PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Local tail bounds for functions of independent random variables
Luc Devroye and Gábor Lugosi
Annals of Probability Volume 36, pp. 143-159, 2008.

Abstract

It is shown that functions defined on {0, 1, . . . , r − 1} n satisfying certain condi- tions of bounded differences that guarantee subgaussian tail behavior also satisfy a much stronger “local” subgaussian property. For self-bounding and configuration functions we derive analogous locally subexponential behavior. The key tool is Talagrand’s (1994) vari- ance inequality for functions defined on the binary hypercube which we extend to functions of uniformly distributed random variables defined on {0, 1, . . . , r − 1} n for r ≥ 2.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:3928
Deposited By:Gábor Lugosi
Deposited On:25 February 2008