A covariate-dependent Cholesky decomposition for high-dimensional covariance regression
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914459114536960 |
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| author | Kim, Rakheon Zhang, Emma Jingfei |
| author_facet | Kim, Rakheon Zhang, Emma Jingfei |
| contents | Estimation of covariance matrices is a fundamental problem in multivariate statistics. Recently, growing efforts have focused on incorporating covariate effects into these matrices, facilitating subject-specific estimation. Despite these advances, guaranteeing the positive definiteness of the resulting estimators remains a challenging problem. In this paper, we present a new varying-coefficient sequential regression framework that extends the modified Cholesky decomposition to model the positive definite covariance matrix as a function of subject-level covariates. To handle high-dimensional responses and covariates, we impose a joint sparsity structure that simultaneously promotes sparsity in both the covariate effects and the entries in the Cholesky factors that are modulated by these covariates. We approach parameter estimation with a blockwise coordinate descent algorithm, and investigate the $\ell_2$ convergence rate of the estimated parameters. The efficacy of the proposed method is demonstrated through numerical experiments and an application to a gene co-expression network study with brain cancer patients. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_07547 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A covariate-dependent Cholesky decomposition for high-dimensional covariance regression Kim, Rakheon Zhang, Emma Jingfei Methodology Estimation of covariance matrices is a fundamental problem in multivariate statistics. Recently, growing efforts have focused on incorporating covariate effects into these matrices, facilitating subject-specific estimation. Despite these advances, guaranteeing the positive definiteness of the resulting estimators remains a challenging problem. In this paper, we present a new varying-coefficient sequential regression framework that extends the modified Cholesky decomposition to model the positive definite covariance matrix as a function of subject-level covariates. To handle high-dimensional responses and covariates, we impose a joint sparsity structure that simultaneously promotes sparsity in both the covariate effects and the entries in the Cholesky factors that are modulated by these covariates. We approach parameter estimation with a blockwise coordinate descent algorithm, and investigate the $\ell_2$ convergence rate of the estimated parameters. The efficacy of the proposed method is demonstrated through numerical experiments and an application to a gene co-expression network study with brain cancer patients. |
| title | A covariate-dependent Cholesky decomposition for high-dimensional covariance regression |
| topic | Methodology |
| url | https://arxiv.org/abs/2604.07547 |