Sparse PCA with Oracle Rate in High Dimensions
2025-04-11
会议录名称ICASSP 2025 - 2025 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP)
ISSN1520-6149
发表状态已发表
DOI10.1109/ICASSP49660.2025.10888203
摘要

In this paper, we study the sparse principal component analysis (PCA) problem in high-dimensional settings. We propose a novel row-sparse principal subspace estimator, which estimates the subspace spanned by multiple eigenvectors based on the variance maximization problem with a nonconvex sparsity regularizer. To tackle the nonconvex estimation problem, we introduce a minorization-maximization (MM) algorithm to decompose it into a sequence of convex subproblems. Each subproblem is solved based on the alternating direction method of multipliers. Theoretically, we provide a comprehensive analysis of both the computational and statistical properties of the iterates from the MM algorithm. We demonstrate that the proposed sparse PCA estimator can achieve the same statistical rate as the oracle estimator. Simulation results corroborate the theoretical findings and highlight the superiority of the proposed sparse PCA estimator.

会议录编者/会议主办者IEEE ; IEEE Signal Processing Society
会议名称2025 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2025
会议地点Hyderabad, India
会议日期6-11 April 2025
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收录类别EI
语种英语
出版者Institute of Electrical and Electronics Engineers Inc.
EI入藏号20251818340883
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/496899
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
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
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
Wenfu Zhong,Ziping Zhao. Sparse PCA with Oracle Rate in High Dimensions[C]//IEEE, IEEE Signal Processing Society:Institute of Electrical and Electronics Engineers Inc.,2025.
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