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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]

CollectionsANU Research Publications
Date published: 2011
Type: Journal article
URI: http://hdl.handle.net/1885/97980
Source: The Annals of Probability
DOI: 10.1214/10-AOP575

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