A0580
Title: Scalable Bayesian structure learning for Gaussian graphical models using marginal pseudo-likelihood
Authors: Reza Mohammadi - University of Amsterdam (Netherlands) [presenting]
Lucas Vogels - University of Amsterdam (Netherlands)
Marit Schoonhoven - University of Amsterdam (Netherlands)
Ilker Birbil - University of Amsterdam (Netherlands)
Abstract: Bayesian methods for learning Gaussian graphical models provide a powerful framework for addressing model uncertainty and incorporating prior knowledge. However, their applicability is often constrained by the high computational cost of exploring the joint space of graphs and precision matrices, particularly in large-scale settings. To overcome this limitation, an MCMC-based method is introduced that integrates the birth-death and reversible jump algorithms with the marginal pseudo-likelihood approach. By operating directly in the graph space, the method eliminates the need for intractable normalizing constants and precision matrix sampling, significantly reducing computational cost while preserving accuracy. These algorithms efficiently explore the full posterior graph space, enabling comprehensive model uncertainty quantification and seamless integration of prior structural knowledge. Notably, they produce reliable results in under an hour on standard hardware, even for datasets with over 1000 variables. The theoretical properties of the method are established, and its effectiveness is validated through an extensive simulation study and applications to gene expression data. Results show that the proposed algorithms outperform state-of-the-art Bayesian methods in both computational efficiency and accuracy. The algorithms are implemented in C++ and R and are accessible via the R package BDgraph.
