Robust Lasso-Zero for sparse corruption and model selection with missing covariates
This work addresses variable selection with missing covariates, particularly for medical applications, but is incremental as it extends an existing method.
The authors tackled the problem of variable selection with missing covariates by proposing Robust Lasso-Zero, an extension of Lasso-Zero for sparse corruptions, which handles missing not-at-random values without requiring parametric models or covariance estimation, and demonstrated its relevance in numerical experiments and a medical application with few competitors.
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.