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2012 Consistency of maximum-likelihood and variational estimators in the stochastic block model
Alain Celisse, Jean-Jacques Daudin, Laurent Pierre
Electron. J. Statist. 6(none): 1847-1899 (2012). DOI: 10.1214/12-EJS729


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.


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Alain Celisse. Jean-Jacques Daudin. Laurent Pierre. "Consistency of maximum-likelihood and variational estimators in the stochastic block model." Electron. J. Statist. 6 1847 - 1899, 2012.


Published: 2012
First available in Project Euclid: 4 October 2012

zbMATH: 1295.62028
MathSciNet: MR2988467
Digital Object Identifier: 10.1214/12-EJS729

Primary: 62G05, 62G20
Secondary: 62E17, 62H30

Rights: Copyright © 2012 The Institute of Mathematical Statistics and the Bernoulli Society


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