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Journal Articles Scandinavian Journal of Statistics Year : 2022

Robust Lasso-Zero for sparse corruption and model selection with missing covariates

Abstract

We propose Robust Lasso-Zero, an extension of the Lasso-Zero methodology, initially introduced for sparse linear models, to the sparse corruptions problem. We give theoretical guarantees on the sign recovery of the parameters for a slightly simplified version of the estimator, called Thresholded Justice Pursuit. The use of Robust Lasso-Zero is showcased for variable selection with missing values in the covariates. In addition to not requiring the specification of a model for the covariates, nor estimating their covariance matrix or the noise variance, the method has the great advantage of handling missing not-at random values without specifying a parametric model. Numerical experiments and a medical application underline the relevance of Robust Lasso-Zero in such a context with few available competitors. The method is easy to use and implemented in the R library lass0.
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Dates and versions

hal-02569696 , version 1 (11-05-2020)
hal-02569696 , version 2 (22-03-2022)

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Pascaline Descloux, Claire Boyer, Julie Josse, Aude Sportisse, Sylvain Sardy. Robust Lasso-Zero for sparse corruption and model selection with missing covariates. Scandinavian Journal of Statistics, 2022. ⟨hal-02569696v2⟩
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