Title :
A distribution dependent refinement of Pinsker´s inequality
Author :
Ordentlich, Erik ; Weinberger, Marcelo J.
Author_Institution :
Hewlett-Packard Labs., Palo Alto, CA, USA
fDate :
5/1/2005 12:00:00 AM
Abstract :
Given two probability distributions Q and P, let ||Q-P||1 and D(Q||P), respectively, denote the L1 distance and divergence between Q and P. We derive a refinement of Pinsker´s inequality of the form D(Q||P)≥c(P)||Q-P||12 and characterize the best P-dependent factor c(P). We apply the refined inequality to large deviations and measure concentration.
Keywords :
information theory; probability; Hoeffding inequality; P-dependent factor; Pinsker inequality; Sanov theorem; distribution dependent refinement; measure concentration; probability distribution; Pattern recognition; Probability distribution; Statistical learning; Divergence; Hoeffding´s inequality; Pinsker´s inequality; Sanov´s theorem; measure concentration;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2005.846407
