Scaling It Up: Stochastic Search Structure Learning in Graphical Models

Abstract

Gaussian concentration graph models and covariance graph models are two classes of graphical models that are useful for uncovering latent dependence structures among multivariate variables. In the Bayesian literature, graphs are often determined through the use of 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 concentration and covariance graph models. The new approach produces reliable estimates of graphs and efficiently handles problems with hundreds of variables.

Published at http://dx.doi.org/10.1214/14-BA916 in the Bayesian Analysis (http://projecteuclid.org/euclid.ba) by the International Society of Bayesian Analysis (http://bayesian.org/)

References in corpus (5)

• Covariance regularization by thresholding
• Sparse permutation invariant covariance estimation
• Network exploration via the adaptive LASSO and SCAD penalties
• Estimation of a Covariance Matrix with Zeros
• Wishart distributions for decomposable covariance graph models

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