Skip navigation
Skip navigation

Entropy and the Combinatorial Dimension

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]

CollectionsANU Research Publications
Date published: 2003
Type: Journal article
URI: http://hdl.handle.net/1885/86106
Source: Inventiones Mathematicae
DOI: 10.1007/s00222-002-0266-3

Download

File Description SizeFormat Image
01_Mendelson_Entropy_and_the_Combinatorial_2003.pdf322.32 kBAdobe PDF    Request a copy


Items in Open Research are protected by copyright, with all rights reserved, unless otherwise indicated.

Updated:  23 August 2018/ Responsible Officer:  University Librarian/ Page Contact:  Library Systems & Web Coordinator