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Estimation and selection for the latent block model on categorical data. (English) Zbl 1331.62149

Summary: 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.

MSC:

62F15 Bayesian inference
62H12 Estimation in multivariate analysis
62H30 Classification and discrimination; cluster analysis (statistical aspects)
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