Bayesian Joint Spike-and-Slab Graphical Lasso

TL;DR

This paper introduces a Bayesian framework with spike-and-slab priors for Gaussian graphical models, enabling adaptive model selection and sparse estimation with improved bias performance, demonstrated through simulations and real data.

Contribution

It extends group and fused graphical lasso methods to a Bayesian spike-and-slab framework with an efficient EM algorithm for model selection.

Findings

Efficient sparse model selection with reduced bias.

Superior performance demonstrated in simulations.

Effective application to real data examples.

Abstract

In this article, we propose a new class of priors for Bayesian inference with multiple Gaussian graphical models. We introduce fully Bayesian treatments of two popular procedures, the group graphical lasso and the fused graphical lasso, and extend them to a continuous spike-and-slab framework to allow self-adaptive shrinkage and model selection simultaneously. We develop an EM algorithm that performs fast and dynamic explorations of posterior modes. Our approach selects sparse models efficiently with substantially smaller bias than would be induced by alternative regularization procedures. The performance of the proposed methods are demonstrated through simulation and two real data examples.