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dc.contributor.authorBresler, Guy
dc.contributor.authorKarzand, Mina
dc.date.accessioned2021-02-02T13:01:12Z
dc.date.available2021-02-02T13:01:12Z
dc.date.issued2020-04
dc.identifier.issn0090-5364
dc.identifier.urihttps://hdl.handle.net/1721.1/129620
dc.description.abstractWe study the problem of learning a tree Ising model from samples such that subsequent predictions made using the model are accurate. The prediction task considered in this paper is that of predicting the values of a subset of variables given values of some other subset of variables. Virtually all previous work on graphical model learning has focused on recovering the true underlying graph. We define a distance (“small set TV” or ssTV) between distributions P and Q by taking the maximum, over all subsets S of a given size, of the total variation between the marginals of P and Q on S; this distance captures the accuracy of the prediction task of interest. We derive nonasymptotic bounds on the number of samples needed to get a distribution (from the same class) with small ssTV relative to the one generating the samples. One of the main messages of this paper is that far fewer samples are needed than for recovering the underlying tree, which means that accurate predictions are possible using the wrong tree.en_US
dc.description.sponsorshipUnited States. Office of Naval Research (Grant N00014-17-1-2147)en_US
dc.description.sponsorshipUnited States. Defense Advanced Research Projects Agency (Grant W911NF-16-1-0551)en_US
dc.description.sponsorshipNational Science Foundation (U.S.). Computing and Communication Foundation (Grant CCF-1565516)en_US
dc.language.isoen
dc.publisherInstitute of Mathematical Statisticsen_US
dc.relation.isversionof10.1214/19-AOS1808en_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.titleLearning a tree-structured ising model in order to make predictionsen_US
dc.typeArticleen_US
dc.identifier.citationBresler, Guy and Mina Karzand. “Learning a tree-structured ising model in order to make predictions.” Annals of Statistics, 48, 2 (April 2020): 713-737 © 2020 The Author(s)en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Scienceen_US
dc.contributor.departmentMassachusetts Institute of Technology. Laboratory for Information and Decision Systemsen_US
dc.relation.journalAnnals of Statisticsen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2020-12-03T17:34:34Z
dspace.orderedauthorsBresler, G; Karzand, Men_US
dspace.date.submission2020-12-03T17:34:35Z
mit.journal.volume48en_US
mit.journal.issue2en_US
mit.licenseOPEN_ACCESS_POLICY


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