Concentration Inequalities for Sub-Additive Functions Using the Entropy Method

Bousquet, O

doi:10.1007/978-3-0348-8069-5_14

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Concentration Inequalities for Sub-Additive Functions Using the Entropy Method

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

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Citation

Bousquet, O. (2003). Concentration Inequalities for Sub-Additive Functions Using the Entropy Method. In E. Giné, C. Houdré, & D. Nualart (Eds.), Stochastic Inequalities and Applications (pp. 213-247). Basel, Switzerland: Birkhäuser.

Cite as: https://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.