arXiv:1007.4037 Abstract | arXiv Analytics

arXiv:1007.4037 [math.PR]Abstract References Reviews Resources

Uniform Approximation and Bracketing Properties of VC classes

Published 2010-07-23Version 1

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.

Comments: 10 pages

Categories: math.PR, math.ST, stat.ML, stat.TH

Subjects: 60F15, 60G10, 62G05

Keywords: vc classes, uniform approximation, bracketing properties, work concerning uniform laws, satisfy uniform laws

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