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Empirical minimization

Bartlett, Peter L; Mendelson, Shahar

Description

We investigate the behavior of the empirical minimization algorithm using various methods. We first analyze it by comparing the empirical, random, structure and the original one on the class, either in an additive sense, via the uniform law of large numbers, or in a multiplicative sense, using isomorphic coordinate projections. We then show that a direct analysis of the empirical minimization algorithm yields a significantly better bound, and that the estimates we obtain are essentially sharp....[Show more]

dc.contributor.authorBartlett, Peter L
dc.contributor.authorMendelson, Shahar
dc.date.accessioned2015-12-07T22:49:12Z
dc.identifier.issn0178-8051
dc.identifier.urihttp://hdl.handle.net/1885/26652
dc.description.abstractWe investigate the behavior of the empirical minimization algorithm using various methods. We first analyze it by comparing the empirical, random, structure and the original one on the class, either in an additive sense, via the uniform law of large numbers, or in a multiplicative sense, using isomorphic coordinate projections. We then show that a direct analysis of the empirical minimization algorithm yields a significantly better bound, and that the estimates we obtain are essentially sharp. The method of proof we use is based on Talagrand's concentration inequality for empirical processes.
dc.publisherSpringer
dc.sourceProbability Theory and Related Fields
dc.subjectKeywords: Empirical minimization; Empirical processes; Error bounds; Isomorphic coordinate projections
dc.titleEmpirical minimization
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume135
dc.date.issued2006
local.identifier.absfor010102 - Algebraic and Differential Geometry
local.identifier.absfor010404 - Probability Theory
local.identifier.ariespublicationu3488905xPUB46
local.type.statusPublished Version
local.contributor.affiliationBartlett, Peter L, University of California
local.contributor.affiliationMendelson, Shahar, College of Physical and Mathematical Sciences, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.startpage311
local.bibliographicCitation.lastpage334
local.identifier.doi10.1007/s00440-005-0462-3
dc.date.updated2015-12-07T12:06:38Z
local.identifier.scopusID2-s2.0-33645979357
CollectionsANU Research Publications

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