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A sharp concentration inequality with applications

✍ Scribed by Stéphane Boucheron; Gábor Lugosi; Pascal Massart

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
146 KB
Volume
16
Category
Article
ISSN
1042-9832

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✦ Synopsis

We derive a new general concentration-of-measure inequality. The concentration inequality applies, among others, to configuration functions as defined by Talagrand and also to combinatorial entropies such as the logarithm of the number of increasing subsequences in a random permutation and to Vapnik-Chervonenkis (VC) entropies. The results find direct applications in statistical learning theory, substantiating the possibility to use the empirical VC entropy in penalization techniques.

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