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Large Covariance Matrix Estimation With Oracle Statistical Rate via Majorization-Minimization | |
2023 | |
发表期刊 | IEEE TRANSACTIONS ON SIGNAL PROCESSING (IF:4.6[JCR-2023],5.2[5-Year]) |
ISSN | 1053-587X |
EISSN | 1941-0476 |
卷号 | 71页码:3328-3342 |
发表状态 | 已发表 |
DOI | 10.1109/TSP.2023.3311523 |
摘要 | The 1 penalized covariance estimator has been widely used for estimating large sparse covariance matrices. It is recognized that 1 penalty introduces a non-negligible estimation bias, while a proper utilization of non-convex penalty may lead to an estimator with a refined statistical rate of convergence. To eliminate the estimation bias, in this paper we propose to estimate large sparse covariance matrices using the non-convex penalty. It is challenging to analyze the theoretical properties of the resulting estimator because popular iterative algorithms for convex optimization no longer have global convergence guarantees for non-convex optimization. To tackle this issue, an efficient algorithm based on the majorization-minimization (MM) framework is developed by solving a sequence of convex relaxation subproblems. An approximation solution to each subproblem is obtained via the proximal gradient method with a linear convergence rate. We clearly establish the statistical properties of all the approximate solutions generated by the MM-based algorithm and prove that the proposed estimator achieves the oracle statistical rate in the Frobenius norm under weak technical assumptions. We also consider a modification of the proposed estimation method using the correlation matrix and show that the modified correlation-based covariance estimator enjoys a better rate in the spectral norm. Our theoretical findings are corroborated through extensive numerical experiments on both synthetic data and real-world datasets. © 2023 IEEE. |
关键词 | Covariance estimation sparsity positive definiteness majorization-minimization non-convex statistical optimization |
URL | 查看原文 |
收录类别 | SCI |
语种 | 英语 |
出版者 | Institute of Electrical and Electronics Engineers Inc. |
EI入藏号 | 20233814765940 |
EI主题词 | Convex optimization |
EI分类号 | 716.1 Information Theory and Signal Processing ; 801.3 Colloid Chemistry ; 921 Mathematics ; 921.6 Numerical Methods ; 922.2 Mathematical Statistics ; 931.1 Mechanics |
原始文献类型 | Journal article (JA) |
来源库 | IEEE |
引用统计 | 正在获取...
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文献类型 | 期刊论文 |
条目标识符 | https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/331132 |
专题 | 信息科学与技术学院 信息科学与技术学院_硕士生 信息科学与技术学院_PI研究组_赵子平组 |
通讯作者 | Ziping Zhao |
作者单位 | School of Information Science and Technology, ShanghaiTech University, Shanghai, China |
第一作者单位 | 信息科学与技术学院 |
通讯作者单位 | 信息科学与技术学院 |
第一作者的第一单位 | 信息科学与技术学院 |
推荐引用方式 GB/T 7714 | Quan Wei,Ziping Zhao. Large Covariance Matrix Estimation With Oracle Statistical Rate via Majorization-Minimization[J]. IEEE TRANSACTIONS ON SIGNAL PROCESSING,2023,71:3328-3342. |
APA | Quan Wei,&Ziping Zhao.(2023).Large Covariance Matrix Estimation With Oracle Statistical Rate via Majorization-Minimization.IEEE TRANSACTIONS ON SIGNAL PROCESSING,71,3328-3342. |
MLA | Quan Wei,et al."Large Covariance Matrix Estimation With Oracle Statistical Rate via Majorization-Minimization".IEEE TRANSACTIONS ON SIGNAL PROCESSING 71(2023):3328-3342. |
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