Uniform Approximation of Vapnik-Chervonenkis Classes

10/21/2010
by   Terrence M. Adams, et al.
0

For any family of measurable sets in a probability space, we show that either (i) the family has infinite Vapnik-Chervonenkis (VC) dimension or (ii) for every epsilon > 0 there is a finite partition pi such the pi-boundary of each set has measure at most epsilon. Immediate corollaries include the fact that a family with finite VC dimension has finite bracketing numbers, and satisfies uniform laws of large numbers for every ergodic process. From these corollaries, we derive analogous results for VC major and VC graph families of functions.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset