The Experts below are selected from a list of 300 Experts worldwide ranked by ideXlab platform
Giuseppe Notarstefano - One of the best experts on this subject based on the ideXlab platform.
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An Empirical Bayes Approach for Distributed Estimation of Spatial Fields
arXiv: Systems and Control, 2018Co-Authors: Francesco Sasso, Angelo Coluccia, Giuseppe NotarstefanoAbstract:In this paper we consider a network of spatially distributed sensors which collect measurement samples of a spatial field, and aim at estimating in a distributed way (without any central coordinator) the entire field by suitably fusing all network data. We propose a general probabilistic model that can handle both partial knowledge of the physics generating the spatial field as well as a purely data-driven inference. Specifically, we adopt an Empirical Bayes Approach in which the spatial field is modeled as a Gaussian Process, whose mean function is described by means of parametrized equations. We characterize the Empirical Bayes estimator when nodes are heterogeneous, i.e., perform a different number of measurements. Moreover, by exploiting the sparsity of both the covariance and the (parametrized) mean function of the Gaussian Process, we are able to design a distributed spatial field estimator. We corroborate the theoretical results with two numerical simulations: a stationary temperature field estimation in which the field is described by a partial differential (heat) equation, and a data driven inference in which the mean is parametrized by a cubic spline.
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ECC - An Empirical Bayes Approach for Distributed Estimation of Spatial Fields
2018 European Control Conference (ECC), 2018Co-Authors: Francesco Sasso, Angelo Coluccia, Giuseppe NotarstefanoAbstract:In this paper we consider a network of spatially distributed sensors which collect measurement samples of a spatial field, and aim at estimating in a distributed way (without any central coordinator) the entire field by suitably fusing all network data. We propose a general probabilistic model that can handle both partial knowledge of the physics generating the spatial field as well as a purely data-driven inference. Specifically, we adopt an Empirical Bayes Approach in which the spatial field is modeled as a Gaussian Process, whose mean function isdescribed by means of parametrized equations. We characterize the Empirical Bayes estimator when nodes are heterogeneous, i.e., perform a different number of measurements. Moreover, by exploiting the sparsity of both the covariance and the (parametrized) mean function of the Gaussian Process, we are able to design a distributed spatial field estimator. We corroborate the theoretical results with two numerical simulations: a stationary temperature field estimation in which the field is described by a partial differential (heat) equation, and a data driven inference in which the mean is parametrized by a cubic spline.
Arne Leijon - One of the best experts on this subject based on the ideXlab platform.
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a variational Bayes Approach to the underdetermined blind source separation with automatic determination of the number of sources
International Conference on Acoustics Speech and Signal Processing, 2012Co-Authors: Jalil Taghia, Nasser Mohammadiha, Arne LeijonAbstract:In this paper, we propose a variational Bayes Approach to the underdetermined blind source separation and show how a variational treatment can open up the possibility of determining the actual number of sources. The procedure is performed in a frequency bin-wise manner. In every frequency bin, we model the time-frequency mixture by a variational mixture of Gaussians with a circular-symmetric complex-Gaussian density function. In the Bayesian inference, we consider appropriate conjugate prior distributions for modeling the parameters of this distribution. The learning task consists of estimating the hyper-parameters characterizing the parameter distributions for the optimization of the variational posterior distribution. The proposed Approach requires no prior knowledge on the number of sources in a mixture.
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ICASSP - A variational Bayes Approach to the underdetermined blind source separation with automatic determination of the number of sources
2012 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2012Co-Authors: Jalil Taghia, Nasser Mohammadiha, Arne LeijonAbstract:In this paper, we propose a variational Bayes Approach to the underdetermined blind source separation and show how a variational treatment can open up the possibility of determining the actual number of sources. The procedure is performed in a frequency bin-wise manner. In every frequency bin, we model the time-frequency mixture by a variational mixture of Gaussians with a circular-symmetric complex-Gaussian density function. In the Bayesian inference, we consider appropriate conjugate prior distributions for modeling the parameters of this distribution. The learning task consists of estimating the hyper-parameters characterizing the parameter distributions for the optimization of the variational posterior distribution. The proposed Approach requires no prior knowledge on the number of sources in a mixture.
Theofanis Sapatinas - One of the best experts on this subject based on the ideXlab platform.
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EMPIRICAL Bayes Approach TO WAVELET REGRESSION USING ε-CONTAMINATED PRIORS
Journal of Statistical Computation and Simulation, 2004Co-Authors: Claudia Angelini, Theofanis SapatinasAbstract:We consider an empirical Bayes Approach to standard nonparametric regression estimation using a nonlinear wavelet methodology. Instead of specifying a single prior distribution on the parameter space of wavelet coefficients, which is usually the case in the existing literature, we elicit the e-contamination class of prior distributions that is particularly attractive to work with when one seeks robust priors in Bayesian analysis. The type II maximum likelihood Approach to prior selection is used by maximizing the predictive distribution for the data in the wavelet domain over a suitable subclass of the e-contamination class of prior distributions. For the prior selected, the posterior mean yields a thresholding procedure which depends on one free prior parameter and it is level- and amplitude-dependent, thus allowing better adaptation in function estimation. We consider an automatic choice of the free prior parameter, guided by considerations on an exact risk analysis and on the shape of the thresholding rule, enabling the resulting estimator to be fully automated in practice. We also compute pointwise Bayesian credible intervals for the resulting function estimate using a simulation-based Approach. We use several simulated examples to illustrate the performance of the proposed empirical Bayes term-by-term wavelet scheme, and we make comparisons with other classical and empirical Bayes term-by-term wavelet schemes. As a practical illustration, we present an application to a real-life data set that was collected in an atomic force microscopy study.
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empirical Bayes Approach to block wavelet function estimation
Computational Statistics & Data Analysis, 2002Co-Authors: Felix Abramovich, Panagiotis Besbeas, Theofanis SapatinasAbstract:Wavelet methods have demonstrated considerable success in function estimation through term-by-term thresholding of the empirical wavelet coefficients. However, it has been shown that grouping the empirical wavelet coefficients into blocks and making simultaneous threshold decisions about all the coefficients in each block has a number of advantages over term-by-term wavelet thresholding, including asymptotic optimality and better mean squared error performance in finite sample situations. An empirical Bayes Approach to incorporating information on neighbouring empirical wavelet coefficients into function estimation that results in block wavelet shrinkage and block wavelet thresholding estimators is considered. Simulated examples are used to illustrate the performance of the resulting estimators, and to compare these estimators with several existing non-Bayesian block wavelet thresholding estimators. It is observed that the proposed empirical Bayes block wavelet shrinkage and block wavelet thresholding estimators outperform the non-Bayesian block wavelet thresholding estimators in finite sample situations. An application to a data set that was collected in an anaesthesiological study is also presented.
Francesco Sasso - One of the best experts on this subject based on the ideXlab platform.
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An Empirical Bayes Approach for Distributed Estimation of Spatial Fields
arXiv: Systems and Control, 2018Co-Authors: Francesco Sasso, Angelo Coluccia, Giuseppe NotarstefanoAbstract:In this paper we consider a network of spatially distributed sensors which collect measurement samples of a spatial field, and aim at estimating in a distributed way (without any central coordinator) the entire field by suitably fusing all network data. We propose a general probabilistic model that can handle both partial knowledge of the physics generating the spatial field as well as a purely data-driven inference. Specifically, we adopt an Empirical Bayes Approach in which the spatial field is modeled as a Gaussian Process, whose mean function is described by means of parametrized equations. We characterize the Empirical Bayes estimator when nodes are heterogeneous, i.e., perform a different number of measurements. Moreover, by exploiting the sparsity of both the covariance and the (parametrized) mean function of the Gaussian Process, we are able to design a distributed spatial field estimator. We corroborate the theoretical results with two numerical simulations: a stationary temperature field estimation in which the field is described by a partial differential (heat) equation, and a data driven inference in which the mean is parametrized by a cubic spline.
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ECC - An Empirical Bayes Approach for Distributed Estimation of Spatial Fields
2018 European Control Conference (ECC), 2018Co-Authors: Francesco Sasso, Angelo Coluccia, Giuseppe NotarstefanoAbstract:In this paper we consider a network of spatially distributed sensors which collect measurement samples of a spatial field, and aim at estimating in a distributed way (without any central coordinator) the entire field by suitably fusing all network data. We propose a general probabilistic model that can handle both partial knowledge of the physics generating the spatial field as well as a purely data-driven inference. Specifically, we adopt an Empirical Bayes Approach in which the spatial field is modeled as a Gaussian Process, whose mean function isdescribed by means of parametrized equations. We characterize the Empirical Bayes estimator when nodes are heterogeneous, i.e., perform a different number of measurements. Moreover, by exploiting the sparsity of both the covariance and the (parametrized) mean function of the Gaussian Process, we are able to design a distributed spatial field estimator. We corroborate the theoretical results with two numerical simulations: a stationary temperature field estimation in which the field is described by a partial differential (heat) equation, and a data driven inference in which the mean is parametrized by a cubic spline.
Jalil Taghia - One of the best experts on this subject based on the ideXlab platform.
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a variational Bayes Approach to the underdetermined blind source separation with automatic determination of the number of sources
International Conference on Acoustics Speech and Signal Processing, 2012Co-Authors: Jalil Taghia, Nasser Mohammadiha, Arne LeijonAbstract:In this paper, we propose a variational Bayes Approach to the underdetermined blind source separation and show how a variational treatment can open up the possibility of determining the actual number of sources. The procedure is performed in a frequency bin-wise manner. In every frequency bin, we model the time-frequency mixture by a variational mixture of Gaussians with a circular-symmetric complex-Gaussian density function. In the Bayesian inference, we consider appropriate conjugate prior distributions for modeling the parameters of this distribution. The learning task consists of estimating the hyper-parameters characterizing the parameter distributions for the optimization of the variational posterior distribution. The proposed Approach requires no prior knowledge on the number of sources in a mixture.
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ICASSP - A variational Bayes Approach to the underdetermined blind source separation with automatic determination of the number of sources
2012 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2012Co-Authors: Jalil Taghia, Nasser Mohammadiha, Arne LeijonAbstract:In this paper, we propose a variational Bayes Approach to the underdetermined blind source separation and show how a variational treatment can open up the possibility of determining the actual number of sources. The procedure is performed in a frequency bin-wise manner. In every frequency bin, we model the time-frequency mixture by a variational mixture of Gaussians with a circular-symmetric complex-Gaussian density function. In the Bayesian inference, we consider appropriate conjugate prior distributions for modeling the parameters of this distribution. The learning task consists of estimating the hyper-parameters characterizing the parameter distributions for the optimization of the variational posterior distribution. The proposed Approach requires no prior knowledge on the number of sources in a mixture.
