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Finite mixture regression: a sparse variable selection by model selection for clustering.

Emilie Devijver 1, 2
1 SELECT - Model selection in statistical learning
LMO - Laboratoire de Mathématiques d'Orsay, Inria Saclay - Ile de France
Abstract : We consider a finite mixture of Gaussian regression model for high- dimensional data, where the number of covariates may be much larger than the sample size. We propose to estimate the unknown conditional mixture density by a maximum likelihood estimator, restricted on relevant variables selected by an 1-penalized maximum likelihood estimator. We get an oracle inequality satisfied by this estimator with a Jensen-Kullback-Leibler type loss. Our oracle inequality is deduced from a general model selection theorem for maximum likelihood estimators with a random model collection. We can derive the penalty shape of the criterion, which depends on the complexity of the random model collection.
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https://hal.archives-ouvertes.fr/hal-01060079
Contributor : Emilie Devijver <>
Submitted on : Wednesday, September 3, 2014 - 9:26:29 PM
Last modification on : Monday, February 10, 2020 - 6:13:44 PM
Document(s) archivé(s) le : Thursday, December 4, 2014 - 10:10:48 AM

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  • HAL Id : hal-01060079, version 1
  • ARXIV : 1409.1331

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Emilie Devijver. Finite mixture regression: a sparse variable selection by model selection for clustering.. Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2015. ⟨hal-01060079⟩

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