Bayesian Community Detection | Zendy

Stéphanie van der Pas | Zendy; Aad van der Vaart | Zendy

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Bayesian Community Detection

Author(s) -

Stéphanie van der Pas,

Aad van der Vaart

Publication year - 2017

Publication title -

bayesian analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.685

H-Index - 58

eISSN - 1936-0975

pISSN - 1931-6690

DOI - 10.1214/17-ba1078

Subject(s) - mathematics , dirichlet distribution , estimator , stochastic block model , class (philosophy) , bayesian probability , statistics , bernoulli's principle , dirichlet process , bayesian network , combinatorics , artificial intelligence , computer science , mathematical analysis , cluster analysis , engineering , boundary value problem , aerospace engineering

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.

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