Consistency of maximum-likelihood and variational estimators in the Stochastic Block Model
نویسندگان
چکیده
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 maximumlikelihood 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. AMS 2000 subject classifications: Primary 62G05, 62G20; secondary 62E17, 62H30.
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