12 Scalable Bayesian Estimation of Gaussian Graphical Models

Oregon Convention Center 

Gaussian graphical models (GGMs) encode the conditional independence structure between multivariate normal random variables as zero entries in the precision matrix. They are powerful tools with diverse applications in genetics, portfolio optimization and computational neuroscience. Bayesian approaches have advantages over frequentist methods because they encourage graphs' sparsity, incorporate prior information, and account for uncertainty in the graph structure. However, due to the computational burden of MCMC, scalable Bayesian estimation of GGMs remains an open problem. We propose a novel approach that uses empirical Bayes nodewise regression that allows for efficient estimation of the precision matrix and flexibility in incorporating prior information in large dimensional settings. Empirical Bayes variable selection methods considered in our study include SEMMS, Zellner's g-prior, and nonlocal priors. If necessary, a post-filling model selection step is used to discover the underlying graph. Simulation results show that our Bayesian method compares favorably with competing methods in terms of accuracy metrics and excels in computational speed.

Gaussian graphical model

high-dimensional statistics

network analysis

empirical Bayes

nodewise regression

sparsity 

Section on Bayesian Statistical Science