Bayesian Group Selection in Logistic Regression with Application to MRI Data Analysis

TL;DR

This paper introduces a Bayesian hierarchical model with spike and slab priors for high-dimensional logistic regression, demonstrating strong theoretical guarantees and superior performance in simulations and MRI data analysis for Parkinson's disease prediction.

Contribution

It provides the first theoretical proof of Bayesian group selection consistency in logistic regression and shows improved empirical performance over existing methods.

Findings

Achieves strong Bayesian group selection consistency.

Outperforms existing methods in simulation studies.

Successfully applied to MRI data for Parkinson's disease prediction.

Abstract

We consider Bayesian logistic regression models with group-structured covariates. In high-dimensional settings, it is often assumed that only small portion of groups are significant, thus consistent group selection is of significant importance. While consistent frequentist group selection methods have been proposed, theoretical properties of Bayesian group selection methods for logistic regression models have not been investigated yet. In this paper, we consider a hierarchical group spike and slab prior for logistic regression models in high-dimensional settings. Under mild conditions, we establish strong group selection consistency of the induced posterior, which is the first theoretical result in the Bayesian literature. Through simulation studies, we demonstrate that the performance of the proposed method outperforms existing state-of-the-art methods in various settings. We further apply our method to an MRI data set for predicting Parkinson's disease and show its benefits over other contenders.