  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.
