High-dimensional covariance matrix regularization using informative targets

2025/03/12 by Atiq Ur Rehman, Muhammad Farooq, Rehman, Atiq Ur +1
Engineering · #FOS: Computer and information sciences #Infrared Target Detection Methodologies #Methodology (stat.ME)

paper · pdf · doi:10.48550/arxiv.2503.09072

openalex publication_date 2025/03/12 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

Abstract

The sample covariance matrix becomes non-invertible in high-dimensional settings, making classical multivariate statistical methods inapplicable. Various regularization techniques address this issue by imposing a structured target matrix to improve stability and invertibility. While diagonal matrices are commonly used as targets due to their simplicity, more informative target matrices can enhance performance. This paper explores the use of such targets and estimates the underlying correlation parameter using maximum likelihood. The proposed method is analytically straightforward, computationally efficient, and more accurate than recent regularization techniques when targets are correctly specified. Its effectiveness is demonstrated through extensive simulations and a real-world application.

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• High-dimensional inference on covariance structures via the extended cross-data-matrix methodology
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• A Pathwise Algorithm for Covariance Selection
• Fast Robust Correlation for High-Dimensional Data