# Scalable Bayesian Structure Learning for Gaussian Graphical Models Using Marginal Pseudo-likelihood

arXiv: https://arxiv.org/abs/2307.00127 · HTML: https://mlsanity.com/paper/2307.00127/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 73 references that are in the map.
- First posted on arXiv 30 Jun 2023.

## Builds on (most cited first, 16 of 16)

- [Evaluation: from precision, recall and F-measure to ROC, informedness, markedness and correlation](https://mlsanity.com/paper/2010.16061/) (2020)
- [Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributions](https://mlsanity.com/paper/1301.6697/) (2013)
- [The Graphical Horseshoe Estimator for Inverse Covariance Matrices](https://mlsanity.com/paper/1707.06661/) (2017)
- [Bayesian Regularization for Graphical Models with Unequal Shrinkage](https://mlsanity.com/paper/1805.02257/) (2018)
- [A Direct Sampler for G-Wishart Variates](https://mlsanity.com/paper/1304.1350/) (2013)
- [BDgraph: An R Package for Bayesian Structure Learning in Graphical Models](https://mlsanity.com/paper/1501.05108/) (2015)
- [Scaling It Up: Stochastic Search Structure Learning in Graphical Models](https://mlsanity.com/paper/1505.01687/) (2015)
- [Precision Matrix Estimation under the Horseshoe-like Prior-Penalty Dual](https://mlsanity.com/paper/2104.10750/) (2021)
- [Learning block structured graphs in Gaussian graphical models](https://mlsanity.com/paper/2206.14274/) (2022)
- [Efficient sampling of Gaussian graphical models using conditional Bayes factors](https://mlsanity.com/paper/1409.2676/) (2014)
- [Learning Gaussian Graphical Models With Fractional Marginal Pseudo-likelihood](https://mlsanity.com/paper/1602.07863/) (2016)
- [Accelerating Bayesian Structure Learning in Sparse Gaussian Graphical Models](https://mlsanity.com/paper/1706.04416/) (2017)
- [Loglinear model selection and human mobility](https://mlsanity.com/paper/1711.02623/) (2017)
- [Fast Bayesian inference in large Gaussian graphical models](https://mlsanity.com/paper/1803.08155/) (2018)
- [B-CONCORD -- A scalable Bayesian high-dimensional precision matrix estimation procedure](https://mlsanity.com/paper/2005.09017/) (2020)
- [Bayesian Learning of Graph Substructures](https://mlsanity.com/paper/2203.11664/) (2022)

## Abstract (arXiv)

Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly exploring graph structures and precision matrices. To address this challenge, we perform inference directly on the graph by integrating out the precision matrix. We adopt a marginal pseudo-likelihood approach, eliminating the need to compute intractable normalizing constants and perform computationally intensive precision matrix sampling. Building on this framework, we develop continuous-time (birth-death) and discrete-time (reversible jump) Markov chain Monte Carlo (MCMC) algorithms that efficiently explore the posterior over graph space. We establish theoretical guarantees for posterior contraction, convergence, and graph selection consistency. The algorithms scale to large graph spaces, enabling parallel exploration for graphs with over 1,000 nodes, while providing uncertainty quantification and supporting flexible prior specification over the graph space. Extensive simulations show substantial computational gains over state-of-the-art Bayesian approaches without sacrificing graph recovery accuracy. Applications to human and mouse gene expression datasets demonstrate the ability of our approach to recover biologically meaningful structures and quantify uncertainty in complex networks. An implementation is available in the R package BDgraph.