Some Extensions of an Inequality of Vapnik and Chervonenkis
Dmitriy Panchenko, University of New Mexico
Abstract
The inequality of Vapnik and Chervonenkis controls
the expectation of the function by its sample
average uniformly over a VC-major class of functions taking into account
the size of the expectation.
Using Talagrand's kernel method we prove a similar result for the classes
of functions for which Dudley's
uniform entropy integral or bracketing entropy integral is finite.
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