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Bayesian community detection. (English) Zbl 1407.62240

Summary: We introduce a Bayesian estimator of the underlying class structure in the stochastic block model, when the number of classes is known. The estimator is the posterior mode corresponding to a Dirichlet prior on the class proportions, a generalized Bernoulli prior on the class labels, and a beta prior on the edge probabilities. We show that this estimator is strongly consistent when the expected degree is at least of order \(\log^{2}{n}\), where \(n\) is the number of nodes in the network.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
62G20 Asymptotic properties of nonparametric inference
62F15 Bayesian inference

Software:

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References:

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