An Expectation Conditional Maximization approach for Gaussian graphical models
This provides a more efficient method for statisticians and data scientists working with high-dimensional graphical models, though it is incremental as it extends existing EM approaches.
The paper tackles the computational infeasibility of Bayesian stochastic search for high-dimensional Gaussian graphical models by proposing a deterministic Expectation Conditional Maximization (ECM) algorithm, which enables fast posterior exploration and can incorporate multiple information sources.
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.