  Brain networks has attracted the interests of many neuroscientists. From
functional MRI (fMRI) data, statistical tools have been developed to recover
brain networks. However, the dimensionality of whole-brain fMRI, usually in
hundreds of thousands, challenges the applicability of these methods. We
develop a hierarchical graphical model (HGM) to remediate this difficulty. This
model introduces a hidden layer of networks based on sparse Gaussian graphical
models, and the observed data are sampled from individual network nodes. In
fMRI, the network layer models the underlying signals of different brain
functional units, and how these units directly interact with each other. The
introduction of this hierarchical structure not only provides a formal and
interpretable approach, but also enables efficient computation for inferring
big networks with hundreds of thousands of nodes. Based on the conditional
convexity of our formulation, we develop an alternating update algorithm to
compute the HGM model parameters simultaneously. The effectiveness of this
approach is demonstrated on simulated data and a real dataset from a stop/go
fMRI experiment.
