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April 1997 Information inequalities and concentration of measure
Amir Dembo
Ann. Probab. 25(2): 927-939 (April 1997). DOI: 10.1214/aop/1024404424

Abstract

We derive inequalities of the form $\Delta (P, Q) \leq H(P|R) + H(Q|R)$ which hold for every choice of probability measures P, Q, R, where $H(P|R)$ denotes the relative entropy of $P$ with respect to $R$ and $\Delta (P, Q)$ stands for a coupling type "distance" between $P$ and $Q$. Using the chain rule for relative entropies and then specializing to $Q$ with a given support we recover some of Talagrand's concentration of measure inequalities for product spaces.

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Amir Dembo. "Information inequalities and concentration of measure." Ann. Probab. 25 (2) 927 - 939, April 1997. https://doi.org/10.1214/aop/1024404424

Information

Published: April 1997
First available in Project Euclid: 18 June 2002

zbMATH: 0880.60018
MathSciNet: MR1434131
Digital Object Identifier: 10.1214/aop/1024404424

Subjects:
Primary: 28A35, 60E15

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.25 • No. 2 • April 1997
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