Consistent and Scalable Bayesian Joint Variable and Graph Selection for Disease Diagnosis Leveraging Functional Brain Network

• Activity Number: 74 - Invited E-Poster Session I
• Type: Invited
• Date/Time: Sunday, August 7, 2022 : 8:30 PM to 9:25 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Xuan Cao* and Kyoungjae Lee
• Companies: University of Cincinnati and Sungkyunkwan University
• Keywords: Joint selection consistency; Markov random field prior; Parkinson’s disease

Abstract

We consider the joint inference of regression coefficients and the inverse covariance matrix for covariates in high-dimensional probit regression, where the predictors are both relevant to the binary response and functionally related to one another. A hierarchical model with spike and slab priors over regression coefficients and the elements in the inverse covariance matrix is employed to simultaneously perform variable and graph selection. We establish joint selection consistency for both the variable and the underlying graph when the dimension of predictors is allowed to grow much larger than the sample size, which is the first theoretical result in the Bayesian literature. A scalable Gibbs sampler is derived that outperforms other state-of-art methods in high-dimensional settings. We illustrate the practical impact and utilities of the proposed method via a functional MRI dataset, where both the regions of interest with altered functional activities and the underlying functional brain network are inferred and integrated together for stratifying disease risk.