Large Covariance Matrix Estimation with Oracle Statistical Rate

doi:10.1109/ICASSP49357.2023.10095334

	Large Covariance Matrix Estimation with Oracle Statistical Rate
	Quan Wei; Ziping ZHao
	2023
会议录名称	ICASSP 2023 - 2023 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP)
ISSN	1520-6149
发表状态	已发表
DOI	10.1109/ICASSP49357.2023.10095334
摘要	The ℓ1 penalized covariance estimator has been widely used for estimating large sparse covariance matrices. It was recognized that ℓ1 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. In this paper, to eliminate the estimation bias we propose to estimate large sparse covariance matrices using the non-convex penalty. It is a challenging task to analyze the theoretical properties of the resulting covariance 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) is developed by solving a sequence of convex relaxation subproblems. We prove that the proposed estimator computed exactly by the MM-based algorithm achieves the oracle statistical rate under weak assumptions. Our theoretical findings are corroborated through extensive numerical experiments.
关键词	Covariance estimation sparsity non-convex statistical optimization majorization-minimization
会议名称	48th IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2023
会议地点	Rhodes Island, Greece
会议日期	4-10 June 2023
URL	查看原文
收录类别	EI
语种	英语
出版者	Institute of Electrical and Electronics Engineers Inc.
EI入藏号	20234715105369
原始文献类型	Conference article (CA)
来源库	IEEE
文献类型	会议论文
条目标识符	https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/331131
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[C]:Institute of Electrical and Electronics Engineers Inc.,2023.