Entropy, dimension and the Elton-Pajor Theorem
Functional Analysis
2016-12-23 v1 Combinatorics
Abstract
The Vapnik-Chervonenkis dimension of a set K in R^n is the maximal dimension of the coordinate cube of a given size, which can be found in coordinate projections of K. We show that the VC dimension of a convex body governs its entropy. This has a number of consequences, including the optimal Elton's theorem and a uniform central limit theorem in the real valued case.
Cite
@article{arxiv.math/0201048,
title = {Entropy, dimension and the Elton-Pajor Theorem},
author = {S. Mendelson and R. Vershynin},
journal= {arXiv preprint arXiv:math/0201048},
year = {2016}
}