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Brain networks has attracted the interests of many neuroscientists. Fromfunctional MRI (fMRI) data, statistical tools have been developed to recoverbrain networks. However, the dimensionality of whole-brain fMRI, usually inhundreds of thousands, challenges the applicability of these methods. Wedevelop a hierarchical graphical model (HGM) to remediate this difficulty. Thismodel introduces a hidden layer of networks based on sparse Gaussian graphicalmodels, and the observed data are sampled from individual network nodes. InfMRI, the network layer models the underlying signals of different brainfunctional units, and how these units directly interact with each other. Theintroduction of this hierarchical structure not only provides a formal andinterpretable approach, but also enables efficient computation for inferringbig networks with hundreds of thousands of nodes. Based on the conditionalconvexity of our formulation, we develop an alternating update algorithm tocompute the HGM model parameters simultaneously. The effectiveness of thisapproach is demonstrated on simulated data and a real dataset from a stop/gofMRI experiment.

A Hierarchical Graphical Model for Big Inverse Covariance Estimation with an Application to fMRI