Handling cellwise outliers by sparse regression and robust covariance

TL;DR

This paper introduces a novel method for detecting cellwise outliers using sparse regression and robust covariance estimation, improving outlier detection accuracy in multivariate data.

Contribution

The paper presents a new approach combining lasso regression with robust covariance estimation for effective cellwise outlier detection and imputation.

Findings

Method effectively detects cellwise outliers in simulated data.

Application to real VOC data demonstrates practical utility.

Outperforms existing techniques in robustness and accuracy.

Abstract

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.