A Cholesky-based sparse covariance estimation with an application to genes data

ABSTRACT

The modified Cholesky decomposition (MCD) is a powerful tool for estimating a covariance matrix. The regularization can be conveniently imposed on the linear regressions to encourage the sparsity in the estimated covariance matrix to accommodate the high-dimensional data. In this paper, we propose a Cholesky-based sparse ensemble estimate for covariance matrix by averaging a set of Cholesky factor estimates obtained from multiple variable orderings used in the MCD. The sparse estimation is enabled by encouraging the sparsity in the Cholesky factor. The theoretical consistent property is established under some regular conditions. The merits of the proposed method are illustrated through simulation and a maize genes data set.

KEYWORDS:

• Covariance matrix
• gene expressions
• model averaging
• modified Cholesky decomposition
• sparsity

Acknowledgments

The authors thank the Editor and referees for their insightful and constructive comments that have greatly improved the original manuscript. This work was supported by Ministry of Education of China (20YJC910007, 19YJC790171), National Natural Science Foundation of China (11771250), and Natural Science Foundation of Shandong Province (ZR2019MA002).

Disclosure of potential conflicts of interest

No potential conflict of interest was reported by the authors.