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Mise en oeuvre de l'échantillonneur de Gibbs pour le modèle des blocs latents

Vincent Brault 1, 2 Gilles Celeux 2 Christine Keribin 2, 1
2 SELECT - Model selection in statistical learning
LMO - Laboratoire de Mathématiques d'Orsay, Inria Saclay - Ile de France
Abstract : Mixture models can be used to deal with the simultaneous clustering of a set of objects and a set of variables. The latent block model defines a distribution for each combinaison of an object cluster and a variable cluster, and the data is supposed to be independent, given the object and the variable clusters. But the factorization of the joint distribution of the labels, conditionally to the observed data, is not tractable, and the E-step of the EM algorithm cannot be performed. To solve this problem, the variational EM has been proposed by Govaert and Nadif (2008), the SEM algorithm by Keribin and al (2010) and the V-Bayes algorithm by Keribin and al (2012).In theory, the Gibbs sampler (Keribin et al (2012)) samples the exact a posteriori law while some algorithms use an approximation. In practice, the problem is to determine when the chain begins to be stationary. In this presentation, we study the Brooks-Gelman statistic (1998) as stop criterion for the latent block model and propose some improvement to decrease the convergence period.
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https://hal.inria.fr/hal-01090349
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Submitted on : Wednesday, December 3, 2014 - 3:18:41 PM
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Vincent Brault, Gilles Celeux, Christine Keribin. Mise en oeuvre de l'échantillonneur de Gibbs pour le modèle des blocs latents. 46èmes journées de statistique de la SFdS, SFdS, Jun 2014, Rennes, France. ⟨hal-01090349⟩

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