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dc.contributor.authorCanonne, Clement L
dc.contributor.authorGouleakis, Themistoklis
dc.contributor.authorRubinfeld, Ronitt
dc.date.accessioned2017-10-27T15:30:38Z
dc.date.available2017-10-27T15:30:38Z
dc.date.issued2016-01
dc.identifier.isbn978-1-4503-4057-1
dc.identifier.urihttp://hdl.handle.net/1721.1/111986
dc.description.abstractIn many situations, sample data is obtained from a noisy or imperfect source. In order to address such corruptions, this paper introduces the concept of a sampling corrector. Such algorithms use structure that the distribution is purported to have, in order to allow one to make "on-the-fly" corrections to samples drawn from probability distributions. These algorithms then act as filters between the noisy data and the end user. We show connections between sampling correctors, distribution learning algorithms, and distribution property testing algorithms. We show that these connections can be utilized to expand the applicability of known distribution learning and property testing algorithms as well as to achieve improved algorithms for those tasks. As a first step, we show how to design sampling correctors using proper learning algorithms. We then focus on the question of whether algorithms for sampling correctors can be more efficient in terms of sample complexity than learning algorithms for the analogous families of distributions. When correcting monotonicity, we show that this is indeed the case when also granted query access to the cumulative distribution function. We also obtain sampling correctors for monotonicity without this stronger type of access, provided that the distribution be originally very close to monotone (namely, at a distance O(1/log2 n)). In addition to that, we consider a restricted error model that aims at capturing "missing data" corruptions. In this model, we show that distributions that are close to monotone have sampling correctors that are significantly more efficient than achievable by the learning approach. We then consider the question of whether an additional source of independent random bits is required by sampling correctors to implement the correction process. We show that for correcting close-to-uniform distributions and close-to-monotone distributions, no additional source of random bits is required, as the samples from the input source itself can be used to produce this randomness.en_US
dc.language.isoen_US
dc.publisherAssociation for Computing Machinery (ACM)en_US
dc.relation.isversionofhttp://dx.doi.org/10.1145/2840728.2840729en_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.titleSampling correctorsen_US
dc.typeArticleen_US
dc.identifier.citationCanonne, Clement L et al. "Sampling correctors." Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science (ITCS '16), January 14-17 2016, Cambridge, Massachusetts, USA, Association for Computing Machinery (ACM), January 2016 © 2016 Association for Computing Machinery (ACM)en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Scienceen_US
dc.contributor.mitauthorGouleakis, Themistoklis
dc.contributor.mitauthorRubinfeld, Ronitt
dc.relation.journalProceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science (ITCS '16)en_US
dc.eprint.versionOriginal manuscripten_US
dc.type.urihttp://purl.org/eprint/type/ConferencePaperen_US
eprint.statushttp://purl.org/eprint/status/NonPeerRevieweden_US
dspace.orderedauthorsCanonne, Clement L; Gouleakis, Themis; Rubinfeld, Ronitten_US
dspace.embargo.termsNen_US
dc.identifier.orcidhttps://orcid.org/0000-0002-4056-0489
dc.identifier.orcidhttps://orcid.org/0000-0002-4353-7639
mit.licenseOPEN_ACCESS_POLICYen_US


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