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Pinsker's inequality - Wikipedia

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In information theory, Pinsker's inequality, named after its inventor Mark Semenovich Pinsker, is an inequality that bounds the total variation distance (or statistical distance) in terms of the Kullback–Leibler divergence. The inequality is tight up to constant factors.[1] Pinsker's inequality states that, if 𝑃 and 𝑄 are two probability distributions on a measurable space ( 𝑋 , Σ ) , then where is the total variation distance (or statistical distance) between 𝑃 and 𝑄 and is the Kullback–Leibler divergence in nats. When the sample space 𝑋 is a finite set, the Kullback–Leibler divergence is given by Note that in terms of the total variation norm ‖ 𝑃 − 𝑄 ‖ of the signed measure 𝑃 − 𝑄 , Pinsker's inequality differs from the one given above by a factor of two: A proof of Pinsker's inequality uses the partition inequality for f-divergences. Note that the expression of Pinsker inequality depends on what basis of logarithm is used in the definition of KL-divergence. �

Pinsker's inequality - Wikipedia Jump to content From Wikipedia, the free encyclopedia Inequality in information theory In information theory , Pinsker's inequality , named after its inventor Mark Semenovich Pinsker , is an inequality that bounds the total variation distance (or statistical distance) in terms of the Kullback–Leibler divergence . The inequality is tight up to constant factors. [ 1 ] Formal statement [ edit ] Pinsker's inequality states that, if P {\displaystyle P} and Q {\displaystyle Q} are two probability distributions on a measurable space ( X , Σ ) {\displaystyle (X,\Sigma

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