Electronic Journal of Statistics

Consistency of maximum-likelihood and variational estimators in the stochastic block model

Alain Celisse, Jean-Jacques Daudin, and Laurent Pierre

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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.

Article information

Electron. J. Statist., Volume 6 (2012), 1847-1899.

First available in Project Euclid: 4 October 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation 62G20: Asymptotic properties
Secondary: 62E17: Approximations to distributions (nonasymptotic) 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20]

Random graphs stochastic block model maximum likelihood estimators variational estimators consistency concentration inequalities


Celisse, Alain; Daudin, Jean-Jacques; Pierre, Laurent. Consistency of maximum-likelihood and variational estimators in the stochastic block model. Electron. J. Statist. 6 (2012), 1847--1899. doi:10.1214/12-EJS729. https://projecteuclid.org/euclid.ejs/1349355605

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