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2015 Finite mixture regression: A sparse variable selection by model selection for clustering
Emilie Devijver
Electron. J. Statist. 9(2): 2642-2674 (2015). DOI: 10.1214/15-EJS1082


We consider a finite mixture of Gaussian regression models 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 $\ell_{1}$-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 on a random model subcollection. We can derive the penalty shape of the criterion, which depends on the complexity of the random model collection.


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Emilie Devijver. "Finite mixture regression: A sparse variable selection by model selection for clustering." Electron. J. Statist. 9 (2) 2642 - 2674, 2015.


Received: 1 September 2014; Published: 2015
First available in Project Euclid: 8 December 2015

zbMATH: 1329.62279
MathSciNet: MR3432429
Digital Object Identifier: 10.1214/15-EJS1082

Primary: 62H30

Keywords: $\ell_{1}$-regularized method , finite mixture regression , non-asymptotic penalized criterion , Variable selection

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society


Vol.9 • No. 2 • 2015
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