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Optimal Bayes estimators for block models

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SNAW05 - Bayesian methods for networks

In cluster analysis interest lies in probabilistically capturing partitions of individuals, items or nodes of a network into groups, such that those belonging to the same group share similar attributes or relational profiles. Bayesian posterior samples for the latent allocation variables can be effectively obtained in a wide range of clustering models, including finite mixtures, infinite mixtures, hidden markov models and block models for networks. However, due to the categorical nature of the clustering variables and the lack of scalable algorithms, summary tools that can interpret such samples are not available. We adopt a Bayesian decision theoretic approach to define an optimality criterion for clusterings, and propose a fast and context-independent greedy algorithm to find the best allocations. One important facet of our approach is that the optimal number of groups is automatically selected, thereby solving the clustering and the model-choice problems at the same time. We discuss the choice of loss functions to compare partitions, and show that our approach can accommodate a wide range of cases. Finally, we illustrate our approach on a variety of real-data applications for the stochastic block model and latent block model.  

This is joint work with Riccardo Rastelli. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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