Empirical Bayesian localization of event-related time-frequency neural activity dynamics

Cai, Chang; Hinkley, Leighton B.; Gao, Yijing; Hashemi, Ali; Haufe, Stefan; Sekihara, Kensuke; Nagarajan, Srikantan S.

doi:10.1016/j.neuroimage.2022.119369

Cited by 3 publications

(1 citation statement)

References 55 publications

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“…Furthermore, in contrast to these Type-I likelihood estimation methods, FUN is a Type-II method, which learns the prior source distribution as part of the model fitting. Type-II methods have been reported to yield results that are consistently superior to those of Type-I methods [8], [9], [46], [47], [59]. Our numerical results show that the same holds also for FUN learning, which performs on par or better than existing variants from the Type-II family (including conventional Champagne) in this study.…”

Section: Discussionsupporting

confidence: 76%

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

Hashemi

Cai

Gao

et al. 2021

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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 accuracy of source estimation are not only the noise level but also its correlation structure, but existing approaches have not addressed 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 fully-structured. Our method has applications in many domains beyond biomagnetic inverse problems.

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