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Some extensions of an inequality of Vapnik and Chervonenkis

Dmitry Panchenko
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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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Dmitry Panchenko. 2004-05-18. Some extensions of an inequality of Vapnik and Chervonenkis. https://arxiv.org/abs/math/0405342

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