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Information Inequalities and Concentration of Measure

Amir Dembo
The Annals of Probability
Vol. 25, No. 2 (Apr., 1997), pp. 927-939
Stable URL: http://www.jstor.org/stable/2959616
Page Count: 13
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Information Inequalities and Concentration of Measure
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Abstract

We derive inequalities of the form Δ(P, Q) ≤ 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 Δ(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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