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We consider the joint inference of regression coefficients and the inversecovariance matrix for covariates in high-dimensional probit regression, wherethe predictors are both relevant to the binary response and functionallyrelated to one another. A hierarchical model with spike and slab priors overregression coefficients and the elements in the inverse covariance matrix isemployed to simultaneously perform variable and graph selection. We establishjoint selection consistency for both the variable and the underlying graph whenthe dimension of predictors is allowed to grow much larger than the samplesize, which is the first theoretical result in the Bayesian literature. Ascalable Gibbs sampler is derived that performs better in high-dimensionalsimulation studies compared with other state-of-art methods. We illustrate thepractical impact and utilities of the proposed method via a functional MRIdataset, where both the regions of interest with altered functional activitiesand the underlying functional brain network are inferred and integratedtogether for stratifying disease risk.

Consistent and scalable Bayesian joint variable and graph selection for disease diagnosis leveraging functional brain network