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Discrepancy, chaining and subgaussian processes

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dc.contributor.authorMendelson, Shahar
dc.date.accessioned2016-02-08T05:05:44Z
dc.date.available2016-02-08T05:05:44Z
dc.date.issued2011
dc.date.updated2016-02-24T11:17:16Z
dc.description.abstractWe show that for a typical coordinate projection of a subgaussian class of functions, the infimum over signs inf(εi) supf∈F Σi=1k εif (Xi)| is asymptotically smaller than the expectation over signs as a function of the dimension k, if the canonical Gaussian process indexed by F is continuous. To that end, we establish a bound on the discrepancy of an arbitrary subset of R{double-struck}k using properties of the canonical Gaussian process the set indexes, and then obtain quantitative structural information on a typical coordinate projection of a subgaussian class.
dc.description.sponsorshipThe research leading to the results presented here has received funding from the European Research Council under the European Community’s Seventh Frame-work Programme (FP7/2007-2013)/ERC Grant Agreement [203134], from the Israel Science Foundation Grant 666/06 and from the Australian Research Council Grant DP0986563.en_AU
dc.identifier.issn0091-1798en_AU
dc.identifier.urihttp://hdl.handle.net/1885/97980
dc.publisherInstitute of Mathematical Statistics
dc.relationhttp://purl.org/au-research/grants/arc/DP0986563
dc.rights© Institute of Mathematical Statistics, 2011. http://www.sherpa.ac.uk/romeo/issn/0091-1798..."author can archive publisher's version/PDF. On author's personal website or open access repository" from SHERPA/RoMEO site (as at 8/02/16).
dc.sourceThe Annals of Probability
dc.subjectKeywords: Discrepancy; Generic chaining
dc.titleDiscrepancy, chaining and subgaussian processes
dc.typeJournal article
local.bibliographicCitation.issue3en_AU
local.bibliographicCitation.lastpage1026en_AU
local.bibliographicCitation.startpage985en_AU
local.contributor.affiliationMendelson, Shahar, College of Physical and Mathematical Sciences, CPMS Mathematical Sciences Institute, Centre for Mathematics and Its Applications, The Australian National Universityen_AU
local.contributor.authoruidu4011413en_AU
local.description.notesImported from ARIESen_AU
local.identifier.absfor010404en_AU
local.identifier.absseo970101en_AU
local.identifier.ariespublicationu4685828xPUB26en_AU
local.identifier.citationvolume39en_AU
local.identifier.doi10.1214/10-AOP575en_AU
local.identifier.scopusID2-s2.0-79953204327
local.type.statusPublished Versionen_AU

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