A1375
Title: Graph of graphs: From nodes to supernodes in graphical models
Authors: Alexandros Beskos - University College London (United Kingdom) [presenting]
Maria De Iorio - National University of Singapore (Singapore)
Willem van den Boom - National University of Singapore (Singapore)
Ajay Jasra - The Chinese University of Hong Kong Shenzhen (China)
Andrea Cremaschi - IE University (Spain)
Abstract: High-dimensional data analysis typically focuses on low-dimensional structure, often to aid interpretation and computational efficiency. Graphical models provide a powerful methodology for learning the conditional independence structure in multivariate data by representing variables as nodes and dependencies as edges. Inference is often focused on individual edges in the latent graph. Nonetheless, there is increasing interest in determining more complex structures, such as communities of nodes, for multiple reasons, including more effective information retrieval and better interpretability. A hierarchical graphical model is proposed where nodes are first clustered, and then, at a higher level, the relationships are investigated among groups of nodes. Specifically, nodes are partitioned into supernodes with a data-coherent size-biased tessellation prior, which combines ideas from Bayesian nonparametrics and Voronoi tessellations. This construct also allows accounting for the dependence of nodes within supernodes. At the higher level, the dependence structure among supernodes is modeled through a Gaussian graphical model, where the focus of inference is on superedges. Theoretical justification is provided for the modeling choices. Tailored MCMC schemes are designed to enable parallel computations. The effectiveness of the approach is demonstrated for large-scale structure learning in simulations and a transcriptomics application.
