Bayesian Joint Spike-and-Slab Graphical Lasso
This work addresses the need for improved model selection and shrinkage in graphical models, but it is incremental as it builds on existing regularization procedures.
The authors tackled the problem of Bayesian inference for multiple Gaussian graphical models by proposing a new class of priors that extend group and fused graphical lasso to a continuous spike-and-slab framework, resulting in efficient sparse model selection with substantially smaller bias than alternative methods.
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.