  There is an increasing recognition of the role of brain networks as
neuroimaging biomarkers in mental health and psychiatric studies. Our focus is
posttraumatic stress disorder (PTSD), where the brain network interacts with
environmental exposures in complex ways to drive the disease progression.
Existing linear models seeking to characterize the relation between the
clinical phenotype and the entire edge set in the brain network may be overly
simplistic and often involve inflated number of parameters leading to
computational burden and inaccurate estimation. In one of the first such
efforts, we develop a novel two stage Bayesian framework to find a
node-specific lower dimensional representation for the network using a latent
scale approach in the first stage, and then use a flexible Gaussian process
regression framework for prediction involving the latent scales and other
supplementary covariates in the second stage. The proposed approach relaxes
linearity assumptions, addresses the curse of dimensionality and is scalable to
high dimensional networks while maintaining interpretability at the node level
of the network. Extensive simulations and results from our motivating PTSD
application show a distinct advantage of the proposed approach over competing
linear and non-linear approaches in terms of prediction and coverage.
