Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 6 (2012), 1847-1899.
Consistency of maximum-likelihood and variational estimators in the stochastic block model
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.
Electron. J. Statist., Volume 6 (2012), 1847-1899.
First available in Project Euclid: 4 October 2012
Permanent link to this document
Digital Object Identifier
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]
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