# Handling cellwise outliers by sparse regression and robust covariance

arXiv: https://arxiv.org/abs/1912.12446 · HTML: https://mlsanity.com/paper/1912.12446/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Dec 2019.

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

- [The Cellwise Minimum Covariance Determinant Estimator](https://mlsanity.com/paper/2207.13493/) (2022)
- [Multivariate outlier explanations using Shapley values and Mahalanobis distances](https://mlsanity.com/paper/2210.10063/) (2022)
- [Cellwise Outliers](https://mlsanity.com/paper/2604.14182/) (2026)
- [Explainable Outlier Detection for Interval-valued Data](https://mlsanity.com/paper/2606.26307/) (2026)

## Abstract (arXiv)

We propose a data-analytic method for detecting cellwise outliers. Given a robust covariance matrix, outlying cells (entries) in a row are found by the cellHandler technique which combines lasso regression with a stepwise application of constructed cutoff values. The penalty term of the lasso has a physical interpretation as the total distance that suspicious cells need to move in order to bring their row into the fold. For estimating a cellwise robust covariance matrix we construct a detection-imputation method which alternates between flagging outlying cells and updating the covariance matrix as in the EM algorithm. The proposed methods are illustrated by simulations and on real data about volatile organic compounds in children.