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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 Conditional entropy ： ウィキペディア英語版 Conditional entropy In information theory, the conditional entropy (or equivocation) quantifies the amount of information needed to describe the outcome of a random variable $Y$ given that the value of another random variable $X$ is known. Here, information is measured in shannons, nats, or hartleys. The ''entropy of $Y$ conditioned on $X$'' is written as $H(Y|X)$. == Definition == If $H(Y|X=x)$ is the entropy of the variable $Y$ conditioned on the variable $X$ taking a certain value $x$, then $H(Y|X)$ is the result of averaging $H(Y|X=x)$ over all possible values $x$ that $X$ may take. Given discrete random variables $X$ with domain $\backslash mathcal\; X$ and $Y$ with domain $\backslash mathcal\; Y$, the conditional entropy of $Y$ given $X$ is defined as: :$$ \begin H(Y|X)\ &\equiv \sum_\,p(x)\,H(Y|X=x)\\ & =-\sum_ p(x)\sum_\,p(y|x)\,\log\, p(y|x)\\ & =-\sum_\sum_\,p(x,y)\,\log\,p(y|x)\\ & =-\sum_p(x,y)\log\,p(y|x)\\ & =-\sum_p(x,y)\log \frac . \\ & = \sum_p(x,y)\log \frac . \\ \end ''Note:'' It is understood that the expressions 0 log 0 and 0 log (''c''/0) for fixed ''c''>0 should be treated as being equal to zero. $H(Y|X)=0$ if and only if the value of $Y$ is completely determined by the value of $X$. Conversely, $H(Y|X)\; =\; H(Y)$ if and only if $Y$ and $X$ are independent random variables. 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「Conditional entropy」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.