On concentration of self-bounding functions
Stephane Boucheron, Université Paris-Diderot
Gabor Lugosi, Pompeu Fabra University
Pascal Massart, Université Paris-Sud
Abstract
We prove some new concentration inequalities for self-bounding
functions using the entropy method. As an application, we recover
Talagrand's convex distance inequality. The new Bernstein-like
inequalities for self-bounding functions are derived thanks to a
careful analysis of the so-called Herbst argument. The latter
involves comparison results between solutions of differential
inequalities that may be interesting in their own right.
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