An ℓ 1 -oracle inequality for the Lasso in finite mixture of multivariate Gaussian regression models. - Archive ouverte HAL Access content directly
Journal Articles ESAIM: Probability and Statistics Year : 2015

An ℓ 1 -oracle inequality for the Lasso in finite mixture of multivariate Gaussian regression models.

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Abstract

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 the multivariate case. We focus on the Lasso for its ℓ 1 -regularization properties rather than for the variable selection procedure, as it was done in Städler et al.
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Dates and versions

hal-01075338 , version 1 (17-10-2014)
hal-01075338 , version 2 (14-01-2016)

Identifiers

  • HAL Id : hal-01075338 , version 2

Cite

Emilie Devijver. An ℓ 1 -oracle inequality for the Lasso in finite mixture of multivariate Gaussian regression models.. ESAIM: Probability and Statistics, 2015. ⟨hal-01075338v2⟩
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