25 citations · 49 across the 12 of their papers we have counts for
4 papers · 1 filter
Uniform Approximation of Vapnik-Chervonenkis Classes
Terrence M. Adams, Andrew B. Nobel
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…
Uniform convergence of Vapnik--Chervonenkis classes under ergodic sampling
Terrence M. Adams, Andrew B. Nobel
We show that if is a complete separable metric space and is a countable family of Borel subsets of with finite VC dimension, then, for eve…
Uniform Approximation and Bracketing Properties of VC classes
Terrence M. Adams, Andrew B. Nobel
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…
The Gap Dimension and Uniform Laws of Large Numbers for Ergodic Processes
Terrence M. Adams, Andrew B. Nobel
Let F be a family of Borel measurable functions on a complete separable metric space. The gap (or fat-shattering) dimension of F is a combinatorial quantity that measures the exten…