dc.contributor.author Shah, Rajen en dc.contributor.author Frot, B en dc.contributor.author Thanei, GA en dc.contributor.author Meinshausen, N en dc.date.accessioned 2020-03-20T02:16:28Z dc.date.available 2020-03-20T02:16:28Z dc.date.issued 2020-04-01 en dc.identifier.issn 1369-7412 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/303638 dc.description.abstract In this work we consider the problem of estimating a high-dimensional $p \times p$ covariance matrix $\Sigma$, given $n$ observations of confounded data with covariance $\Sigma + \Gamma \Gamma^T$, where $\Gamma$ is an unknown $p \times q$ matrix of latent factor loadings. We propose a simple and scalable estimator based on the projection on to the right singular vectors of the observed data matrix, which we call RSVP. Our theoretical analysis of this method reveals that in contrast to PCA-based approaches, RSVP is able to cope well with settings where the smallest eigenvalue of $\Gamma^T \Gamma$ is close to the largest eigenvalue of $\Sigma$, as well as settings where the eigenvalues of $\Gamma^T \Gamma$ are diverging fast. It is also able to handle data that may have heavy tails and only requires that the data has an elliptical distribution. RSVP does not require knowledge or estimation of the number of latent factors $q$, but only recovers $\Sigma$ up to an unknown positive scale factor. We argue this suffices in many applications, for example if an estimate of the correlation matrix is desired. We also show that by using subsampling, we can further improve the performance of the method. We demonstrate the favourable performance of RSVP through simulation experiments and an analysis of gene expression datasets collated by the GTEX consortium. dc.description.sponsorship Supported by an EPSRC First Grant and the Alan Turing Institute under the EPSRC grant EP/N510129/1. dc.publisher Wiley-Blackwell dc.rights Attribution 4.0 International dc.rights.uri https://creativecommons.org/licenses/by/4.0/ dc.title Right singular vector projection graphs: fast high dimensional covariance matrix estimation under latent confounding en dc.type Article prism.endingPage 389 prism.issueIdentifier 2 en prism.publicationDate 2020 en prism.publicationName Journal of the Royal Statistical Society. Series B: Statistical Methodology en prism.startingPage 361 prism.volume 82 en dc.identifier.doi 10.17863/CAM.50715 dcterms.dateAccepted 2019-11-13 en rioxxterms.versionofrecord 10.1111/rssb.12359 en rioxxterms.version VoR rioxxterms.licenseref.uri http://www.rioxx.net/licenses/all-rights-reserved en rioxxterms.licenseref.startdate 2020-04-01 en dc.contributor.orcid Shah, Rajen [0000-0001-9073-3782] dc.identifier.eissn 1467-9868 rioxxterms.type Journal Article/Review en pubs.funder-project-id EPSRC (EP/R013381/1) pubs.funder-project-id Alan Turing Institute (unknown)
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Except where otherwise noted, this item's licence is described as Attribution 4.0 International