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There is an increasing recognition of the role of brain networks asneuroimaging biomarkers in mental health and psychiatric studies. Our focus isposttraumatic stress disorder (PTSD), where the brain network interacts withenvironmental exposures in complex ways to drive the disease progression.Existing linear models seeking to characterize the relation between theclinical phenotype and the entire edge set in the brain network may be overlysimplistic and often involve inflated number of parameters leading tocomputational burden and inaccurate estimation. In one of the first suchefforts, we develop a novel two stage Bayesian framework to find anode-specific lower dimensional representation for the network using a latentscale approach in the first stage, and then use a flexible Gaussian processregression framework for prediction involving the latent scales and othersupplementary covariates in the second stage. The proposed approach relaxeslinearity assumptions, addresses the curse of dimensionality and is scalable tohigh dimensional networks while maintaining interpretability at the node levelof the network. Extensive simulations and results from our motivating PTSDapplication show a distinct advantage of the proposed approach over competinglinear and non-linear approaches in terms of prediction and coverage.

Semi-parametric Bayes Regression with Network Valued Covariates