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Abstract:
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Stochastic block models are widely used in network science due to their interpretable structure that allows inference on groups of nodes with common connectivity patterns. Although being well established, such formulations are still the object of active research to address the problem of inferring the unknown number of groups. This has motivated the development of several priors to characterize the nodes partition process, covering solutions with fixed, random and infinite number of groups. In this talk I will present a unified view within a single extended stochastic block model (ESBM), that relies on Gibbs-type priors and encompasses most existing representations as special cases. Connections with Bayesian nonparametric literature allow the inclusion of several unexplored options to model the nodes partition and to incorporate node attributes. Among these new alternatives, I will focus on the Gnedin process as an example of a prior with desirable properties. A Gibbs sampler that can be applied to the whole ESBM class is proposed, and refined methods for estimation and uncertainty quantification are outlined. The performance of ESBM is assessed in simulations and applications.
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