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dc.contributor.authorMatulef, Kevin M.
dc.contributor.authorO'Donnell, Ryan
dc.contributor.authorRubinfeld, Ronitt
dc.contributor.authorServedio, Rocco
dc.date.accessioned2012-08-08T15:59:10Z
dc.date.available2012-08-08T15:59:10Z
dc.date.issued2010-01
dc.identifier.isbn978-3-642-16366-1
dc.identifier.urihttp://hdl.handle.net/1721.1/72033
dc.description.abstractWe address the problem of testing whether a Boolean-valued function f is a halfspace, i.e. a function of the form f(x) = sgn(w . x − θ). We consider halfspaces over the continuous domain R n (endowed with the standard multivariate Gaussian distribution) as well as halfspaces over the Boolean cube { − 1,1} n (endowed with the uniform distribution). In both cases we give an algorithm that distinguishes halfspaces from functions that are ε-far from any halfspace using only poly(1) queries, independent of the dimension n. In contrast to the case of general halfspaces, we show that testing natural subclasses of halfspaces can be markedly harder; for the class of { − 1,1}-weight halfspaces, we show that a tester must make at least Ω(logn) queries. We complement this lower bound with an upper bound showing that O(√n) queries suffice.en_US
dc.description.sponsorshipNational Basic Research Program of China (grant 2007CB807900)en_US
dc.description.sponsorshipNational Basic Research Program of China (grant 2007CB807901)en_US
dc.description.sponsorshipNational Natural Science Foundation (China) (grant 60553001)en_US
dc.language.isoen_US
dc.publisherSpringer-Verlagen_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/978-3-642-16367-8_27en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alike 3.0en_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/en_US
dc.sourceRubinfeld via Amy Stouten_US
dc.titleTesting (subclasses of) halfspacesen_US
dc.typeArticleen_US
dc.identifier.citationMatulef, Kevin et al. “Testing (Subclasses of) Halfspaces.” Property Testing. Ed. Oded Goldreich. (Lecture Notes in Computer Science : Vol. 6390). Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. 334–340.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratoryen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Scienceen_US
dc.contributor.approverRubinfeld, Ronitt
dc.contributor.mitauthorRubinfeld, Ronitt
dc.relation.journalProceedings of the ITCS Mini-workshop on Property Testing (2010 : Beijing, China)en_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
dspace.orderedauthorsMatulef, Kevin; O’Donnell, Ryan; Rubinfeld, Ronitt; Servedio, Roccoen
dc.identifier.orcidhttps://orcid.org/0000-0002-4353-7639
mit.licenseOPEN_ACCESS_POLICYen_US


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