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Title: Extended stochastic block models Authors:  Daniele Durante - Bocconi University (Italy) [presenting]
Sirio Legramanti - Università Bocconi (Italy)
Tommaso Rigon - University of Milano-Bicocca (Italy)
David Dunson - Duke University (United States)
Abstract: Stochastic block models are widely used in network science due to their interpretable structure that allows inference on groups of nodes having common connectivity patterns. Although providing a well established model-based approach for community detection, such formulations are still the object of intense research to address the problem of inferring the unknown number of communities. This has motivated the development of several probabilistic mechanisms to characterize the node partition process, covering solutions with a fixed, random and infinite number of communities. We will provide a unified view of all these formulations within a single extended stochastic block model (ESBM), that relies on Gibbs-type processes and encompasses most existing representations as special cases. Connections with Bayesian nonparametric literature open new avenues that allow the inclusion of unexplored options to model the nodes partition process and to incorporate node attributes. Among these new alternatives, we focus on the Gnedin process as an example of a probabilistic mechanism with desirable properties and empirical performance. A collapsed Gibbs sampler that can be applied to the whole ESBM class is proposed, and refined methods for posterior inference are outlined. The performance of ESBM is assessed in simulations and an application to political networks.