An Expectation Conditional Maximization approach for Gaussian graphical models

TL;DR

This paper introduces a deterministic ECM algorithm for efficient estimation of Gaussian graphical models, enabling faster exploration and incorporation of multiple information sources in high-dimensional settings.

Contribution

It extends the EM approach to graphical model estimation, providing a computationally feasible alternative to stochastic Bayesian methods in high-dimensional contexts.

Findings

ECM enables fast posterior exploration with mixture priors

The method incorporates multiple sources of prior information

It is applicable to Gaussian and Gaussian copula graphical models

Abstract

Bayesian graphical models are a useful tool for understanding dependence relationships among many variables, particularly in situations with external prior information. In high-dimensional settings, the space of possible graphs becomes enormous, rendering even state-of-the-art Bayesian stochastic search computationally infeasible. We propose a deterministic alternative to estimate Gaussian and Gaussian copula graphical models using an Expectation Conditional Maximization (ECM) algorithm, extending the EM approach from Bayesian variable selection to graphical model estimation. We show that the ECM approach enables fast posterior exploration under a sequence of mixture priors, and can incorporate multiple sources of information.