Covariance Matrix Estimation for High-Throughput Biomedical Data with Interconnected Communities

Abstract

Estimating a covariance matrix is central to high-dimensional data analysis. Empirical analyses of high-dimensional biomedical data, including genomics, proteomics, microbiome, and neuroimaging, among others, consistently reveal strong modularity in the dependence patterns. In these analyses, intercorrelated high-dimensional biomedical features often form communities or modules that can be interconnected with others. While the interconnected community structure has been extensively studied in biomedical research (e.g., gene co-expression networks), its potential to assist in the estimation of covariance matrices remains largely unexplored. To address this gap, we propose a procedure that leverages the commonly observed interconnected community structure in high-dimensional biomedical data to estimate large covariance and precision matrices. We derive the uniformly minimum variance unbiased estimators for covariance and precision matrices in closed forms and provide theoretical results on their asymptotic properties. Our proposed method enhances the accuracy of covariance- and precision-matrix estimation and demonstrates superior performance compared to the competing methods in both simulations and real data analyses.

KEYWORDS:

• Closed-from estimate
• Interconnected community network
• Precision matrix
• Structured covariance matrix
• Uniform blocks

Acknowledgments

We appreciate the time and efforts that the editor, the associate editor, and the reviewers have dedicated to providing their valuable feedback on our article.

Disclosure Statement

No potential competing interest was reported by the author(s).

Additional information

Funding

This work was partially supported by the National Institute on Drug Abuse of the National Institutes of Health under award number 1DP1DA048968-01.