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.
Cite
@article{arxiv.2005.05628,
title = {Robust Lasso-Zero for sparse corruption and model selection with missing covariates},
author = {Pascaline Descloux and Claire Boyer and Julie Josse and Aude Sportisse and Sylvain Sardy},
journal= {arXiv preprint arXiv:2005.05628},
year = {2022}
}