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

Zijian Zeng, Meng Li, Marina Vannucci

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 spikeand-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.