Hao Wang (University of South Carolina): Scaling It Up: Stochastic Search Structure Learning in Graphical Models

Gaussian concentration graph models and Gaussian covariance graph models are two classes of graphical models useful for uncovering latent dependence structures among multivariate variables. In the Bayesian literature, structure learning of graphs is often achieved by priors over the space of positive definite matrices with fixed zeros, but these methods present daunting computational burdens in large problems. Motivated by the superior computational efficiency of continuous shrinkage priors for regression analysis, we propose a new framework for structure learning that is based on continuous spike and slab priors and uses latent variables to identify graphs. We discuss model specification, computation, and inference for both covariance graph models and concentration graph models. The new approach produces reliable estimates of graphs and efficiently handles problems of hundreds of variables.