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Concentration Inequalities for Sub-Additive Functions Using the Entropy Method

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons83824

Bousquet,  O
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Bousquet, O. (2003). Concentration Inequalities for Sub-Additive Functions Using the Entropy Method. Stochastic Inequalities and Applications, 56, 213-247.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-DABF-8
Abstract
We obtain exponential concentration inequalities for sub-additive functions of independent random variables under weak conditions on the increments of those functions, like the existence of exponential moments for these increments. As a consequence of these general inequalities, we obtain refinements of Talagrand's inequality for empirical processes and new bounds for randomized empirical processes. These results are obtained by further developing the entropy method introduced by Ledoux.