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])
ISSN1053-587X
EISSN1941-0476
卷号71页码:3328-3342
发表状态已发表
DOI10.1109/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...
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.
条目包含的文件
文件名称/大小 文献类型 版本类型 开放类型 使用许可
个性服务
查看访问统计
谷歌学术
谷歌学术中相似的文章
[Quan Wei]的文章
[Ziping Zhao]的文章
百度学术
百度学术中相似的文章
[Quan Wei]的文章
[Ziping Zhao]的文章
必应学术
必应学术中相似的文章
[Quan Wei]的文章
[Ziping Zhao]的文章
相关权益政策
暂无数据
收藏/分享
所有评论 (0)
暂无评论
 

除非特别说明,本系统中所有内容都受版权保护,并保留所有权利。