| Issue |
ESAIM: PS
Volume 19, 2015
|
|
|---|---|---|
| Page(s) | 649 - 670 | |
| DOI | https://doi.org/10.1051/ps/2015011 | |
| Published online | 04 December 2015 | |
An ℓ1-oracle inequality for the Lasso in multivariate finite mixture of multivariate Gaussian regression models
Laboratoire de Mathématiques d’Orsay, Faculté des Sciences
d’Orsay, Université Paris-Sud, 91405
Orsay,
France
emilie.devijver@math.u-psud.fr
Received: 17 October 2014
Revised: 23 April 2015
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 ℓ1-oracle inequality satisfied by the Lasso estimator according to the Kullback−Leibler loss. This result is an extension of the ℓ1-oracle inequality established by Meynet in [ESAIM: PS 17 (2013) 650–671]. in the multivariate case. We focus on the Lasso for its ℓ1-regularization properties rather than for the variable selection procedure.
Mathematics Subject Classification: 62H30
Key words: Finite mixture of multivariate regression model / Lasso / ℓ1-oracle inequality
© EDP Sciences, SMAI, 2015
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