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

Voir la notice de l'article provenant de la source Numdam

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 
@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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/articles/10.1051/ps/2015011/
DO  - 10.1051/ps/2015011
LA  - en
ID  - PS_2015__19__649_0
ER  - 
%0 Journal Article
%A Devijver, Emilie
%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://geodesic.mathdoc.fr/articles/10.1051/ps/2015011/
%R 10.1051/ps/2015011
%G en
%F PS_2015__19__649_0
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

Cité par Sources :