Robust estimation of precision matrices under cellwise contamination

TL;DR

This paper develops a robust method for estimating sparse precision matrices that effectively handles cellwise contamination, improving reliability in high-dimensional data analysis.

Contribution

It introduces a novel approach combining pairwise covariance estimation with a positive semidefinite transformation, scalable to large feature sets.

Findings

Method produces accurate, sparse precision matrices under contamination.

Scales well with increasing number of variables.

Outperforms traditional robust techniques in contaminated data scenarios.

Abstract

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.