Geodesic
An ℓ 1 -oracle inequality for the Lasso in multivariate finite mixture of multivariate Gaussian regression models
Devijver, Emilie1 
1 Laboratoire de Mathématiques d’Orsay, Faculté des Sciences d’Orsay, Université Paris-Sud, 91405 Orsay, France
ESAIM: Probability and Statistics, Tome 19 (2015), pp. 649-670 Cet article a éte moissonné depuis la source Numdam

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We consider a multivariate finite mixture of Gaussian regression models for high-dimensional data, where the number of covariates and the size of the response may be much larger than the sample size. We provide an ℓ 1 -oracle inequality satisfied by the Lasso estimator according to the Kullback−Leibler loss. This result is an extension of the ℓ 1 -oracle inequality established by Meynet in [ESAIM: PS 17 (2013) 650–671]. in the multivariate case. We focus on the Lasso for its ℓ 1 -regularization properties rather than for the variable selection procedure.

Reçu le :
DOI : 10.1051/ps/2015011
Classification : 62H30
Keywords: Finite mixture of multivariate regression model, Lasso, ℓ1-oracle inequality

Devijver, Emilie 1

1 Laboratoire de Mathématiques d’Orsay, Faculté des Sciences d’Orsay, Université Paris-Sud, 91405 Orsay, France 
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     title = {An $\ell{}_{1}$-oracle inequality for the {Lasso} in multivariate finite mixture of multivariate {Gaussian} regression models},
     journal = {ESAIM: Probability and Statistics},
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     year = {2015},
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Devijver, Emilie. An $\ell{}_{1}$-oracle inequality for the Lasso in multivariate finite mixture of multivariate Gaussian regression models. ESAIM: Probability and Statistics, Tome 19 (2015), pp. 649-670. doi: 10.1051/ps/2015011

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