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

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.