Entropy and the Combinatorial Dimension
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Mendelson, Shahar; Vershynin, Roman
Description
We solve Talagrand's entropy problem: The L2-covering numbers of every uniformly bounded class of functions are exponential in its shattering dimension. This extends Dudley's theorem on classes of {0, l}-valued functions, for which the shattering dimension is the Vapnik-Chervonenkis dimension. In convex geometry, the solution means that the entropy of a convex body K is controlled by the maximal dimension of a cube of a fixed side contained in the coordinate projections of K. This has a number...[Show more]
Collections | ANU Research Publications |
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Date published: | 2003 |
Type: | Journal article |
URI: | http://hdl.handle.net/1885/86106 |
Source: | Inventiones Mathematicae |
DOI: | 10.1007/s00222-002-0266-3 |
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