{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,18]],"date-time":"2026-04-18T12:08:36Z","timestamp":1776514116165,"version":"3.51.2"},"reference-count":20,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2020,7,18]],"date-time":"2020-07-18T00:00:00Z","timestamp":1595030400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,9,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>Models specified by low rank matrices are ubiquitous in contemporary applications. In many of these problem domains, the row\u2013column space structure of a low rank matrix carries information about some underlying phenomenon, and it is of interest in inferential settings to evaluate the extent to which the row\u2013column spaces of an estimated low rank matrix signify discoveries about the phenomenon. However, in contrast with variable selection, we lack a formal framework to assess true or false discoveries in low rank estimation; in particular, the key source of difficulty is that the standard notion of a discovery is a discrete notion that is ill suited to the smooth structure underlying low rank matrices. We address this challenge via a geometric reformulation of the concept of a discovery, which then enables a natural definition in the low rank case. We describe and analyse a generalization of the stability selection method of Meinshausen and B\u00fchlmann to control for false discoveries in low rank estimation, and we demonstrate its utility compared with previous approaches via numerical experiments.<\/jats:p>","DOI":"10.1111\/rssb.12387","type":"journal-article","created":{"date-parts":[[2020,7,18]],"date-time":"2020-07-18T08:16:40Z","timestamp":1595060200000},"page":"997-1027","source":"Crossref","is-referenced-by-count":4,"title":["False Discovery and its Control in Low Rank Estimation"],"prefix":"10.1093","volume":"82","author":[{"given":"Armeen","family":"Taeb","sequence":"first","affiliation":[{"name":"California Institute of Technology , Pasadena , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Parikshit","family":"Shah","sequence":"additional","affiliation":[{"name":"Yahoo Research and Wisconsin Institutes for Discovery , Madison , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Venkat","family":"Chandrasekaran","sequence":"additional","affiliation":[{"name":"California Institute of Technology , Pasadena , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2020,7,18]]},"reference":[{"key":"2023022408364833600_","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1111\/j.2517-6161.1995.tb02031.x","article-title":"Controlling the false discovery rate: a practical and powerful approach to multiple testing","volume":"57","author":"Benjamini","year":"1995","journal-title":"J. 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