# The Cellwise Minimum Covariance Determinant Estimator

arXiv: https://arxiv.org/abs/2207.13493 · HTML: https://mlsanity.com/paper/2207.13493/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 56 references that are in the map.
- First posted on arXiv 27 Jul 2022.

## Builds on (most cited first, 18 of 18)

- [Minimum Covariance Determinant and Extensions](https://mlsanity.com/paper/1709.07045/) (2017)
- [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)
- [Structured Covariance Matrix Estimation with Missing-Data for Radar Applications via Expectation-Maximization](https://mlsanity.com/paper/2105.03738/) (2021)
- [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 Minimum Regularized Covariance Determinant estimator](https://mlsanity.com/paper/1701.07086/) (2017)
- [Gaining Outlier Resistance with Progressive Quantiles: Fast Algorithms and Theoretical Studies](https://mlsanity.com/paper/2112.08471/) (2021)
- [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)
- [Outlier detection in non-elliptical data by kernel MRCD](https://mlsanity.com/paper/2008.02046/) (2020)
- [Cellwise robust regularized discriminant analysis](https://mlsanity.com/paper/1612.07971/) (2016)
- [Outlyingness: why do outliers lie out?](https://mlsanity.com/paper/1708.03761/) (2017)
- [Real-time outlier detection for large datasets by RT-DetMCD](https://mlsanity.com/paper/1910.05615/) (2019)
- [Cellwise Robust M Regression](https://mlsanity.com/paper/1912.03407/) (2019)

## Built on by (most cited first, 5 of 5)

- [Multivariate outlier explanations using Shapley values and Mahalanobis distances](https://mlsanity.com/paper/2210.10063/) (2022)
- [RobPy: a Python Package for Robust Statistical Methods](https://mlsanity.com/paper/2411.01954/) (2024)
- [Cellwise Outliers](https://mlsanity.com/paper/2604.14182/) (2026)
- [Log-Ratio Propagation on the Simplex: A Theory of Cellwise Contamination for Compositional Data](https://mlsanity.com/paper/2605.31345/) (2026)
- [A Unified Detection Framework for AI-Related Content and Artifacts](https://mlsanity.com/paper/2607.07527/) (2026)

## Abstract (arXiv)

The usual Minimum Covariance Determinant (MCD) estimator of a covariance matrix is robust against casewise outliers. These are cases (that is, rows of the data matrix) that behave differently from the majority of cases, raising suspicion that they might belong to a different population. On the other hand, cellwise outliers are individual cells in the data matrix. When a row contains one or more outlying cells, the other cells in the same row still contain useful information that we wish to preserve. We propose a cellwise robust version of the MCD method, called cellMCD. Its main building blocks are observed likelihood and a penalty term on the number of flagged cellwise outliers. It possesses good breakdown properties. We construct a fast algorithm for cellMCD based on concentration steps (C-steps) that always lower the objective. The method performs well in simulations with cellwise outliers, and has high finite-sample efficiency on clean data. It is illustrated on real data with visualizations of the results.