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Consistency of maximum-likelihood and variational estimators in the stochastic block model. (English) Zbl 1295.62028

Summary: The stochastic block model (SBM) is a probabilistic model designed to describe heterogeneous directed and undirected graphs. In this paper, we address the asymptotic inference in SBM by use of maximum-likelihood and variational approaches. The identifiability of SBM is proved while asymptotic properties of maximum-likelihood and variational estimators are derived. In particular, the consistency of these estimators is settled for the probability of an edge between two vertices (and for the group proportions at the price of an additional assumption), which is to the best of our knowledge the first result of this type for variational estimators in random graphs.

MSC:

62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
62E17 Approximations to statistical distributions (nonasymptotic)
62H30 Classification and discrimination; cluster analysis (statistical aspects)
05C80 Random graphs (graph-theoretic aspects)

Software:

Mixnet; StOCNET
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References:

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