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dc.contributor.authorWang, Tengyaoen
dc.contributor.authorBerthet, Quentinen
dc.contributor.authorSamworth, Richarden
dc.date.accessioned2015-08-11T10:39:21Z
dc.date.available2015-08-11T10:39:21Z
dc.date.issued2016-10en
dc.identifier.issn0090-5364
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/249255
dc.description.abstractIn recent years, sparse principal component analysis has emerged as an extremely popular dimension reduction technique for high-dimensional data. The theoretical challenge, in the simplest case, is to estimate the leading eigenvector of a population covariance matrix under the assumption that this eigenvector is sparse. An impressive range of estimators have been proposed; some of these are fast to compute, while others are known to achieve the minimax optimal rate over certain Gaussian or sub-Gaussian classes. In this paper, we show that, under a widely-believed assumption from computational complexity theory, there is a fundamental trade-off between statistical and computational performance in this problem. More precisely, working with new, larger classes satisfying a restricted covariance concentration condition, we show that there is an effective sample size regime in which no randomised polynomial time algorithm can achieve the minimax optimal rate. We also study the theoretical performance of a (polynomial time) variant of the well-known semidefinite relaxation estimator, revealing a subtle interplay between statistical and computational efficiency.
dc.language.isoenen
dc.rightsAttribution-NonCommercial 2.0 UK: England & Wales*
dc.rights.urihttp://creativecommons.org/licenses/by-nc/2.0/uk/*
dc.subjectComputational lower boundsen
dc.subjectplanted clique problemen
dc.subjectpolynomial time algorithmen
dc.subjectsparse principal component analysisen
dc.titleSTATISTICAL AND COMPUTATIONAL TRADE-OFFS IN ESTIMATION OF SPARSE PRINCIPAL COMPONENTSen
dc.typeArticle
prism.endingPage1930
prism.issueIdentifier5en
prism.publicationDate2016en
prism.publicationNameANNALS OF STATISTICSen
prism.startingPage1896
prism.volume44en
dc.rioxxterms.funderEPSRC
dc.rioxxterms.projectidEP/J017213/1
dcterms.dateAccepted2015-07-23en
rioxxterms.versionofrecord10.1214/15-AOS1369en
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2016-10en
dc.contributor.orcidSamworth, Richard [0000-0003-2426-4679]
rioxxterms.typeJournal Article/Reviewen
pubs.funder-project-idEPSRC (EP/J017213/1)
pubs.funder-project-idLeverhulme Trust (PLP-2014-353)
cam.issuedOnline2016-09-12en


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Attribution-NonCommercial 2.0 UK: England & Wales
Except where otherwise noted, this item's licence is described as Attribution-NonCommercial 2.0 UK: England & Wales