CR-Lasso: Robust cellwise regularized sparse regression

TL;DR

CR-Lasso is a new robust sparse regression method designed to handle cellwise outliers effectively, improving feature selection and prediction in contaminated datasets, demonstrated through empirical studies and real data analysis.

Contribution

It introduces CR-Lasso, a novel cellwise regularized sparse regression technique that enhances robustness against cellwise contamination in feature selection tasks.

Findings

CR-Lasso performs competitively with existing methods in selection and prediction.

It effectively handles datasets with cellwise outliers.

Demonstrated success on real bone mineral density data.

Abstract

Cellwise contamination remains a challenging problem for data scientists, particularly in research fields that require the selection of sparse features. Traditional robust methods may not be feasible nor efficient in dealing with such contaminated datasets. We propose CR-Lasso, a robust Lasso-type cellwise regularization procedure that performs feature selection in the presence of cellwise outliers by minimising a regression loss and cell deviation measure simultaneously. To evaluate the approach, we conduct empirical studies comparing its selection and prediction performance with several sparse regression methods. We show that CR-Lasso is competitive under the settings considered. We illustrate the effectiveness of the proposed method on real data through an analysis of a bone mineral density dataset.