# Robust Variable Selection under Cellwise Contamination

arXiv: https://arxiv.org/abs/2110.12406 · HTML: https://mlsanity.com/paper/2110.12406/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2021.

## Built on by (most cited first, 4 of 4)

- [The Cellwise Minimum Covariance Determinant Estimator](https://mlsanity.com/paper/2207.13493/) (2022)
- [2D-OOB: Attributing Data Contribution Through Joint Valuation Framework](https://mlsanity.com/paper/2408.03572/) (2024)
- [Multi-Output Robust and Conjugate Gaussian Processes](https://mlsanity.com/paper/2510.26401/) (2025)
- [Cellwise Outliers](https://mlsanity.com/paper/2604.14182/) (2026)

## Abstract (arXiv)

Cellwise outliers are widespread in data and traditional robust methods may fail when applied to datasets under such contamination. We propose a variable selection procedure, that uses a pairwise robust estimator to obtain an initial empirical covariance matrix among the response and potentially many predictors. Then we replace the primary design matrix and the response vector with their robust counterparts based on the estimated covariance matrix. Finally, we adopt the adaptive Lasso to obtain variable selection results. The proposed approach is robust to cellwise outliers in regular and high dimensional settings and empirical results show good performance in comparison with recently proposed alternative robust approaches, particularly in the challenging setting when contamination rates are high but the magnitude of outliers is moderate. Real data applications demonstrate the practical utility of the proposed method.