Discrepancy, chaining and subgaussian processes
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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]
Collections | ANU Research Publications |
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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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01_Mendelson_Discrepancy,_chaining_and_2011.pdf | Published Version | 362.22 kB | Adobe PDF |
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