Uniform Approximation and Bracketing Properties of VC classes

Details Uniform Approximation and Bracketing Properties of VC classes Uniform Approximation and Bracketing Properties of VC classes

2010-07-23

arxiv.org/abs/1007.4037v1

Mathematics

Probability

10 pages

Scientific paper

We show that the sets in a family with finite VC dimension can be uniformly approximated within a given error by a finite partition. Immediate corollaries include the fact that VC classes have finite bracketing numbers, satisfy uniform laws of averages under strong dependence, and exhibit uniform mixing. Our results are based on recent work concerning uniform laws of averages for VC classes under ergodic sampling.

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