Empirical Bayes PCA in high dimensions

• 成果类型: Article
• 署名作者: Zhong, Xinyi; Su, Chang; Fan, Zhou
• 署名单位: Yale University; Yale University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12490
• 发表日期: 2022
• 页码: 853-878
• 关键词: maximum-likelihood-estimation; Principal Component Analysis; message-passing algorithms; Low-rank Matrix; sparse pca; mixture likelihoods; Covariance matrices; LARGEST EIGENVALUE; Consistency; phase

摘要

When the dimension of data is comparable to or larger than the number of data samples, principal components analysis (PCA) may exhibit problematic high-dimensional noise. In this work, we propose an empirical Bayes PCA method that reduces this noise by estimating a joint prior distribution for the principal components. EB-PCA is based on the classical Kiefer-Wolfowitz non-parametric maximum likelihood estimator for empirical Bayes estimation, distributional results derived from random matrix theory for the sample PCs and iterative refinement using an approximate message passing (AMP) algorithm. In theoretical 'spiked' models, EB-PCA achieves Bayes-optimal estimation accuracy in the same settings as an oracle Bayes AMP procedure that knows the true priors. Empirically, EB-PCA significantly improves over PCA when there is strong prior structure, both in simulation and on quantitative benchmarks constructed from the 1000 Genomes Project and the International HapMap Project. An illustration is presented for analysis of gene expression data obtained by single-cell RNA-seq.