High Dimensional Bayesian Network Classification with Network Global-Local Shrinkage Priors

TL;DR

This paper introduces a Bayesian network classification method using global-local shrinkage priors, effectively identifying influential nodes and edges in high-dimensional brain network data for subject classification.

Contribution

It develops a novel Bayesian logistic regression framework with network-specific priors, enabling accurate node and edge detection and asymptotically optimal classification in high-dimensional settings.

Findings

Accurately detects influential network nodes and edges.

Achieves asymptotically optimal classification performance.

Validated through simulations and brain connectome data analysis.

Abstract

This article proposes a novel Bayesian classification framework for networks with labeled nodes. While literature on statistical modeling of network data typically involves analysis of a single network, the recent emergence of complex data in several biological applications, including brain imaging studies, presents a need to devise a network classifier for subjects. This article considers an application from a brain connectome study, where the overarching goal is to classify subjects into two separate groups based on their brain network data, along with identifying influential regions of interest (ROIs) (referred to as nodes). Existing approaches either treat all edge weights as a long vector or summarize the network information with a few summary measures. Both these approaches ignore the full network structure, may lead to less desirable inference in small samples and are not designed to identify significant network nodes. We propose a novel binary logistic regression framework with the network as the predictor and a binary response, the network predictor coefficient being modeled using a novel class global-local shrinkage priors. The framework is able to accurately detect nodes and edges in the network influencing the classification. Our framework is implemented using an efficient Markov Chain Monte Carlo algorithm. Theoretically, we show asymptotically optimal classification for the proposed framework when the number of network edges grows faster than the sample size. The framework is empirically validated by extensive simulation studies and analysis of a brain connectome data.