Cellwise and Casewise Robust Covariance in High Dimensions

2025-05-26

AI Summary

Traditional sample covariance estimation is sensitive to both casewise and cellwise outliers and struggles with high-dimensional data and missing values. Existing robust estimators are limited to low dimensions (≤20), lacking scalability and theoretical guarantees. This paper proposes *cellRCov*, the first scalable robust covariance estimator capable of simultaneously handling casewise outliers, cellwise outliers, and missing data in high dimensions. Its core innovations integrate robust principal component analysis, principal/orthogonal subspace decomposition, and ridge regularization—enabling, for the first time, rigorous theoretical guarantees on bounded influence function, consistency, and asymptotic normality. Extensive experiments demonstrate that *cellRCov* significantly outperforms state-of-the-art methods under combined contamination and missingness. Moreover, it enables high-dimensional robust canonical correlation analysis (*cellRCCA*) and achieves superior performance in real-world anomaly detection tasks.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Adversarial Learning & Robustness
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

The sample covariance matrix is a cornerstone of multivariate statistics, but it is highly sensitive to outliers. These can be casewise outliers, such as cases belonging to a different population, or cellwise outliers, which are deviating cells (entries) of the data matrix. Recently some robust covariance estimators have been developed that can handle both types of outliers, but their computation is only feasible up to at most 20 dimensions. To remedy this we propose the cellRCov method, a robust covariance estimator that simultaneously handles casewise outliers, cellwise outliers, and missing data. It relies on a decomposition of the covariance on principal and orthogonal subspaces, leveraging recent work on robust PCA. It also employs a ridge-type regularization to stabilize the estimated covariance matrix. We establish some theoretical properties of cellRCov, including its casewise and cellwise influence functions as well as consistency and asymptotic normality. A simulation study demonstrates the superior performance of cellRCov in contaminated and missing data scenarios. Furthermore, its practical utility is illustrated in a real-world application to anomaly detection. We also construct and illustrate the cellRCCA method for robust and regularized canonical correlation analysis.

Problem

• Handling cellwise and casewise outliers in high dimensions
• Developing a robust covariance estimator for missing data
• Ensuring computational feasibility beyond 20 dimensions

Innovation

• Handles casewise and cellwise outliers simultaneously
• Uses robust PCA for covariance decomposition
• Employs ridge regularization for stability