Bayesian Learning of Graph Substructures

TL;DR

This paper introduces a Bayesian nonparametric framework for inferring complex graph structures like communities, propagating uncertainty from edge estimation to large-scale structure detection, with applications in finance and transcriptomics.

Contribution

It develops a novel Bayesian approach using stochastic blockmodels and Dependent Dirichlet processes for large-scale graph structure learning.

Findings

Effective detection of communities in simulated data

Successful application to finance and transcriptomics datasets

Enhanced uncertainty quantification in graph inference

Abstract

Graphical models provide a powerful methodology for learning the conditional independence structure in multivariate data. Inference is often focused on estimating individual edges in the latent graph. Nonetheless, there is increasing interest in inferring more complex structures, such as communities, for multiple reasons, including more effective information retrieval and better interpretability. Stochastic blockmodels offer a powerful tool to detect such structure in a network. We thus propose to exploit advances in random graph theory and embed them within the graphical models framework. A consequence of this approach is the propagation of the uncertainty in graph estimation to large-scale structure learning. We consider Bayesian nonparametric stochastic blockmodels as priors on the graph. We extend such models to consider clique-based blocks and to multiple graph settings introducing a novel prior process based on a Dependent Dirichlet process. Moreover, we devise a tailored computation strategy of Bayes factors for block structure based on the Savage-Dickey ratio to test for presence of larger structure in a graph. We demonstrate our approach in simulations as well as on real data applications in finance and transcriptomics.