A0502
Title: Bayesian learning of graph substructures
Authors: Willem van den Boom - National University of Singapore (Singapore)
Alexandros Beskos - University College London (United Kingdom)
Maria De Iorio - National University of Singapore (Singapore) [presenting]
Abstract: Graphical models provide a powerful methodology for learning the conditional independence structure in multivariate data. The 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 block models offer a powerful tool to detect such structures in a network. Thus exploiting random graph theory, advances are proposed and embedding 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. Bayesian nonparametric stochastic block models as priors on the graph are considered. Such models are extended to consider clique-based blocks and multiple graph settings, introducing a novel prior process based on a Dependent Dirichlet process. Moreover, a tailored computation strategy of Bayes factors for block structure based on the Savage-Dickey ratio is devised to test for the presence of a larger structure in a graph. Our simulation approach is demonstrated in real-data applications in finance and transcriptomics.
