# Robust estimation of precision matrices under cellwise contamination

arXiv: https://arxiv.org/abs/1501.01950 · HTML: https://mlsanity.com/paper/1501.01950/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jan 2015.

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

- [The Cellwise Minimum Covariance Determinant Estimator](https://mlsanity.com/paper/2207.13493/) (2022)
- [Tractable and Near-Optimal Adversarial Algorithms for Robust Estimation in Contaminated Gaussian Models](https://mlsanity.com/paper/2112.12919/) (2021)
- [Convex Parameter Estimation of Perturbed Multivariate Generalized Gaussian Distributions](https://mlsanity.com/paper/2312.07479/) (2023)
- [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)

## Abstract (arXiv)

There is a great need for robust techniques in data mining and machine learning contexts where many standard techniques such as principal component analysis and linear discriminant analysis are inherently susceptible to outliers. Furthermore, standard robust procedures assume that less than half the observation rows of a data matrix are contaminated, which may not be a realistic assumption when the number of observed features is large. This work looks at the problem of estimating covariance and precision matrices under cellwise contamination. We consider using a robust pairwise covariance matrix as an input to various regularisation routines, such as the graphical lasso, QUIC and CLIME. To ensure the input covariance matrix is positive semidefinite, we use a method that transforms a symmetric matrix of pairwise covariances to the nearest covariance matrix. The result is a potentially sparse precision matrix that is resilient to moderate levels of cellwise contamination. Since this procedure is not based on subsampling it scales well as the number of variables increases.