian filter with the so called MRLens treatment based on the modification of the Maximum Entropy Method. For a pure noise field without lensing signals, a Gaussian smoothing results in a residual noise field that is approximately Gaussian in terms of statistics if a large enough number of galaxies are included in the smoothing window. On the other hand, the noise field after the MRLens treatment is significantly non-Gaussian, resulting in complications in characterizing the noise effects. Considering weak-lensing cluster detections, although the MRLens treatment effectively deletes false peaks arising from noise, it removes the real peaks heavily due to its inability to distinguish real signals with relatively low amplitudes from noise in its restoration process. The higher the noise level is, the larger the removal effects are for the real peaks. For a survey with a source density ng ～ 30 arcmin-2, the number of peaks found in an area of 3 × 3 deg2 after MRLens filtering is only ～ 50 for the detection threshold k = 0.02, while the number of halos with M ＞ 5 × 1013 M⊙ and with redshift z ≤ 2 in the same area is expected to be ～ 530. For the Gaussian smoothing treatment, the number of detections is ～ 260, much larger than that of the MRLens. The Gaussianity of the noise statistics in the Gaussian smoothing case adds further advantages for this method to circumvent the problem of the relatively low efficiency in weak-lensing cluster detections.Therefore, in studies aiming to construct large cluster samples from weak-lensing surveys, the Gaussian smoothing method performs significantly better than the MRLens treatment.
Primordial non-Gaussianity in the Bispectrum of the Halo Density Field
Baldauf, Tobias; Senatore, Leonardo
2010-01-01
The bispectrum vanishes for linear Gaussian fields and is thus a sensitive probe of non-linearities and non-Gaussianities in the cosmic density field. Hence, a detection of the bispectrum in the halo density field would enable tight constraints on non-Gaussian processes in the early Universe and allow inference of the dynamics driving inflation. We present a tree level derivation of the halo bispectrum arising from non-linear clustering, non-linear biasing and primordial non-Gaussianity. A diagrammatic description is developed to provide an intuitive understanding of the contributing terms and their dependence on scale, shape and the non-Gaussianity parameter fNL. We compute the terms based on a multivariate bias expansion and the peak-background split method and show that non-Gaussian modifications to the bias parameters lead to amplifications of the tree level bispectrum that were ignored in previous studies. Our results are in a good agreement with published simulation measurements of the halo bispectrum. ...
The Gaussian entropy of fermionic systems
Energy Technology Data Exchange (ETDEWEB)
Prokopec, Tomislav, E-mail: T.Prokopec@uu.nl [Institute for Theoretical Physics (ITP) and Spinoza Institute, Utrecht University, Postbus 80195, 3508 TD Utrecht (Netherlands); Schmidt, Michael G., E-mail: M.G.Schmidt@thphys.uni-heidelberg.de [Institut fuer Theoretische Physik, Heidelberg University, Philosophenweg 16, D-69120 Heidelberg (Germany); Weenink, Jan, E-mail: J.G.Weenink@uu.nl [Institute for Theoretical Physics (ITP) and Spinoza Institute, Utrecht University, Postbus 80195, 3508 TD Utrecht (Netherlands)
2012-12-15
We consider the entropy and decoherence in fermionic quantum systems. By making a Gaussian Ansatz for the density operator of a collection of fermions we study statistical 2-point correlators and express the entropy of a system fermion in terms of these correlators. In a simple case when a set of N thermalised environmental fermionic oscillators interacts bi-linearly with the system fermion we can study its time dependent entropy, which also represents a quantitative measure for decoherence and classicalization. We then consider a relativistic fermionic quantum field theory and take a mass mixing term as a simple model for the Yukawa interaction. It turns out that even in this Gaussian approximation, the fermionic system decoheres quite effectively, such that in a large coupling and high temperature regime the system field approaches the temperature of the environmental fields. - Highlights: Black-Right-Pointing-Pointer We construct the Gaussian density operator for relativistic fermionic systems. Black-Right-Pointing-Pointer The Gaussian entropy of relativistic fermionic systems is described in terms of 2-point correlators. Black-Right-Pointing-Pointer We explicitly show the growth of entropy for fermionic fields mixing with a thermal fermionic environment.
Transitional behavior of quantum Gaussian memory channels
Lupo, C.; Mancini, S.
2010-05-01
We address the question of optimality of entangled input states in quantum Gaussian memory channels. For a class of such channels, which can be traced back to the memoryless setting, we state a criterion which relates the optimality of entangled inputs to the symmetry properties of the channels’ action. Several examples of channel models belonging to this class are discussed.
Modeling text with generalizable Gaussian mixtures
DEFF Research Database (Denmark)
Hansen, Lars Kai; Sigurdsson, Sigurdur; Kolenda, Thomas
2000-01-01
We apply and discuss generalizable Gaussian mixture (GGM) models for text mining. The model automatically adapts model complexity for a given text representation. We show that the generalizability of these models depends on the dimensionality of the representation and the sample size. We discuss...
Non-gaussian CMBR angular power spectra
Magueijo, J
1995-01-01
In this paper we show how the prediction of CMBR angular power spectra C_l in non-Gaussian theories is affected by a cosmic covariance problem, that is (C_l,C_{l'}) correlations impart features on any observed C_l spectrum which are absent from the average C^l spectrum. Therefore the average spectrum is rendered a bad observational prediction, and two new prediction strategies, better adjusted to these theories, are proposed. In one we search for hidden random indices conditional to which the theory is released from the correlations. Contact with experiment can then be made in the form of the conditional power spectra plus the random index distribution. In another approach we apply to the problem a principal component analysis. We discuss the effect of correlations on the predictivity of non-Gaussian theories. We finish by showing how correlations may be crucial in delineating the borderline between predictions made by non-Gaussian and Gaussian theories. In fact, in some particular theories, correlations may ...
How Gaussian can our universe be?
Cabass, Giovanni; Schmidt, Fabian
2016-01-01
Gravity is a non-linear theory, and hence, barring cancellations, the initial super-horizon perturbations produced by inflation must contain some minimum amount of mode coupling, or primordial non-Gaussianity. In single-field slow-roll models, where this lower bound is saturated, non-Gaussianity is controlled by two observables: the tensor-to-scalar ratio, which is uncertain by more than fifty orders of magnitude; and the scalar spectral index, or tilt, which is relatively well measured. It is well known that to leading and next-to-leading order in derivatives, the contributions proportional to the tilt disappear from any local observable, and suspicion has been raised that this might happen to all orders, allowing for an arbitrarily low amount of primordial non-Gaussianity. Employing Conformal Fermi Coordinates, we show explicitly that this is not the case. Instead, a contribution of order the tilt appears in local observables. In summary, the floor of physical primordial non-Gaussianity in our universe has ...
Gaussian mode selection with intracavity diffractive optics
CSIR Research Space (South Africa)
Litvin, IA
2009-10-01
Full Text Available element for mode shaping of a Nd:YAG laser,” Opt. Lett. 19, 108–110 (1994). 4. L. A. Romero, F. M. Dickey, “Lossless laser beam shaping,” J. Opt. Soc. Am. A 13, 751–760 (1996). 5. F. Gori, “Flattened gaussian beams,” Opt. Commun. 107, 335–341 (1994...
Review of Gaussian diffusion-deposition models
Energy Technology Data Exchange (ETDEWEB)
Horst, T.W.
1979-01-01
The assumptions and predictions of several Gaussian diffusion-deposition models are compared. A simple correction to the Chamberlain source depletion model is shown to predict ground-level airborne concentrations and dry deposition fluxes in close agreement with the exact solution of Horst.
How Gaussian can our Universe be?
Cabass, G.; Pajer, E.; Schmidt, F.
2017-01-01
Gravity is a non-linear theory, and hence, barring cancellations, the initial super-horizon perturbations produced by inflation must contain some minimum amount of mode coupling, or primordial non-Gaussianity. In single-field slow-roll models, where this lower bound is saturated, non-Gaussianity is controlled by two observables: the tensor-to-scalar ratio, which is uncertain by more than fifty orders of magnitude; and the scalar spectral index, or tilt, which is relatively well measured. It is well known that to leading and next-to-leading order in derivatives, the contributions proportional to the tilt disappear from any local observable, and suspicion has been raised that this might happen to all orders, allowing for an arbitrarily low amount of primordial non-Gaussianity. Employing Conformal Fermi Coordinates, we show explicitly that this is not the case. Instead, a contribution of order the tilt appears in local observables. In summary, the floor of physical primordial non-Gaussianity in our Universe has a squeezed-limit scaling of kl2/ks2, similar to equilateral and orthogonal shapes, and a dimensionless amplitude of order 0.1 × (ns‑1).
Advanced LIGO: non-Gaussian beams
Energy Technology Data Exchange (ETDEWEB)
D' Ambrosio, Erika [California Institute of Technology, Pasadena, CA (United States); O' Shaugnessy, Richard [California Institute of Technology, Pasadena, CA (United States); Thorne, Kip [California Institute of Technology, Pasadena, CA (United States); Willems, Phil [California Institute of Technology, Pasadena, CA (United States); Strigin, Sergey [Moscow State University, Moscow (Russian Federation); Vyatchanin, Sergey [Moscow State University, Moscow (Russian Federation)
2004-03-07
By using non-Gaussian, flat-topped beams in the advanced gravitational wave interferometers currently being designed, one can reduce the impact on the interferometer sensitivity of a variety of fundamental disturbances (thermoelastic noise, noise in mirror coatings, thermal lensing, etc). This may make beating the standard quantum limit an achievable goal.
Advanced LIGO: non-Gaussian beams
D’Ambrosio, Erika; O’Shaugnessy, Richard; Thorne, Kip; Willems, Phil; Strigin, Sergey; Vyatchanin, Sergey
2004-01-01
By using non-Gaussian, flat-topped beams in the advanced gravitational wave interferometers currently being designed, one can reduce the impact on the interferometer sensitivity of a variety of fundamental disturbances (thermoelastic noise, noise in mirror coatings, thermal lensing, etc). This may make beating the standard quantum limit an achievable goal.
Gaussian vector fields on triangulated surfaces
DEFF Research Database (Denmark)
Ipsen, John H
2016-01-01
proven to be very useful to resolve the complex interplay between in-plane ordering of membranes and membrane conformations. In the present work we have developed a procedure for realistic representations of Gaussian models with in-plane vector degrees of freedoms on a triangulated surface. The method...
Turbo Equalization Using Partial Gaussian Approximation
DEFF Research Database (Denmark)
Zhang, Chuanzong; Wang, Zhongyong; Manchón, Carles Navarro
2016-01-01
returned by the equalizer by using a partial Gaussian approximation (PGA). We exploit the specific structure of the ISI channel model to compute the latter messages from the beliefs obtained using a Kalman smoother/equalizer. Doing so leads to a significant complexity reduction compared to the initial PGA...
Modak, Viraj P.; Wyslouzil, Barbara E.; Singer, Sherwin J.
2016-08-01
The crystal-vapor surface free energy γ is an important physical parameter governing physical processes, such as wetting and adhesion. We explore exact and approximate routes to calculate γ based on cleaving an intact crystal into non-interacting sub-systems with crystal-vapor interfaces. We do this by turning off the interactions, ΔV, between the sub-systems. Using the soft-core scheme for turning off ΔV, we find that the free energy varies smoothly with the coupling parameter λ, and a single thermodynamic integration yields the exact γ. We generate another exact method, and a cumulant expansion for γ by expressing the surface free energy in terms of an average of e-βΔV in the intact crystal. The second cumulant, or Gaussian approximation for γ is surprisingly accurate in most situations, even though we find that the underlying probability distribution for ΔV is clearly not Gaussian. We account for this fact by developing a non-Gaussian theory for γ and find that the difference between the non-Gaussian and Gaussian expressions for γ consist of terms that are negligible in many situations. Exact and approximate methods are applied to the (111) surface of a Lennard-Jones crystal and are also tested for more complex molecular solids, the surface of octane and nonadecane. Alkane surfaces were chosen for study because their crystal-vapor surface free energy has been of particular interest for understanding surface freezing in these systems.
a Distributed Gaussian Discrete Variable Representation
Karabulut, Hasan
In this work a discrete variable representation (DVR) is constructed from a distributed Gaussian basis (DGB). A DGB is a finite or infinite chain of uniformly distributed Gaussians g_{n}(x) = e^{-c^2(x/d-n)^2} where n takes integer values. There are three main parts of this thesis. In the first part (Chapter III) the finite chain distributed Gaussian DVR (Finite Chain DG-DVR) is derived. In order to accomplish this, the distributed Gaussian orthogonal polynomials are introduced. The connection of these polynomials to Stieltjes-Wigert polynomials is shown. The recurrence relation for these orthogonal polynomials is derived. Tested recipes are given to calculate the quadrature points and weights and to construct the corresponding Lagrange functions which are analogs of Lagrange interpolation polynomials. The symmetries of quadrature points, weights, and Lagrange functions are derived. Limit cases ctoinfty and cto 0 are studied. In the second part (Chapter IV)the infinite chain limit DG-DVR is derived from a limit of the finite chain DG-DVR. The quadrature points and weights and the Lagrange functions are found in this limit and kinetic energy operator is constructed. It is shown that in the limit c to 0 the infinite chain DG-DVR reduces to Colbert and Miller's DVR. A discussion of ability of a distributed Gaussian basis to represent an arbitrary function is given. The results of this treatment yield a possible explanation of surprising accuracy of Colbert-Miller DVR. In the third part construction of the DG-DVR is given when one point is chosen arbitrarily. Some interesting identities and integral representations for the b _{n} and sigma_ {n} coefficients that are introduced in the second part are found.
Radial Hilbert transform with Laguerre-Gaussian spatial filters.
Guo, Cheng-Shan; Han, Yu-Jing; Xu, Jian-Bo; Ding, Jianping
2006-05-15
We analyze the point spread function (PSF) of the image processing system for radial Hilbert transform and propose a novel spiral phase filter, called the Laguerre-Gaussian spatial filter (LGSF). Theoretical analysis and real experiments show that the LGSF possesses some advantages in comparison with the conventional spiral phase plate (SPP). For example, the PSF of the imaging system with a LGSF presents smaller suboscillations than that with the conventional SPP, which allows us to realize a radial Hilbert transform for achieving a high contrast edge enhancement with high resolution.
Gaussian Weighted Trajectory Method IV: No Rainbow Effect in Practice
Institute of Scientific and Technical Information of China (English)
L. Bonnet
2009-01-01
The Gaussian weighted trajectory method (GWTM) is a practical implementation of classical S matrix theory (CSMT) in the random phase approximation, CSMT being the first and simplest semi-classical approach of molecular collisions, developped in the early seventies.Though very close in spirit to the purely classical description, GWTM accounts to some extent for the quantization of the different degrees-of-freedom involved in the processes.While CSMT may give diverging final state distributions, in relation to the rainbow effect of elastic scattering theory, GWTM has never led to such a mathematical catastrophe. The goal of the present note is to explain this finding.
Granger causality and transfer entropy are equivalent for Gaussian variables.
Barnett, Lionel; Barrett, Adam B; Seth, Anil K
2009-12-01
Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. Developed originally in the field of econometrics, it has since found application in a broader arena, particularly in neuroscience. More recently transfer entropy, an information-theoretic measure of time-directed information transfer between jointly dependent processes, has gained traction in a similarly wide field. While it has been recognized that the two concepts must be related, the exact relationship has until now not been formally described. Here we show that for Gaussian variables, Granger causality and transfer entropy are entirely equivalent, thus bridging autoregressive and information-theoretic approaches to data-driven causal inference.
Granger causality and transfer entropy are equivalent for Gaussian variables
Barnett, Lionel; Seth, Anil
2009-01-01
Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. Developed originally in the field of econometrics, it has since found application in a broader arena, particularly in neuroscience. More recently transfer entropy, an information-theoretic measure of time-directed information transfer between jointly dependent processes, has gained traction in a similarly wide field. It has always seemed plausible that the two concepts ought to be related. Here we show that for Gaussian variables, Granger causality and transfer entropy are entirely equivalent, thus bridging autoregressive and information-theoretic approaches to data-driven causal inference.
Chaotic time series prediction and additive white Gaussian noise
Energy Technology Data Exchange (ETDEWEB)
Lim, Teck Por [Department of Mathematics, 6M30 Huxley, Imperial College London, 180 Queen' s Gate, London, SW7 2BZ (United Kingdom)]. E-mail: teckpor@gmail.com; Puthusserypady, Sadasivan [Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore 117576 (Singapore)]. E-mail: elespk@nus.edu.sg
2007-06-04
Taken's delay embedding theorem states that a pseudo state-space can be reconstructed from a time series consisting of observations of a chaotic process. However, experimental observations are inevitably corrupted by measurement noise, which can be modelled as Additive White Gaussian Noise (AWGN). This Letter analyses time series prediction in the presence of AWGN using the triangle inequality and the mean of the Nakagami distribution. It is shown that using more delay coordinates than those used by a typical delay embedding can improve prediction accuracy, when the mean magnitude of the input vector dominates the mean magnitude of AWGN.
Gaussian memory in kinematic matrix theory for self-propellers.
Nourhani, Amir; Crespi, Vincent H; Lammert, Paul E
2014-12-01
We extend the kinematic matrix ("kinematrix") formalism [Phys. Rev. E 89, 062304 (2014)], which via simple matrix algebra accesses ensemble properties of self-propellers influenced by uncorrelated noise, to treat Gaussian correlated noises. This extension brings into reach many real-world biological and biomimetic self-propellers for which inertia is significant. Applying the formalism, we analyze in detail ensemble behaviors of a 2D self-propeller with velocity fluctuations and orientation evolution driven by an Ornstein-Uhlenbeck process. On the basis of exact results, a variety of dynamical regimes determined by the inertial, speed-fluctuation, orientational diffusion, and emergent disorientation time scales are delineated and discussed.
Brain tumour classification using Gaussian decomposition and neural networks.
Arizmendi, Carlos; Sierra, Daniel A; Vellido, Alfredo; Romero, Enrique
2011-01-01
The development, implementation and use of computer-based medical decision support systems (MDSS) based on pattern recognition techniques holds the promise of substantially improving the quality of medical practice in diagnostic and prognostic tasks. In this study, the core of a decision support system for brain tumour classification from magnetic resonance spectroscopy (MRS) data is presented. It combines data pre-processing using Gaussian decomposition, dimensionality reduction using moving window with variance analysis, and classification using artificial neural networks (ANN). This combination of techniques is shown to yield high diagnostic classification accuracy in problems concerning diverse brain tumour pathologies, some of which have received little attention in the literature.
The Achievable Distortion Region of Bivariate Gaussian Source on Gaussian Broadcast Channel
Tian, Chao; Shamai, Shlomo
2010-01-01
We provide a complete characterization of the achievable distortion region for the problem of sending a bivariate Gaussian source over bandwidth-matched Gaussian broadcast channels, where each receiver is interested in only one component of the source. This setting naturally generalizes the simple single Gaussian source bandwidth-matched broadcast problem for which the uncoded scheme is known to be optimal. We show that a hybrid scheme can achieve the optimum for the bivariate case, but neither an uncoded scheme alone nor a separation-based scheme alone is sufficient. We further show that in this joint source channel coding setting, the Gaussian setting is the worst scenario among the sources and channel noises with the same covariances.
Cumulant Based Harmonic Retrieval in Mixed Colored Gaussian and Non-Gaussian ARMA Noises
Institute of Scientific and Technical Information of China (English)
LI Shenghong; ZHU Hongwen
2001-01-01
This paper studies the problem of retrieving one-dimensional real harmonic signals in presence of mixed colored Gaussian and non-Gaussian autoregressive moving-average (ARMA) noises, and proposes a new approach to harmonic retrieval. In the approach, Hilbert transform is first used to transform the real noisy observed data into their complex form; and then, some kind of fourth-order cumulant,which is defined particularly, is employed to identify the autoregressive (AR) parameters of the colored non-Gaussian ARMA noise model; after the real noisy observed data are filtered with the identified AR parameters, cumulant based methods can be used to compute the frequencies and the amplitudes of the harmonics. The proposed new approach can be applied to retrieve one-dimensional real harmonic signals in mixed colored Gaussian and non-Gaussian ARMA noises, no matter whether there is quadratic phase coupling or not in the harmonic signals and no matter whether the distribution of the colored non-Gaussian ARMA noise is symmetrical or not. Simulation examples are presented to demonstrate its effectiveness.
CSIR Research Space (South Africa)
Miya, WS
2008-10-01
Full Text Available In this paper, a comparison between Extension Neural Network (ENN), Gaussian Mixture Model (GMM) and Hidden Markov model (HMM) is conducted for bushing condition monitoring. The monitoring process is a two-stage implementation of a classification...
Level density for deformations of the Gaussian orthogonal ensemble
Bertuola, A C; Hussein, M S; Pato, M P; Sargeant, A J
2004-01-01
Formulas are derived for the average level density of deformed, or transition, Gaussian orthogonal random matrix ensembles. After some general considerations about Gaussian ensembles we derive formulas for the average level density for (i) the transition from the Gaussian orthogonal ensemble (GOE) to the Poisson ensemble and (ii) the transition from the GOE to $m$ GOEs.
On the classical capacity of quantum Gaussian channels
Lupo, Cosmo; Pirandola, Stefano; Aniello, Paolo; Mancini, Stefano
2011-02-01
The set of quantum Gaussian channels acting on one bosonic mode can be classified according to the action of the group of Gaussian unitaries. We look for bounds on the classical capacity for channels belonging to such a classification. Lower bounds can be efficiently calculated by restricting the study to Gaussian encodings, for which we provide analytical expressions.
On the classical capacity of quantum Gaussian channels
Lupo, Cosmo; Aniello, Paolo; Mancini, Stefano
2010-01-01
The set of quantum Gaussian channels acting on one bosonic mode can be classified according to the action of the group of Gaussian unitaries. We look for bounds on the classical capacity for channels belonging to such a classification. Lower bounds can be efficiently calculated by restricting to Gaussian encodings, for which we provide analytical expressions.
On the classical capacity of quantum Gaussian channels
Energy Technology Data Exchange (ETDEWEB)
Lupo, Cosmo; Mancini, Stefano [School of Science and Technology, University of Camerino, I-62032 Camerino (Italy); Pirandola, Stefano [Department of Computer Science, University of York, York YO10 5GH (United Kingdom); Aniello, Paolo, E-mail: cosmo.lupo@unicam.it, E-mail: pirs@cs.york.ac.uk, E-mail: paolo.aniello@na.infn.it, E-mail: stefano.mancini@unicam.it [Dipartimento di Scienze Fisiche dell' Universita di Napoli Federico II, Complesso Universitario di Monte Sant' Angelo, Via Cintia, I-80126 Napoli (Italy)
2011-02-15
The set of quantum Gaussian channels acting on one bosonic mode can be classified according to the action of the group of Gaussian unitaries. We look for bounds on the classical capacity for channels belonging to such a classification. Lower bounds can be efficiently calculated by restricting the study to Gaussian encodings, for which we provide analytical expressions.
Linking network usage patterns to traffic Gaussianity fit
Oliveira Schmidt, de Ricardo; Sadre, Ramin; Melnikov, Nikolay; Schönwälder, Jürgen; Pras, Aiko
2014-01-01
Gaussian traffic models are widely used in the domain of network traffic modeling. The central assumption is that traffic aggregates are Gaussian distributed. Due to its importance, the Gaussian character of network traffic has been extensively assessed by researchers in the past years. In 2001, res
Where is the COBE maps' non-Gaussianity?
Magueijo, Joao; Ferreira, Pedro G; Gorski, Krzysztof M.
1999-01-01
We review our recent claim that there is evidence of non-Gaussianity in the 4 Year COBE DMR data. We present some new results concerning the effect of the galactic cut upon the non-Gaussian signal. These findings imply a localization of the non-Gaussian signal on the Northern galactic hemisphere.
Primordial non-Gaussianity from the large scale structure
Desjacques, Vincent
2010-01-01
Primordial non-Gaussianity is a potentially powerful discriminant of the physical mechanisms that generated the cosmological fluctuations observed today. Any detection of non-Gaussianity would have profound implications for our understanding of cosmic structure formation. In this paper, we review past and current efforts in the search for primordial non-Gaussianity in the large scale structure of the Universe.
A feedback control strategy for the airfoil system under non-Gaussian colored noise excitation
Energy Technology Data Exchange (ETDEWEB)
Huang, Yong, E-mail: hy@njust.edu.cn, E-mail: taogang@njust.edu.cn; Tao, Gang, E-mail: hy@njust.edu.cn, E-mail: taogang@njust.edu.cn [School of Energy and Power Engineering, Nanjing University of Science and Technology, 200 XiaoLingwei Street, Nanjing 210094 (China)
2014-09-01
The stability of a binary airfoil with feedback control under stochastic disturbances, a non-Gaussian colored noise, is studied in this paper. First, based on some approximated theories and methods the non-Gaussian colored noise is simplified to an Ornstein-Uhlenbeck process. Furthermore, via the stochastic averaging method and the logarithmic polar transformation, one dimensional diffusion process can be obtained. At last by applying the boundary conditions, the largest Lyapunov exponent which can determine the almost-sure stability of the system and the effective region of control parameters is calculated.
Primordial Non-Gaussianity and Reionization
Lidz, Adam; Adshead, Peter; Dodelson, Scott
2013-01-01
The statistical properties of the primordial perturbations contain clues about the origins of those fluctuations. Although the Planck collaboration has recently obtained tight constraints on primordial non-gaussianity from cosmic microwave background measurements, it is still worthwhile to mine upcoming data sets in effort to place independent or competitive limits. The ionized bubbles that formed at redshift z~6-20 during the Epoch of Reionization are seeded by primordial overdensities, and so the statistics of the ionization field at high redshift are related to the statistics of the primordial field. Here we model the effect of primordial non-gaussianity on the reionization field. The epoch and duration of reionization are affected as are the sizes of the ionized bubbles, but these changes are degenerate with variations in the properties of the ionizing sources and the surrounding intergalactic medium. A more promising signature is the power spectrum of the spatial fluctuations in the ionization field, whi...
Entropic cosmology through non-gaussian statistics
Nunes, Rafael C; Abreu, Everton M C; Neto, Jorge Ananias
2015-01-01
Based on the relationship between thermodynamics and gravity, and with the aid of Verlinde's formalism, we propose an alternative interpretation of the dynamical evolution of the Friedmann-Robertson-Walker Universe, which takes into account the entropy and temperature intrinsic to the horizon of the universe due to the information holographically stored there through non-gaussian statistical theories proposed by Tsallis and Kaniadakis. We use the most recent data of type Ia supernovae, baryon acoustic oscillations, and the Hubble expansion rate function to constrain the free parameters on the $\\Lambda$CDM and $w$CDM models modified by the non-gaussian statistics. We evaluate the problem of age and we note that such modifications solve the problem at 1$\\sigma$ level confidence. Also we analyze the effects on the linear growth of matter density perturbations.
Large non-gaussianity in axion inflation.
Barnaby, Neil; Peloso, Marco
2011-05-06
The inflationary paradigm has enjoyed phenomenological success; however, a compelling particle physics realization is still lacking. Axions are among the best-motivated inflaton candidates, since the flatness of their potential is naturally protected by a shift symmetry. We reconsider the cosmological perturbations in axion inflation, consistently accounting for the coupling to gauge fields cΦFF, which is generically present in these models. This coupling leads to production of gauge quanta, which provide a new source of inflaton fluctuations, δΦ. For c≥10(2)M(p)(-1), these dominate over the vacuum fluctuations, and non-Gaussianity exceeds the current observational bound. This regime is typical for concrete realizations that admit a UV completion; hence, large non-Gaussianity is easily obtained in minimal and natural realizations of inflation.
On Alternate Relaying with Improper Gaussian Signaling
Gaafar, Mohamed
2016-06-06
In this letter, we investigate the potential benefits of adopting improper Gaussian signaling (IGS) in a two-hop alternate relaying (AR) system. Given the known benefits of using IGS in interference-limited networks, we propose to use IGS to relieve the inter-relay interference (IRI) impact on the AR system assuming no channel state information is available at the source. In this regard, we assume that the two relays use IGS and the source uses proper Gaussian signaling (PGS). Then, we optimize the degree of impropriety of the relays signal, measured by the circularity coefficient, to maximize the total achievable rate. Simulation results show that using IGS yields a significant performance improvement over PGS, especially when the first hop is a bottleneck due to weak source-relay channel gains and/or strong IRI.
Bregman Cost for Non-Gaussian Noise
DEFF Research Database (Denmark)
Burger, Martin; Dong, Yiqiu; Sciacchitano, Federica
. From a theoretical point of view it has been argued that the MAP estimate is only in an asymptotic sense a Bayes estimator for the uniform cost function, while the CM estimate is a Bayes estimator for the means squared cost function. Recently, it has been proven that the MAP estimate is a proper Bayes...... estimator for the Bregman cost if the image is corrupted by Gaussian noise. In this work we extend this result to other noise models with log-concave likelihood density, by introducing two related Bregman cost functions for which the CM and the MAP estimates are proper Bayes estima-tors. Moreover, we also...... prove that the CM estimate outperforms the MAP estimate, when the error is measured in a certain Bregman distance, a result previously unknown also in the case of additive Gaussian noise....
The Supervised Learning Gaussian Mixture Model
Institute of Scientific and Technical Information of China (English)
马继涌; 高文
1998-01-01
The traditional Gaussian Mixture Model(GMM)for pattern recognition is an unsupervised learning method.The parameters in the model are derived only by the training samples in one class without taking into account the effect of sample distributions of other classes,hence,its recognition accuracy is not ideal sometimes.This paper introduces an approach for estimating the parameters in GMM in a supervising way.The Supervised Learning Gaussian Mixture Model(SLGMM)improves the recognition accuracy of the GMM.An experimental example has shown its effectiveness.The experimental results have shown that the recognition accuracy derived by the approach is higher than those obtained by the Vector Quantization(VQ)approach,the Radial Basis Function (RBF) network model,the Learning Vector Quantization (LVQ) approach and the GMM.In addition,the training time of the approach is less than that of Multilayer Perceptrom(MLP).
Fock expansion of multimode pure Gaussian states
Energy Technology Data Exchange (ETDEWEB)
Cariolaro, Gianfranco; Pierobon, Gianfranco, E-mail: gianfranco.pierobon@unipd.it [Università di Padova, Padova (Italy)
2015-12-15
The Fock expansion of multimode pure Gaussian states is derived starting from their representation as displaced and squeezed multimode vacuum states. The approach is new and appears to be simpler and more general than previous ones starting from the phase-space representation given by the characteristic or Wigner function. Fock expansion is performed in terms of easily evaluable two-variable Hermite–Kampé de Fériet polynomials. A relatively simple and compact expression for the joint statistical distribution of the photon numbers in the different modes is obtained. In particular, this result enables one to give a simple characterization of separable and entangled states, as shown for two-mode and three-mode Gaussian states.
Quantum fidelity for arbitrary Gaussian states
Banchi, Leonardo; Pirandola, Stefano
2015-01-01
We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can be written in terms of symplectic invariants and used to derive closed forms for a variety of basic quantities and tools, such as the Bures metric, the quantum Fisher information and various fidelity-based bounds. Our result can be used to extend the study of continuous-variable protocols, such as quantum teleportation and cloning, beyond the current one-mode or two-mode analyses, and paves the way to solve general problems in quantum metrology and quantum hypothesis testing with arbitrary multimode Gaussian resources.
Explicit Optimal Hardness via Gaussian stability results
De, Anindya
2012-01-01
The results of Raghavendra (2008) show that assuming Khot's Unique Games Conjecture (2002), for every constraint satisfaction problem there exists a generic semi-definite program that achieves the optimal approximation factor. This result is existential as it does not provide an explicit optimal rounding procedure nor does it allow to calculate exactly the Unique Games hardness of the problem. Obtaining an explicit optimal approximation scheme and the corresponding approximation factor is a difficult challenge for each specific approximation problem. An approach for determining the exact approximation factor and the corresponding optimal rounding was established in the analysis of MAX-CUT (KKMO 2004) and the use of the Invariance Principle (MOO 2005). However, this approach crucially relies on results explicitly proving optimal partitions in Gaussian space. Until recently, Borell's result (Borell 1985) was the only non-trivial Gaussian partition result known. In this paper we derive the first explicit optimal...
Trap split with Laguerre-Gaussian beams
Kazemi, Seyedeh Hamideh; Mahmoud, Mohammad
2016-01-01
The optical trapping techniques have been extensively used in physics, biophysics, micro-chemistry, and micro-mechanics to allow trapping and manipulation of materials ranging from particles, cells, biological substances, and polymers to DNA and RNA molecules. In this Letter, we present a convenient and effective way to generate a novel phenomenon of trapping, named trap split, in a conventional four-level double-$\\Lambda$ atomic system driven by four femtosecond Laguerre-Gaussian laser pulses. We find that trap split can be always achieved when atoms are trapped by such laser pulses, as compared to Gaussian ones. This work would greatly facilitate the trapping and manipulating the particles and generation of trap split. It may also suggest the possibility of extension into new research fields, such as micro-machining and biophysics.