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dc.contributor.authorMao, Cheng
dc.contributor.authorRigollet, Philippe
dc.date.accessioned2020-08-24T17:32:25Z
dc.date.available2020-08-24T17:32:25Z
dc.date.issued2019
dc.identifier.issn1350-7265
dc.identifier.urihttps://hdl.handle.net/1721.1/126756
dc.description.abstractGiven a matrix, the seriation problem consists in permuting its rows in such way that all its columns have the same shape, for example, they are monotone increasing. We propose a statistical approach to this problem where the matrix of interest is observed with noise and study the corresponding minimax rate of estimation of the matrices. Specifically, when the columns are either unimodal or monotone, we show that the least squares estimator is optimal up to logarithmic factors and adapts to matrices with a certain natural structure. Finally, we propose a computationally efficient estimator in the monotonic case and study its performance both theoretically and experimentally. Our work is at the intersection of shape constrained estimation and recent work that involves permutation learning, such as graph denoising and ranking.en_US
dc.language.isoen
dc.publisherBernoulli Society for Mathematical Statistics and Probabilityen_US
dc.relation.isversionof10.3150/17-BEJ1000en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourcearXiven_US
dc.titleOptimal rates of statistical seriationen_US
dc.typeArticleen_US
dc.identifier.citationFlammarion, Nicolas, Cheng Mao and Philippe Rigollet. “Optimal rates of statistical seriation.” Bernoulli, 25, 1 (2019): 623-653 © 2019 The Author(s)en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.relation.journalBernoullien_US
dc.eprint.versionOriginal manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/NonPeerRevieweden_US
dc.date.updated2019-11-19T18:16:08Z
dspace.date.submission2019-11-19T18:16:14Z
mit.journal.volume25en_US
mit.journal.issue1en_US


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