Bayesian Covariate-Dependent Graph Learning with a Dual Group Spike-and-Slab Prior

TL;DR

This paper introduces a novel Bayesian method with a dual group spike-and-slab prior for covariate-dependent graph learning, enabling multi-level selection and improving graph recovery accuracy in heterogeneous data analysis.

Contribution

It proposes a new dual group spike-and-slab prior and a nested inference strategy for multi-level selection in covariate-dependent graph models, along with a tuning-free Gibbs sampler.

Findings

Outperforms existing methods in graph recovery accuracy

Demonstrates practical utility on microbiome data

Provides a scalable, tuning-free inference algorithm

Abstract

Covariate-dependent graph learning has gained increasing interest in the graphical modeling literature for the analysis of heterogeneous data. This task, however, poses challenges to modeling, computational efficiency, and interpretability. The parameter of interest can be naturally represented as a three-dimensional array with elements that can be grouped according to two directions, corresponding to node level and covariate level, respectively. In this article, we propose a novel dual group spike-and-slab prior that enables multi-level selection at covariate-level and node-level, as well as individual (local) level sparsity. We introduce a nested strategy with specific choices to address distinct challenges posed by the various grouping directions. For posterior inference, we develop a tuning-free Gibbs sampler for all parameters, which mitigates the difficulties of parameter tuning often encountered in high-dimensional graphical models and facilitates routine implementation. Through simulation studies, we demonstrate that the proposed model outperforms existing methods in its accuracy of graph recovery. We show the practical utility of our model via an application to microbiome data where we seek to better understand the interactions among microbes as well as how these are affected by relevant covariates.