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Bayesian Learning of Graph Substructures

Boom, Willem van den; De Iorio, Maria; Beskos, Alexandros; (2022) Bayesian Learning of Graph Substructures. Bayesian Analysis 10.1214/22-BA1338. (In press). Green open access

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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.

Type: Article
Title: Bayesian Learning of Graph Substructures
Open access status: An open access version is available from UCL Discovery
DOI: 10.1214/22-BA1338
Publisher version: https://doi.org/10.1214/22-BA1338
Language: English
Additional information: Rights: Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).
Keywords: Bayesian nonparametrics , degree-corrected stochastic blockmodels , dependent Dirichlet process , Gaussian graphical models , multiple graphical models , multivariate data analysis
UCL classification: UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL
URI: https://discovery.ucl.ac.uk/id/eprint/10156395
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