Learning Gaussian Graphical Models With Fractional Marginal Pseudo-likelihood

TL;DR

This paper introduces a Bayesian approximate inference method for learning Gaussian graphical models using pseudo-likelihood, enabling structure learning without decomposability assumptions and demonstrating strong performance in high-dimensional settings.

Contribution

It develops a fast, scalable scoring function for non-decomposable Gaussian graphical models using fractional marginal pseudo-likelihood, without requiring tuning parameters.

Findings

Performs well in high-dimensional data scenarios

Provides a consistent estimator of the graph structure

Outperforms existing methods in large-scale comparisons

Abstract

We propose a Bayesian approximate inference method for learning the dependence structure of a Gaussian graphical model. Using pseudo-likelihood, we derive an analytical expression to approximate the marginal likelihood for an arbitrary graph structure without invoking any assumptions about decomposability. The majority of the existing methods for learning Gaussian graphical models are either restricted to decomposable graphs or require specification of a tuning parameter that may have a substantial impact on learned structures. By combining a simple sparsity inducing prior for the graph structures with a default reference prior for the model parameters, we obtain a fast and easily applicable scoring function that works well for even high-dimensional data. We demonstrate the favourable performance of our approach by large-scale comparisons against the leading methods for learning non-decomposable Gaussian graphical models. A theoretical justification for our method is provided by showing that it yields a consistent estimator of the graph structure.