Open Access
February 2015 Convergence of the groups posterior distribution in latent or stochastic block models
Mahendra Mariadassou, Catherine Matias
Bernoulli 21(1): 537-573 (February 2015). DOI: 10.3150/13-BEJ579


We propose a unified framework for studying both latent and stochastic block models, which are used to cluster simultaneously rows and columns of a data matrix. In this new framework, we study the behaviour of the groups posterior distribution, given the data. We characterize whether it is possible to asymptotically recover the actual groups on the rows and columns of the matrix, relying on a consistent estimate of the parameter. In other words, we establish sufficient conditions for the groups posterior distribution to converge (as the size of the data increases) to a Dirac mass located at the actual (random) groups configuration. In particular, we highlight some cases where the model assumes symmetries in the matrix of connection probabilities that prevents recovering the original groups. We also discuss the validity of these results when the proportion of non-null entries in the data matrix converges to zero.


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Mahendra Mariadassou. Catherine Matias. "Convergence of the groups posterior distribution in latent or stochastic block models." Bernoulli 21 (1) 537 - 573, February 2015.


Published: February 2015
First available in Project Euclid: 17 March 2015

zbMATH: 1329.62285
MathSciNet: MR3322330
Digital Object Identifier: 10.3150/13-BEJ579

Keywords: Biclustering , block clustering , block modelling , co-clustering , Latent Block Model , posterior distribution , Stochastic block model

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

Vol.21 • No. 1 • February 2015
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