Joint Learning of Full-structure Noise in Hierarchical Bayesian Regression Models

We consider the reconstruction of brain activity from electroencephalography (EEG). This inverse problem can be formulated as a linear regression with independent Gaussian scale mixture priors for both the source and noise components. Crucial factors influencing the accuracy of the source estimation...

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Veröffentlicht in:	IEEE transactions on medical imaging Jg. 43; H. 2; S. 1
Hauptverfasser:	Hashemi, Ali, Cai, Chang, Gao, Yijing, Ghosh, Sanjay, Muller, Klaus-Robert, Nagarajan, Srikantan S., Haufe, Stefan
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	United States IEEE 01.02.2024 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Algorithms Bayes methods Bayes Theorem Bayesian analysis Brain modeling Computer Simulation Covariance matrices Covariance matrix EEG EEG/MEG Brain Source Imaging Electroencephalography Electroencephalography - methods Gaussian noise Hierarchical Bayesian Learning Imaging Inverse problems Machine learning Magnetoencephalography - methods Majorization Minimization Manifolds Mathematical models Noise levels Observational learning Random noise Regression analysis Regression models Sparse Bayesian Learning Type-II Maximum-Likelihood
ISSN:	0278-0062, 1558-254X, 1558-254X
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Abstract	We consider the reconstruction of brain activity from electroencephalography (EEG). This inverse problem can be formulated as a linear regression with independent Gaussian scale mixture priors for both the source and noise components. Crucial factors influencing the accuracy of the source estimation are not only the noise level but also its correlation structure, but existing approaches have not addressed the estimation of noise covariance matrices with full structure. To address this shortcoming, we develop hierarchical Bayesian (type-II maximum likelihood) models for observations with latent variables for source and noise, which are estimated jointly from data. As an extension to classical sparse Bayesian learning (SBL), where across-sensor observations are assumed to be independent and identically distributed, we consider Gaussian noise with full covariance structure. Using the majorization-maximization framework and Riemannian geometry, we derive an efficient algorithm for updating the noise covariance along the manifold of positive definite matrices. We demonstrate that our algorithm has guaranteed and fast convergence and validate it in simulations and with real MEG data. Our results demonstrate that the novel framework significantly improves upon state-of-the-art techniques in the real-world scenario where the noise is indeed non-diagonal and fullstructured. Our method has applications in many domains beyond biomagnetic inverse problems.
AbstractList	We consider the reconstruction of brain activity from electroencephalography (EEG). This inverse problem can be formulated as a linear regression with independent Gaussian scale mixture priors for both the source and noise components. Crucial factors influencing the accuracy of the source estimation are not only the noise level but also its correlation structure, but existing approaches have not addressed the estimation of noise covariance matrices with full structure. To address this shortcoming, we develop hierarchical Bayesian (type-II maximum likelihood) models for observations with latent variables for source and noise, which are estimated jointly from data. As an extension to classical sparse Bayesian learning (SBL), where across-sensor observations are assumed to be independent and identically distributed, we consider Gaussian noise with full covariance structure. Using the majorization-maximization framework and Riemannian geometry, we derive an efficient algorithm for updating the noise covariance along the manifold of positive definite matrices. We demonstrate that our algorithm has guaranteed and fast convergence and validate it in simulations and with real MEG data. Our results demonstrate that the novel framework significantly improves upon state-of-the-art techniques in the real-world scenario where the noise is indeed non-diagonal and fullstructured. Our method has applications in many domains beyond biomagnetic inverse problems. We consider the reconstruction of brain activity from electroencephalography (EEG). This inverse problem can be formulated as a linear regression with independent Gaussian scale mixture priors for both the source and noise components. Crucial factors influencing the accuracy of the source estimation are not only the noise level but also its correlation structure, but existing approaches have not addressed the estimation of noise covariance matrices with full structure. To address this shortcoming, we develop hierarchical Bayesian (type-II maximum likelihood) models for observations with latent variables for source and noise, which are estimated jointly from data. As an extension to classical sparse Bayesian learning (SBL), where acrosssensor observations are assumed to be independent and identically distributed, we consider Gaussian noise with full covariance structure. Using the majorization-maximization framework and Riemannian geometry, we derive an efficient algorithm for updating the noise covariance along the manifold of positive definite matrices. We demonstrate that our algorithm has guaranteed and fast convergence and validate it in simulations and with real MEG data. Our results demonstrate that the novel framework significantly improves upon state-of-the-art techniques in the real-world scenario where the noise is indeed non-diagonal and full-structured. Our method has applications in many domains beyond biomagnetic inverse problems. We consider the reconstruction of brain activity from electroencephalography (EEG). This inverse problem can be formulated as a linear regression with independent Gaussian scale mixture priors for both the source and noise components. Crucial factors influencing the accuracy of the source estimation are not only the noise level but also its correlation structure, but existing approaches have not addressed the estimation of noise covariance matrices with full structure. To address this shortcoming, we develop hierarchical Bayesian (type-II maximum likelihood) models for observations with latent variables for source and noise, which are estimated jointly from data. As an extension to classical sparse Bayesian learning (SBL), where across-sensor observations are assumed to be independent and identically distributed, we consider Gaussian noise with full covariance structure. Using the majorization-maximization framework and Riemannian geometry, we derive an efficient algorithm for updating the noise covariance along the manifold of positive definite matrices. We demonstrate that our algorithm has guaranteed and fast convergence and validate it in simulations and with real MEG data. Our results demonstrate that the novel framework significantly improves upon state-of-the-art techniques in the real-world scenario where the noise is indeed non-diagonal and full-structured. Our method has applications in many domains beyond biomagnetic inverse problems. We consider the reconstruction of brain activity from electroencephalography (EEG). This inverse problem can be formulated as a linear regression with independent Gaussian scale mixture priors for both the source and noise components. Crucial factors influencing the accuracy of the source estimation are not only the noise level but also its correlation structure, but existing approaches have not addressed the estimation of noise covariance matrices with full structure. To address this shortcoming, we develop hierarchical Bayesian (type-II maximum likelihood) models for observations with latent variables for source and noise, which are estimated jointly from data. As an extension to classical sparse Bayesian learning (SBL), where across-sensor observations are assumed to be independent and identically distributed, we consider Gaussian noise with full covariance structure. Using the majorization-maximization framework and Riemannian geometry, we derive an efficient algorithm for updating the noise covariance along the manifold of positive definite matrices. We demonstrate that our algorithm has guaranteed and fast convergence and validate it in simulations and with real MEG data. Our results demonstrate that the novel framework significantly improves upon state-of-the-art techniques in the real-world scenario where the noise is indeed non-diagonal and full-structured. Our method has applications in many domains beyond biomagnetic inverse problems.We consider the reconstruction of brain activity from electroencephalography (EEG). This inverse problem can be formulated as a linear regression with independent Gaussian scale mixture priors for both the source and noise components. Crucial factors influencing the accuracy of the source estimation are not only the noise level but also its correlation structure, but existing approaches have not addressed the estimation of noise covariance matrices with full structure. To address this shortcoming, we develop hierarchical Bayesian (type-II maximum likelihood) models for observations with latent variables for source and noise, which are estimated jointly from data. As an extension to classical sparse Bayesian learning (SBL), where across-sensor observations are assumed to be independent and identically distributed, we consider Gaussian noise with full covariance structure. Using the majorization-maximization framework and Riemannian geometry, we derive an efficient algorithm for updating the noise covariance along the manifold of positive definite matrices. We demonstrate that our algorithm has guaranteed and fast convergence and validate it in simulations and with real MEG data. Our results demonstrate that the novel framework significantly improves upon state-of-the-art techniques in the real-world scenario where the noise is indeed non-diagonal and full-structured. Our method has applications in many domains beyond biomagnetic inverse problems.
Author	Gao, Yijing Muller, Klaus-Robert Nagarajan, Srikantan S. Cai, Chang Ghosh, Sanjay Hashemi, Ali Haufe, Stefan
Author_xml	– sequence: 1 givenname: Ali orcidid: 0000-0003-4957-4630 surname: Hashemi fullname: Hashemi, Ali organization: Uncertainty, Inverse Modeling and Machine Learning Group, Technische Universität Berlin, Germany – sequence: 2 givenname: Chang orcidid: 0000-0003-1082-3388 surname: Cai fullname: Cai, Chang organization: Department of Radiology and Biomedical Imaging, University of California, San Francisco, CA, USA – sequence: 3 givenname: Yijing surname: Gao fullname: Gao, Yijing organization: Department of Radiology and Biomedical Imaging, University of California, San Francisco, CA, USA – sequence: 4 givenname: Sanjay orcidid: 0000-0002-0474-5072 surname: Ghosh fullname: Ghosh, Sanjay organization: Department of Radiology and Biomedical Imaging, University of California, San Francisco, CA, USA – sequence: 5 givenname: Klaus-Robert orcidid: 0000-0002-3861-7685 surname: Muller fullname: Muller, Klaus-Robert organization: Machine Learning Group, Technische Universität Berlin, Germany – sequence: 6 givenname: Srikantan S. orcidid: 0000-0001-7209-3857 surname: Nagarajan fullname: Nagarajan, Srikantan S. organization: Department of Radiology and Biomedical Imaging, University of California, San Francisco, CA, USA – sequence: 7 givenname: Stefan surname: Haufe fullname: Haufe, Stefan organization: Uncertainty, Inverse Modeling and Machine Learning Group, Technische Universität Berlin, Germany
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Snippet	We consider the reconstruction of brain activity from electroencephalography (EEG). This inverse problem can be formulated as a linear regression with...
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SubjectTerms	Algorithms Bayes methods Bayes Theorem Bayesian analysis Brain modeling Computer Simulation Covariance matrices Covariance matrix EEG EEG/MEG Brain Source Imaging Electroencephalography Electroencephalography - methods Gaussian noise Hierarchical Bayesian Learning Imaging Inverse problems Machine learning Magnetoencephalography - methods Majorization Minimization Manifolds Mathematical models Noise levels Observational learning Random noise Regression analysis Regression models Sparse Bayesian Learning Type-II Maximum-Likelihood
Title	Joint Learning of Full-structure Noise in Hierarchical Bayesian Regression Models
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