An empirical Bayes procedure for the selection of Gaussian graphical models

TL;DR

This paper introduces an empirical Bayes method for selecting Gaussian graphical models, utilizing a data-driven approach to hyper-parameter estimation and a novel MCMC sampling scheme, demonstrated on simulated and real data.

Contribution

It proposes an empirical Bayes strategy with a new MCMC sampling scheme for better model selection in Gaussian graphical models.

Findings

Efficient hyper-parameter estimation via MCMC-SAEM algorithm.

Improved graph sampling scheme enhances model selection.

Method performs well on simulated and real datasets.

Abstract

A new methodology for model determination in decomposable graphical Gaussian models is developed. The Bayesian paradigm is used and, for each given graph, a hyper inverse Wishart prior distribution on the covariance matrix is considered. This prior distribution depends on hyper-parameters. It is well-known that the models's posterior distribution is sensitive to the specification of these hyper-parameters and no completely satisfactory method is registered. In order to avoid this problem, we suggest adopting an empirical Bayes strategy, that is a strategy for which the values of the hyper-parameters are determined using the data. Typically, the hyper-parameters are fixed to their maximum likelihood estimations. In order to calculate these maximum likelihood estimations, we suggest a Markov chain Monte Carlo version of the Stochastic Approximation EM algorithm. Moreover, we introduce a new sampling scheme in the space of graphs that improves the add and delete proposal of Armstrong et al. (2009). We illustrate the efficiency of this new scheme on simulated and real datasets.