Discrepancy, chaining and subgaussian processes
Date
2011
Authors
Mendelson, Shahar
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Institute of Mathematical Statistics
Abstract
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 information on a typical coordinate projection of a subgaussian class.
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Keywords: Discrepancy; Generic chaining
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The Annals of Probability
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Journal article
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