Learning Gaussian Graphical Models With Fractional Marginal Pseudo-likelihood
This addresses a bottleneck in statistical modeling for researchers and practitioners by enabling efficient structure learning without restrictive assumptions, though it is incremental as it builds on existing pseudo-likelihood methods.
The authors tackled the problem of learning Gaussian graphical models without requiring decomposable graphs or tuning parameters, by proposing a Bayesian approximate inference method using pseudo-likelihood and sparsity priors, resulting in a fast scoring function that performs well in high-dimensional data and is theoretically consistent.
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.