Convergence of the groups posterior distribution in latent or stochastic block modelsReport as inadecuate




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1 MIG - Unité de Mathématique, Informatique et Génome 2 SG - Laboratoire Statistique et Génome

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.

Keywords : co-clustering block modelling Biclustering block clustering stochastic block model stochastic block model. posterior distribution latent block model





Author: Mahendra Mariadassou - Catherine Matias -

Source: https://hal.archives-ouvertes.fr/



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