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

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.
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https://hal.archives-ouvertes.fr/hal-00713120
Contributor : Catherine Matias <>
Submitted on : Friday, August 9, 2013 - 11:22:44 AM
Last modification on : Sunday, June 28, 2020 - 3:17:07 AM
Long-term archiving on: : Sunday, November 10, 2013 - 4:17:24 AM

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  • HAL Id : hal-00713120, version 2
  • ARXIV : 1206.7101

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Mahendra Mariadassou, Catherine Matias. Convergence of the groups posterior distribution in latent or stochastic block models. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2015, 21 (1), pp.537-573. ⟨hal-00713120v2⟩

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