Uniform Approximation and Bracketing Properties of VC classes
Probability
2010-07-26 v1 Statistics Theory
Machine Learning
Statistics Theory
Abstract
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.
Cite
@article{arxiv.1007.4037,
title = {Uniform Approximation and Bracketing Properties of VC classes},
author = {Terrence M. Adams and Andrew B. Nobel},
journal= {arXiv preprint arXiv:1007.4037},
year = {2010}
}
Comments
10 pages