{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T02:32:15Z","timestamp":1775615535254,"version":"3.50.1"},"reference-count":95,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2023,2,24]],"date-time":"2023-02-24T00:00:00Z","timestamp":1677196800000},"content-version":"vor","delay-in-days":392,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["DMS-1916198"],"award-info":[{"award-number":["DMS-1916198"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>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\u2013Wolfowitz 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 \u2018spiked\u2019 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.<\/jats:p>","DOI":"10.1111\/rssb.12490","type":"journal-article","created":{"date-parts":[[2022,1,28]],"date-time":"2022-01-28T14:03:59Z","timestamp":1643378639000},"page":"853-878","source":"Crossref","is-referenced-by-count":18,"title":["Empirical Bayes PCA in High Dimensions"],"prefix":"10.1093","volume":"84","author":[{"given":"Xinyi","family":"Zhong","sequence":"first","affiliation":[{"name":"Department of Statistics and Data Science, Yale University , New Haven , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chang","family":"Su","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, Yale University , New Haven , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhou","family":"Fan","sequence":"additional","affiliation":[{"name":"Department of Statistics and Data Science, Yale University , New Haven , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2022,1,28]]},"reference":[{"key":"2023022501101110800_","volume-title":"A direct formulation for sparse PCA using semidefinite programming","author":"d'Aspremont","year":"2005"},{"key":"2023022501101110800_","volume-title":"Estimation in the spiked Wigner model: A short proof of the replica formula","author":"Alaoui","year":"2018"},{"key":"2023022501101110800_","doi-asserted-by":"crossref","DOI":"10.1109\/ISIT.2008.4595432","volume-title":"High-dimensional analysis of semidefinite relaxations for sparse principal components","author":"Amini","year":"2008"},{"key":"2023022501101110800_","doi-asserted-by":"crossref","first-page":"011020","DOI":"10.1103\/PhysRevX.9.011020","article-title":"Glassy nature of the hard phase in inference problems","volume":"9","author":"Antenucci","year":"2019","journal-title":"Physical Review 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