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Discrepancy, chaining and subgaussian processes

Mendelson, Shahar

Description

We 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...[Show more]

dc.contributor.authorMendelson, Shahar
dc.date.accessioned2016-02-08T05:05:44Z
dc.date.available2016-02-08T05:05:44Z
dc.identifier.issn0091-1798
dc.identifier.urihttp://hdl.handle.net/1885/97980
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.
dc.publisherInstitute of Mathematical Statistics
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.description.notesImported from ARIES
local.identifier.citationvolume39
dc.date.issued2011
local.identifier.absfor010404
local.identifier.ariespublicationu4685828xPUB26
local.type.statusPublished Version
local.contributor.affiliationMendelson, Shahar, College of Physical and Mathematical Sciences, CPMS Mathematical Sciences Institute, Centre for Mathematics and Its Applications, The Australian National University
dc.relationhttp://purl.org/au-research/grants/arc/DP0986563
local.bibliographicCitation.issue3
local.bibliographicCitation.startpage985
local.bibliographicCitation.lastpage1026
local.identifier.doi10.1214/10-AOP575
local.identifier.absseo970101
dc.date.updated2016-02-24T11:17:16Z
local.identifier.scopusID2-s2.0-79953204327
CollectionsANU Research Publications

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