Scalable Bayesian matrix normal graphical models for brain functional networks.

Recently, there has been an explosive growth in graphical modeling approaches for estimating brain functional networks. In a detailed study, we show that surprisingly, standard graphical modeling approaches for fMRI data may not yield accurate estimates of the brain network due to the inability to suitably account for temporal correlations. We propose a novel Bayesian matrix normal graphical model that jointly models the temporal covariance and the brain network under a separable structure for the covariance to obtain improved estimates. The approach is implemented via an efficient optimization algorithm that computes the maximum-a-posteriori network estimates having desirable theoretical properties and which is scalable to high dimensions. The proposed method leads to substantial gains in network estimation accuracy compared to standard brain network modeling approaches as illustrated via extensive simulations. We apply the method to resting state fMRI data from the Human Connectome Project involving a large number of time scans and brain regions, to study the relationships between fluid intelligence and functional connectivity, where it is not computationally feasible to apply existing matrix normal graphical models. Our proposed approach led to the detection of differences in connectivity between high and low fluid intelligence groups, whereas these differences were less pronounced or absent using the graphical lasso.