INFERENCE FOR HETEROSKEDASTIC PCA WITH MISSING DATA

• 成果类型: Article
• 署名作者: Yan, Yuling; Chen, Yuxin; Fan, Jianqing
• 署名单位: Massachusetts Institute of Technology (MIT); University of Pennsylvania; Princeton University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2366
• 发表日期: 2024
• 页码: 729-756
• 关键词: low-rank matrix; confidence-intervals; Uncertainty Quantification; principal components; singular subspaces; LARGEST EIGENVALUE; robust regression; Gradient descent; completion; noisy

摘要

This paper studies how to construct confidence regions for principal component analysis (PCA) in high dimension, a problem that has been vastly underexplored. While computing measures of uncertainty for nonlinear/nonconvex estimators is in general difficult in high dimension, the challenge is further compounded by the prevalent presence of missing data and heteroskedastic noise. We propose a novel approach to performing valid inference on the principal subspace, on the basis of an estimator called HeteroPCA guarantees for HeteroPCA, and demonstrate how these can be invoked to compute both confidence regions for the principal subspace and entrywise confidence intervals for the spiked covariance matrix. Our inference procedures are fully data-driven and adaptive to heteroskedastic random noise, without requiring prior knowledge about the noise levels.