Cellwise Outliers
Not on the map. Why?
Abstract (arXiv)
In statistics and machine learning, the traditional meaning of the terms `outlier' and `anomaly' is a case in the dataset that behaves differently from the bulk of the data, which raises suspicion that it may belong to a different population. But nowadays increasing attention is being paid to so-called cellwise outliers, which are individual values somewhere in the data matrix. Depending on the dimension, even a relatively small proportion of outlying cells can pollute over half the cases, which is a problem for existing methods that work by downweighting or dropping outlying cases. It turns out that detecting cellwise outliers as well as constructing cellwise robust methods requires techniques that are quite different from the casewise setting. For instance, one has to let go of some intuitive equivariance properties. The problem is difficult, but the past decade has seen substantial progress. For high-dimensional data the cellwise approach is becoming dominant, and typically can deal with missing values as well. We review developments in the estimation of location and covariance matrices as well as regression methods, principal component analysis, methods for tensor data, and various other settings.
Key facts. No citing papers in the map yet (data through 13 Oct 2026). Builds on 31 of its 94 references that are in the map. First posted on arXiv 31 Mar 2026.
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31 of 94 references.
References · 31
- 2017Tensor-on-tensor regressioncited by 22
- 2020Transforming variables to central normalitycited by 9
- 2016Detecting deviating data cellscited by 8
- 2017Fast robust correlation for high-dimensional datacited by 7
- 2015Robust high-dimensional precision matrix estimationcited by 5
- 2015Robust estimation of precision matrices under cellwise contaminationcited by 5
- 2022The Cellwise Minimum Covariance Determinant Estimatorcited by 5
- 2023Challenges of cellwise outlierscited by 5
- 2015The shooting S-estimator for robust regressioncited by 4
- 2018MacroPCA: An all-in-one PCA method allowing for missing values as well as cellwise and rowwise outlierscited by 4
- 2019Handling cellwise outliers by sparse regression and robust covariancecited by 4
- 2021Robust Variable Selection under Cellwise Contaminationcited by 4
19 more
- 2025Conformal Prediction with Cellwise Outliers: A Detect-then-Impute Approachcited by 4
- 2018Robust and sparse Gaussian graphical modeling under cell-wise contaminationcited by 3
- 2016Cellwise robust regularized discriminant analysiscited by 2
- 2023Multivariate Singular Spectrum Analysis by Robust Diagonalwise Low-Rank Approximationcited by 2
- 2023MacroPARAFAC for handling rowwise and cellwise outliers in incomplete multi-way datacited by 2
- 2024Robust Principal Components by Casewise and Cellwise Weightingcited by 2
- 2024Cellwise robust and sparse principal component analysiscited by 2
- 2024Cellwise outlier detection in heterogeneous populationscited by 2
- 2025Cellwise and Casewise Robust Covariance in High Dimensionscited by 2
- 2025Robust fuzzy clustering with cellwise outlierscited by 2
- 2021A Robust Seemingly Unrelated Regressions For Row-Wise And Cell-Wise Contaminationcited by 1
- 2022Analyzing cellwise weighted datacited by 1
- 2023CR-Lasso: Robust cellwise regularized sparse regressioncited by 1
- 2024Robust covariance estimation and explainable outlier detection for matrix-valued datacited by 1
- 2024MDDC: An R and Python Package for Adverse Event Identification in Pharmacovigilance Datacited by 1
- 2025Casewise and Cellwise Robust Multilinear Principal Component Analysiscited by 1
- 2026Least trimmed squares regression with missing values and cellwise outlierscited by 1
- 2026Fast and Scalable Cellwise-Robust Ensembles for High-Dimensional Datacited by 1
- 2026Casewise and Cellwise Robust Tensor-on-Tensor Regressioncited by 1
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