# Efficient Hierarchical Bayesian Inference for Spatio-temporal Regression Models in Neuroimaging

arXiv: https://arxiv.org/abs/2111.01692 · HTML: https://mlsanity.com/paper/2111.01692/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 114 references that are in the map.
- First posted on arXiv 2 Nov 2021.

## Builds on (most cited first, 21 of 21)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [A Review of Convolutional Neural Networks for Inverse Problems in Imaging](https://mlsanity.com/paper/1710.04011/) (2017)
- [A Unified Framework for Structured Graph Learning via Spectral Constraints](https://mlsanity.com/paper/1904.09792/) (2019)
- [Learning The Invisible: A Hybrid Deep Learning-Shearlet Framework for Limited Angle Computed Tomography](https://mlsanity.com/paper/1811.04602/) (2018)
- [Geometric Mean Metric Learning](https://mlsanity.com/paper/1607.05002/) (2016)
- [Covariance Estimation in High Dimensions via Kronecker Product Expansions](https://mlsanity.com/paper/1302.2686/) (2013)
- [Geodesic Convex Optimization: Differentiation on Manifolds, Geodesics, and Convexity](https://mlsanity.com/paper/1806.06373/) (2018)
- [Robust Estimation of Structured Covariance Matrix for Heavy-Tailed Elliptical Distributions](https://mlsanity.com/paper/1506.05215/) (2015)
- [A Proximal Approach for a Class of Matrix Optimization Problems](https://mlsanity.com/paper/1801.07452/) (2018)
- [Shrinking the eigenvalues of M-estimators of covariance matrix](https://mlsanity.com/paper/2006.10005/) (2020)
- [Statistical control for spatio-temporal MEG/EEG source imaging with desparsified multi-task Lasso](https://mlsanity.com/paper/2009.14310/) (2020)
- [Channel Vector Subspace Estimation from Low-Dimensional Projections](https://mlsanity.com/paper/1509.07469/) (2015)
- [Generalized Concomitant Multi-Task Lasso for sparse multimodal regression](https://mlsanity.com/paper/1705.09778/) (2017)
- [Structured Channel Covariance Estimation from Limited Samples in Massive MIMO](https://mlsanity.com/paper/1910.14467/) (2019)
- [Dependent relevance determination for smooth and structured sparse regression](https://mlsanity.com/paper/1711.10058/) (2017)
- [Bayesian fusion and multimodal DCM for EEG and fMRI](https://mlsanity.com/paper/1906.07354/) (2019)
- [Incorporating structured assumptions with probabilistic graphical models in fMRI data analysis](https://mlsanity.com/paper/2005.04879/) (2020)
- [Spectral independent component analysis with noise modeling for M/EEG source separation](https://mlsanity.com/paper/2008.09693/) (2020)
- [Regularizing Solutions to the MEG Inverse Problem Using Space-Time Separable Covariance Functions](https://mlsanity.com/paper/1604.04931/) (2016)
- [Thermal Source Localization Through Infinite-Dimensional Compressed Sensing](https://mlsanity.com/paper/1710.02016/) (2017)
- [Matrix-normal models for fMRI analysis](https://mlsanity.com/paper/1711.03058/) (2017)

## Built on by (most cited first, 3 of 3)

- [Introducing Block-Toeplitz Covariance Matrices to Remaster Linear Discriminant Analysis for Event-related Potential Brain-computer Interfaces](https://mlsanity.com/paper/2202.02001/) (2022)
- [Structure-Preserving Correction Learning for Sparse Bayesian Inference in Brain Source Imaging](https://mlsanity.com/paper/2606.07196/) (2026)
- [Bayesian Inference of Psychometric Variables From Brain and Behavior in Implicit Association Tests](https://mlsanity.com/paper/2603.16741/) (2026)

## Abstract (arXiv)

Several problems in neuroimaging and beyond require inference on the parameters of multi-task sparse hierarchical regression models. Examples include M/EEG inverse problems, neural encoding models for task-based fMRI analyses, and climate science. In these domains, both the model parameters to be inferred and the measurement noise may exhibit a complex spatio-temporal structure. Existing work either neglects the temporal structure or leads to computationally demanding inference schemes. Overcoming these limitations, we devise a novel flexible hierarchical Bayesian framework within which the spatio-temporal dynamics of model parameters and noise are modeled to have Kronecker product covariance structure. Inference in our framework is based on majorization-minimization optimization and has guaranteed convergence properties. Our highly efficient algorithms exploit the intrinsic Riemannian geometry of temporal autocovariance matrices. For stationary dynamics described by Toeplitz matrices, the theory of circulant embeddings is employed. We prove convex bounding properties and derive update rules of the resulting algorithms. On both synthetic and real neural data from M/EEG, we demonstrate that our methods lead to improved performance.