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A distribution dependent refinement of Pinsker's inequality

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2 Author(s)
E. Ordentlich ; Hewlett-Packard Labs., Palo Alto, CA, USA ; M. J. Weinberger

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.

Published in:

IEEE Transactions on Information Theory  (Volume:51 ,  Issue: 5 )