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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 Gibbs' inequality ： ウィキペディア英語版 Gibbs' inequality In information theory, Gibbs' inequality is a statement about the mathematical entropy of a discrete probability distribution. Several other bounds on the entropy of probability distributions are derived from Gibbs' inequality, including Fano's inequality. It was first presented by J. Willard Gibbs in the 19th century. ==Gibbs' inequality== Suppose that :$P\; =\; \backslash$ is a probability distribution. Then for any other probability distribution :$Q\; =\; \backslash$ the following inequality between positive quantities (since the pi and qi are positive numbers less than one) holds :$-\; \backslash sum\_^n\; p\_i\; \backslash log\_2\; p\_i\; \backslash leq\; -\; \backslash sum\_^n\; p\_i\; \backslash log\_2\; q\_i$ with equality if and only if :$p\_i\; =\; q\_i\; \backslash ,$ for all ''i''. Put in words, the information entropy of a distribution P is less than or equal to its cross entropy with any other distribution Q. The difference between the two quantities is the Kullback–Leibler divergence or relative entropy, so the inequality can also be written: :$D\_^n\; p\_i\; \backslash log\_2\; \backslash frac\; \backslash geq\; 0.$ Note that the use of base-2 logarithms is optional, and allows one to refer to the quantity on each side of the inequality as an "average surprisal" measured in bits. 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「Gibbs' 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.