An improved modified cholesky decomposition approach for precision matrix estimation

ABSTRACT

The modified Cholesky decomposition is commonly used for precision matrix estimation given a specified order of random variables. However, the order of variables is often not available or cannot be pre-determined. In this work, we propose a sparse precision matrix estimation by addressing the variable order issue in the modified Cholesky decomposition. The idea is to effectively combine a set of estimates obtained from multiple permutations of variable orders, and to efficiently encourage the sparse structure for the resultant estimate by the thresholding technique on the ensemble Cholesky factor matrix. The consistent property of the proposed estimate is established under some weak regularity conditions. Simulation studies are conducted to evaluate the performance of the proposed method in comparison with several existing approaches. The proposed method is also applied into linear discriminant analysis of real data for classification.

KEYWORDS:

• LDA
• modified Cholesky decomposition
• precision matrix
• sparsity
• order of variables

Acknowledgement

The authors thank the Editor and referees for their insightful and helpful comments that have improved the original manuscript. Xiaoning Kang’s research was supported by the Science Education Foundation of Liaoning Province (LN2019Q21), and the National Natural Science Foundation of China (71871047). Xinwei Deng’s research was supported by the National Natural Science Foundation of China (71531004).

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Xiaoning Kang  http://orcid.org/0000-0003-0394-6240

Xinwei Deng  http://orcid.org/0000-0002-1560-2405