Estimation and selection for the latent block model on categorical data

Christine Keribin 1, 2 Vincent Brault 3 Gilles Celeux 2 Gérard Govaert 4
1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 SELECT - Model selection in statistical learning
Inria Saclay - Ile de France, LMO - Laboratoire de Mathématiques d'Orsay, CNRS - Centre National de la Recherche Scientifique : UMR
3 SVQV - Santé de la vigne et qualité du vin
4 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]
Abstract : This paper deals with estimation and model selection in the Latent Block Model (LBM) for categorical data. First, after providing sufficient conditions ensuring the identifiability of this model, we generalise estimation procedures and model selection criteria derived for binary data. Secondly, we develop Bayesian inference through Gibbs sampling and with a well calibrated non informative prior distribution, in order to get the MAP estimator: this is proved to avoid the traps encountered by the LBM with the maximum likelihood methodology. Then model selection criteria are presented. In particular an exact expression of the integrated completed likelihood criterion requiring no asymptotic approximation is derived. Finally numerical experiments on both simulated and real data sets highlight the appeal of the proposed estimation and model selection procedures.
Keywords : Gibbs sampling EM algorithm BIC criterion Variational approximation Integrated completed likelihood Stochastic EM Bayesian inference
Type de document :
Article dans une revue
Statistics and Computing, Springer Verlag (Germany), 2015, 25 (6), pp.1201-1216. 〈10.1007/s11222-014-9472-2〉
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https://hal.inria.fr/hal-01256840
Contributeur : Gilles Celeux <>
Soumis le : vendredi 15 janvier 2016 - 13:49:56
Dernière modification le : mercredi 4 juillet 2018 - 16:44:02

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INRA | INSMI | LM-ORSAY | INRIA | UNIV-PARIS-SACLAY

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Christine Keribin, Vincent Brault, Gilles Celeux, Gérard Govaert. Estimation and selection for the latent block model on categorical data. Statistics and Computing, Springer Verlag (Germany), 2015, 25 (6), pp.1201-1216. 〈10.1007/s11222-014-9472-2〉. 〈hal-01256840〉

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