A fast ADMM algorithm for sparse precision matrix estimation using lasso penalized D-trace loss
Sparse precision matrix estimation, also known as the estimation of the inverse covariance matrix in statistical contexts, represents a critical challenge in numerous multivariate analysis applications. This challenge becomes notably complex when the dimension of the data is far greater than the cap...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024-03-01
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| Series: | Egyptian Informatics Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110866523000816 |
| _version_ | 1827311199586353152 |
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| author | Mingmin Zhu Jiewei Jiang Weifeng Gao |
| author_facet | Mingmin Zhu Jiewei Jiang Weifeng Gao |
| author_sort | Mingmin Zhu |
| collection | DOAJ |
| description | Sparse precision matrix estimation, also known as the estimation of the inverse covariance matrix in statistical contexts, represents a critical challenge in numerous multivariate analysis applications. This challenge becomes notably complex when the dimension of the data is far greater than the capacity of samples. To address this issue, we introduce a convex relaxation model that employs the first-order optimality conditions associated with the lasso-penalized D-trace loss for the purpose of estimating sparse precision matrix. The proposed model is effectively solved through the widely recognized alternating direction method of multipliers. Additionally, we provide closed-form solutions to subproblems in each iteration with a computational complexity of O(np2), and establish the convergence of our proposed algorithm. Numerical investigations demonstrate that our algorithm exhibits the capability to handle large-scale datasets and significantly outperforms the existing methods, particularly when dealing with high-dimensional scenarios characterized by a large dimension p. |
| first_indexed | 2024-04-24T20:13:00Z |
| format | Article |
| id | doaj.art-4dbea82e9d334ae7b34dbf3bfbebd44d |
| institution | Directory Open Access Journal |
| issn | 1110-8665 |
| language | English |
| last_indexed | 2024-04-24T20:13:00Z |
| publishDate | 2024-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Egyptian Informatics Journal |
| spelling | doaj.art-4dbea82e9d334ae7b34dbf3bfbebd44d2024-03-23T06:23:18ZengElsevierEgyptian Informatics Journal1110-86652024-03-0125100425A fast ADMM algorithm for sparse precision matrix estimation using lasso penalized D-trace lossMingmin Zhu0Jiewei Jiang1Weifeng Gao2School of Mathematics and Statistics, Xidian University, Xi'an, 710126, PR China; Corresponding author.School of Electronic Engineering, Xi'an University of Posts and Telecommunications, Xi'an, 710121, PR ChinaSchool of Mathematics and Statistics, Xidian University, Xi'an, 710126, PR ChinaSparse precision matrix estimation, also known as the estimation of the inverse covariance matrix in statistical contexts, represents a critical challenge in numerous multivariate analysis applications. This challenge becomes notably complex when the dimension of the data is far greater than the capacity of samples. To address this issue, we introduce a convex relaxation model that employs the first-order optimality conditions associated with the lasso-penalized D-trace loss for the purpose of estimating sparse precision matrix. The proposed model is effectively solved through the widely recognized alternating direction method of multipliers. Additionally, we provide closed-form solutions to subproblems in each iteration with a computational complexity of O(np2), and establish the convergence of our proposed algorithm. Numerical investigations demonstrate that our algorithm exhibits the capability to handle large-scale datasets and significantly outperforms the existing methods, particularly when dealing with high-dimensional scenarios characterized by a large dimension p.http://www.sciencedirect.com/science/article/pii/S1110866523000816Precision matrixPenalized quadratic lossConvex relaxationGaussian graphical modelADMM |
| spellingShingle | Mingmin Zhu Jiewei Jiang Weifeng Gao A fast ADMM algorithm for sparse precision matrix estimation using lasso penalized D-trace loss Egyptian Informatics Journal Precision matrix Penalized quadratic loss Convex relaxation Gaussian graphical model ADMM |
| title | A fast ADMM algorithm for sparse precision matrix estimation using lasso penalized D-trace loss |
| title_full | A fast ADMM algorithm for sparse precision matrix estimation using lasso penalized D-trace loss |
| title_fullStr | A fast ADMM algorithm for sparse precision matrix estimation using lasso penalized D-trace loss |
| title_full_unstemmed | A fast ADMM algorithm for sparse precision matrix estimation using lasso penalized D-trace loss |
| title_short | A fast ADMM algorithm for sparse precision matrix estimation using lasso penalized D-trace loss |
| title_sort | fast admm algorithm for sparse precision matrix estimation using lasso penalized d trace loss |
| topic | Precision matrix Penalized quadratic loss Convex relaxation Gaussian graphical model ADMM |
| url | http://www.sciencedirect.com/science/article/pii/S1110866523000816 |
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