Covariance Matrix Estimation for High-Throughput Biomedical Data with Interconnected Communities
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866912142564786176 |
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| author | Yang, Yifan Chen, Chixiang Chen, Shuo |
| author_facet | Yang, Yifan Chen, Chixiang Chen, Shuo |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2302_01861 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Covariance Matrix Estimation for High-Throughput Biomedical Data with Interconnected Communities Yang, Yifan Chen, Chixiang Chen, Shuo Methodology 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. |
| title | Covariance Matrix Estimation for High-Throughput Biomedical Data with Interconnected Communities |
| topic | Methodology |
| url | https://arxiv.org/abs/2302.01861 |