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

Pascaline Descloux (1) , Claire Boyer (2) , Julie Josse (3) , Aude Sportisse (2) , Sylvain Sardy (4)

1 UNIGE - Université de Genève = University of Geneva
2 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation
3 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
4 Section de mathématiques [Genève]

We propose Robust Lasso-Zero, an extension of the Lasso-Zero methodology [Descloux and Sardy, 2018], 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.

Domaines: Théorie [stat.TH]; Méthodologie [stat.ME]; Applications [stat.AP]; Autres [stat.ML]

Pascaline Descloux, Claire Boyer, Julie Josse, Aude Sportisse, Sylvain Sardy. Robust Lasso-Zero for sparse corruption and model selection with missing covariates. 2020. ⟨hal-02569696v1⟩