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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Pinsker's inequality ： ウィキペディア英語版 Pinsker's inequality 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. ==Formal statement== Pinsker's inequality states that, if $P$ and $Q$ are two probability distributions on a measurable space $(X,\; \backslash Sigma)$, then :$\backslash delta(P,Q)\; \backslash le\; \backslash sqrt\; D\_,$ where :$\backslash delta(P,Q)=\backslash sup\; \backslash bigl\backslash$ is the total variation distance (or statistical distance) between $P$ and $Q$ and :$D\_\_\; \backslash left(\; \backslash log\; \backslash frac\; \backslash right)\; =\; \backslash int\_\; \backslash left(\; \backslash log\; \backslash frac\; \backslash right)\; \backslash ,\; \backslash mathrm\; P$ is the Kullback–Leibler divergence in nats. When the sample space $X$ is a finite set, the Kullback–Leibler divergence is given by :$D\_\; \backslash left(\; \backslash log\; \backslash frac\backslash right)\; P(i)\backslash !$ Note that in terms of the total variation norm $\backslash |\; P\; -\; Q\; \backslash |$ of the signed measure $P\; -\; Q$, Pinsker's inequality differs from the one given above by a factor of two: :$\backslash |\; P\; -\; Q\; \backslash |\; \backslash le\; \backslash sqrt.$ The proof of Pinsker's inequality uses the partition inequality for ''f''-divergences. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Pinsker's inequality」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.