Sparse PCA with Oracle Property

2023/12/28 by Quanquan Gu, Gu, Quanquan, Zhaoran Wang +3
Engineering · Mathematics · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Random Matrices and Applications #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference

paper · doi:10.48550/arxiv.2312.16793

openalex publication_date 2023/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

the sample size. Compared to existing support recovery results for sparse PCA, our approach does not hinge on the spiked covariance model or the limited correlation condition. As a complement to the first estimator that enjoys the oracle property, we prove that, another estimator within the family achieves a sharper statistical rate of convergence than the standard semidefinite relaxation of sparse PCA, even when the previous assumption on the magnitude of the projection matrix is violated. We validate the theoretical results by numerical experiments on synthetic datasets.

Citations

• Computational Lower Bounds for Sparse PCA
• Nearly unbiased variable selection under minimax concave penalty
• Sparse Principal Component Analysis
• Generalized power method for sparse principal component analysis
• Augmented sparse principal component analysis for high dimensional data

Cited by

• An efficient adaptive accelerated inexact proximal point method for solving linearly constrained nonconvex composite problems

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