A0323
Title: Exact Bayesian computation for large Gaussian graphical models
Authors: David Rossell - Universitat Pompeu Fabra (Spain) [presenting]
Jack Jewson - Universitat Pompeu Fabra and Barcelona Graduate School of Economics (Spain)
Deborah Sulem - Barcelona School of Economics (Spain)
Abstract: Bayesian methods possess appealing properties for quantifying the uncertainty associated with learning the dependence structure in a graphical model from data, as well as the uncertainty in parameter estimates. Computational bottlenecks limited their application when the number of variables is large, which prompted the use of pseudo-Bayesian approaches. Computational algorithms are proposed for exact Bayesian inference that provably scale well to high-dimensional settings, when the data-generating precision matrix is sparse. The framework is based on discrete spike-and-slab priors under which, by exploiting sparsity, spectral gaps and the per-iteration cost can be bound. MCMC algorithms are proposed that allow row-wise updates of the precision matrix, either using standard local proposals (e.g., Gibbs, birth-death-swap, LIT) or a novel global proposal that may add/remove multiple edges in one iteration. Examples show that the methods extend the applicability of exact Bayesian inference from roughly 100 to roughly 1,000 variables (equivalently, from 5,000 edges to 500,000 edges, or from $2^5000$ models to $2^500000$ models).
