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

TL;DR

This paper introduces a Bayesian method for joint variable and graph selection in high-dimensional probit regression, effectively identifying relevant predictors and functional brain networks for disease diagnosis.

Contribution

It presents the first theoretical proof of joint selection consistency in Bayesian high-dimensional settings and offers a scalable Gibbs sampler for practical inference.

Findings

Outperforms existing methods in high-dimensional simulations

Successfully identifies disease-related brain regions and networks

Demonstrates utility on functional MRI data for disease stratification

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 performs better in high-dimensional simulation studies compared with other state-of-art methods. 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.