Finite mixture regression: A sparse variable selection by model selection for clustering

Emilie Devijver

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arXiv · 1409.1331

Finite mixture regression: A sparse variable selection by model selection for clustering

Emilie Devijver

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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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BibTeX RIS

Emilie Devijver. 2014-09-04. Finite mixture regression: A sparse variable selection by model selection for clustering. https://arxiv.org/abs/1409.1331

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