# Cellwise Outliers

arXiv: https://arxiv.org/abs/2604.14182 · HTML: https://mlsanity.com/paper/2604.14182/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 94 references that are in the map.
- First posted on arXiv 31 Mar 2026.

## Builds on (most cited first, 30 of 31)

- [Tensor-on-tensor regression](https://mlsanity.com/paper/1701.01037/) (2017)
- [Transforming variables to central normality](https://mlsanity.com/paper/2005.07946/) (2020)
- [Detecting deviating data cells](https://mlsanity.com/paper/1601.07251/) (2016)
- [Fast robust correlation for high-dimensional data](https://mlsanity.com/paper/1712.05151/) (2017)
- [Robust high-dimensional precision matrix estimation](https://mlsanity.com/paper/1501.01219/) (2015)
- [Robust estimation of precision matrices under cellwise contamination](https://mlsanity.com/paper/1501.01950/) (2015)
- [The Cellwise Minimum Covariance Determinant Estimator](https://mlsanity.com/paper/2207.13493/) (2022)
- [Challenges of cellwise outliers](https://mlsanity.com/paper/2302.02156/) (2023)
- [Conformal Prediction with Cellwise Outliers: A Detect-then-Impute Approach](https://mlsanity.com/paper/2505.04986/) (2025)
- [The shooting S-estimator for robust regression](https://mlsanity.com/paper/1506.01223/) (2015)
- [MacroPCA: An all-in-one PCA method allowing for missing values as well as cellwise and rowwise outliers](https://mlsanity.com/paper/1806.00954/) (2018)
- [Handling cellwise outliers by sparse regression and robust covariance](https://mlsanity.com/paper/1912.12446/) (2019)
- [Robust Variable Selection under Cellwise Contamination](https://mlsanity.com/paper/2110.12406/) (2021)
- [Robust and sparse Gaussian graphical modeling under cell-wise contamination](https://mlsanity.com/paper/1802.05475/) (2018)
- [Cellwise robust regularized discriminant analysis](https://mlsanity.com/paper/1612.07971/) (2016)
- [Multivariate Singular Spectrum Analysis by Robust Diagonalwise Low-Rank Approximation](https://mlsanity.com/paper/2310.01182/) (2023)
- [MacroPARAFAC for handling rowwise and cellwise outliers in incomplete multi-way data](https://mlsanity.com/paper/2312.01168/) (2023)
- [Robust Principal Components by Casewise and Cellwise Weighting](https://mlsanity.com/paper/2408.13596/) (2024)
- [Cellwise robust and sparse principal component analysis](https://mlsanity.com/paper/2408.15612/) (2024)
- [Cellwise outlier detection in heterogeneous populations](https://mlsanity.com/paper/2409.07881/) (2024)
- [Cellwise and Casewise Robust Covariance in High Dimensions](https://mlsanity.com/paper/2505.19925/) (2025)
- [Robust fuzzy clustering with cellwise outliers](https://mlsanity.com/paper/2508.03310/) (2025)
- [A Robust Seemingly Unrelated Regressions For Row-Wise And Cell-Wise Contamination](https://mlsanity.com/paper/2107.00975/) (2021)
- [Analyzing cellwise weighted data](https://mlsanity.com/paper/2209.12697/) (2022)
- [CR-Lasso: Robust cellwise regularized sparse regression](https://mlsanity.com/paper/2307.05234/) (2023)
- [Robust covariance estimation and explainable outlier detection for matrix-valued data](https://mlsanity.com/paper/2403.03975/) (2024)
- [MDDC: An R and Python Package for Adverse Event Identification in Pharmacovigilance Data](https://mlsanity.com/paper/2410.01168/) (2024)
- [Casewise and Cellwise Robust Multilinear Principal Component Analysis](https://mlsanity.com/paper/2503.07327/) (2025)
- [Least trimmed squares regression with missing values and cellwise outliers](https://mlsanity.com/paper/2603.04632/) (2026)
- [Fast and Scalable Cellwise-Robust Ensembles for High-Dimensional Data](https://mlsanity.com/paper/2603.20940/) (2026)

## 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.