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A Note on the Richness of Convex Hulls of VC Classes

Lugosi, Gabor; Mendelson, Shahar; Koltchinskii, Vladimir

Description

We prove the existence of a class A of subsets of ℝd of VC dimension 1 such that the symmetric convex hull F of the class of characteristic functions of sets in A is rich in the following sense. For any absolutely continuous probability measure μ on �

dc.contributor.authorLugosi, Gabor
dc.contributor.authorMendelson, Shahar
dc.contributor.authorKoltchinskii, Vladimir
dc.date.accessioned2015-12-13T23:07:12Z
dc.date.available2015-12-13T23:07:12Z
dc.identifier.issn1083-589X
dc.identifier.urihttp://hdl.handle.net/1885/86105
dc.description.abstractWe prove the existence of a class A of subsets of ℝd of VC dimension 1 such that the symmetric convex hull F of the class of characteristic functions of sets in A is rich in the following sense. For any absolutely continuous probability measure μ on �
dc.publisherInstitute of Mathematical Statistics
dc.sourceElectronic Communications in Probability
dc.subjectKeywords: Boosting; Convex hull; VC dimension
dc.titleA Note on the Richness of Convex Hulls of VC Classes
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume8
dc.date.issued2003
local.identifier.absfor010404 - Probability Theory
local.identifier.ariespublicationMigratedxPub14854
local.type.statusPublished Version
local.contributor.affiliationLugosi, Gabor, Pompeu Fabra University
local.contributor.affiliationMendelson, Shahar, College of Engineering and Computer Science, ANU
local.contributor.affiliationKoltchinskii, Vladimir, University of New Mexico
local.bibliographicCitation.startpage167
local.bibliographicCitation.lastpage169
dc.date.updated2015-12-12T08:08:16Z
local.identifier.scopusID2-s2.0-3042615979
CollectionsANU Research Publications

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