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Equivalence of concentration inequalities for linear and non-linear functions

Sullivan, T. J. and Owhadi, H. (2010) Equivalence of concentration inequalities for linear and non-linear functions. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20160224-082333411

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Abstract

We consider a random variable X that takes values in a (possibly infinite-dimensional) topological vector space X. We show that, with respect to an appropriate "normal distance" on X, concentration inequalities for linear and non-linear functions of X are equivalent. This normal distance corresponds naturally to the concentration rate in classical concentration results such as Gaussian concentration and concentration on the Euclidean and Hamming cubes. Under suitable assumptions on the roundness of the sets of interest, the concentration inequalities so obtained are asymptotically optimal in the high-dimensional limit.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1009.4913arXivDiscussion Paper
ORCID:
AuthorORCID
Owhadi, H.0000-0002-5677-1600
Additional Information:(Submitted on 24 Sep 2010). Date: September 27, 2010. The authors acknowledge portions of this work supported by the United States Department of Energy National Nuclear Security Administration under Award Number DE-FC52-08NA28613 through the California Institute of Technology’s ASC/PSAAP Center for the Predictive Modeling and Simulation of High Energy Density Dynamic Response of Materials.
Funders:
Funding AgencyGrant Number
Department of Energy (DOE) National Nuclear Security AdministrationDE-FC52-08NA28613
Subject Keywords:words and phrases. concentration of measure, large deviations, quasiconvexity, normal distance.
Classification Code:2010 Mathematics Subject Classification. 60E15, 60F10, 52A07.
Record Number:CaltechAUTHORS:20160224-082333411
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20160224-082333411
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:64721
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:24 Feb 2016 17:55
Last Modified:10 Jul 2017 23:59

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