Intrinsic Dimension Estimation by Maximum Likelihood in Probabilistic PCA

Charles Bouveyron 1 Gilles Celeux 2 Stephane Girard 3
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 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : A central issue in dimension reduction is choosing a sensible number of dimensions to be retained. This work demonstrates the asymptotic consistency of the maximum likelihood criterion for determining the intrinsic dimension of a dataset in a isotropic version of Probabilistic Principal Component Analysis (PPCA). Numerical experiments on simulated and real datasets show that the maximum likelihood criterion can actually be used in practice and outperforms existing intrinsic dimension selection criteria in various situations. This paper exhibits as well the limits of the maximum likelihood criterion and recommends in specific situations the use of the AIC criterion.
Type de document :
Communication dans un congrès
IMS 2010 - 73rd Annual Meeting of the Institute of Mathematical Statistics, Aug 2010, Gothenburg, Sweden
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https://hal.archives-ouvertes.fr/hal-00707049
Contributeur : Charles Bouveyron <>
Soumis le : lundi 11 juin 2012 - 21:27:49
Dernière modification le : mercredi 11 avril 2018 - 01:58:20

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  • HAL Id : hal-00707049, version 1

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Charles Bouveyron, Gilles Celeux, Stephane Girard. Intrinsic Dimension Estimation by Maximum Likelihood in Probabilistic PCA. IMS 2010 - 73rd Annual Meeting of the Institute of Mathematical Statistics, Aug 2010, Gothenburg, Sweden. 〈hal-00707049〉

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