Bernoulli

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  • Volume 21, Number 1 (2015), 537-573.

Convergence of the groups posterior distribution in latent or stochastic block models

Mahendra Mariadassou and Catherine Matias

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Abstract

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.

Article information

Source
Bernoulli Volume 21, Number 1 (2015), 537-573.

Dates
First available in Project Euclid: 17 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.bj/1426597081

Digital Object Identifier
doi:10.3150/13-BEJ579

Mathematical Reviews number (MathSciNet)
MR3322330

Zentralblatt MATH identifier
1329.62285

Keywords
biclustering block clustering block modelling co-clustering latent block model posterior distribution stochastic block model

Citation

Mariadassou, Mahendra; Matias, Catherine. Convergence of the groups posterior distribution in latent or stochastic block models. Bernoulli 21 (2015), no. 1, 537--573. doi:10.3150/13-BEJ579. https://projecteuclid.org/euclid.bj/1426597081


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