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 -oracle inequality satisfied by the Lasso estimator according to the Kullback−Leibler loss. This result is an extension of the -oracle inequality established by Meynet in [ESAIM: PS 17 (2013) 650–671]. in the multivariate case. We focus on the Lasso for its -regularization properties rather than for the variable selection procedure.
DOI : 10.1051/ps/2015011
Mots-clés : Finite mixture of multivariate regression model, Lasso, ℓ1-oracle inequality
@article{PS_2015__19__649_0,
author = {Devijver, Emilie},
title = {An $\ell{}_{1}$-oracle inequality for the {Lasso} in multivariate finite mixture of multivariate {Gaussian} regression models},
journal = {ESAIM: Probability and Statistics},
pages = {649--670},
publisher = {EDP-Sciences},
volume = {19},
year = {2015},
doi = {10.1051/ps/2015011},
mrnumber = {3433431},
zbl = {1392.62179},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps/2015011/}
}
TY - JOUR
AU - Devijver, Emilie
TI - An $\ell{}_{1}$-oracle inequality for the Lasso in multivariate finite mixture of multivariate Gaussian regression models
JO - ESAIM: Probability and Statistics
PY - 2015
SP - 649
EP - 670
VL - 19
PB - EDP-Sciences
UR - http://archive.numdam.org/articles/10.1051/ps/2015011/
DO - 10.1051/ps/2015011
LA - en
ID - PS_2015__19__649_0
ER -
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%T An $\ell{}_{1}$-oracle inequality for the Lasso in multivariate finite mixture of multivariate Gaussian regression models
%J ESAIM: Probability and Statistics
%D 2015
%P 649-670
%V 19
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/ps/2015011/
%R 10.1051/ps/2015011
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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. http://archive.numdam.org/articles/10.1051/ps/2015011/
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