An ℓ₁-oracle inequality for the Lasso in finite mixture of multivariate Gaussian regression models

2014/10/17 by Émilie Devijver, Devijver, Emilie
Computer Science · Mathematics · #62H30 #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1410.4682

openalex publication_date 2014/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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 \citeMeynet in the multivariate case. We focus on the Lasso for its ℓ₁-regularization properties rather than for the variable selection procedure, as it was done in Städler in \citeStadler.

Citations

• Least angle regression
• Exponential Screening and optimal rates of sparse estimation

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