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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 Cross entropy ： ウィキペディア英語版 Cross entropy In information theory, the cross entropy between two probability distributions over the same underlying set of events measures the average number of bits needed to identify an event drawn from the set, if a coding scheme is used that is optimized for an "unnatural" probability distribution $q$, rather than the "true" distribution $p$. The cross entropy for the distributions $p$ and $q$ over a given set is defined as follows: :$H(p,\; q)\; =\; \backslash operatorname\_p(q)\; =\; H(p)\; +\; D\_\}(p\; ||\; q)$ is the Kullback–Leibler divergence of $q$ from $p$ (also known as the ''relative entropy'' of ''p'' with respect to ''q'' — note the reversal of emphasis). For discrete $p$ and $q$ this means :$H(p,\; q)\; =\; -\backslash sum\_x\; p(x)\backslash ,\; \backslash log\; q(x).\; \backslash !$ The situation for continuous distributions is analogous: :$-\backslash int\_X\; p(x)\backslash ,\; \backslash log\; q(x)\backslash ,\; dx.\; \backslash !$ NB: The notation $H(p,q)$ is also used for a different concept, the joint entropy of $p$ and $q$. == Motivation == In information theory, the Kraft–McMillan theorem establishes that any directly decodable coding scheme for coding a message to identify one value $x\_i$ out of a set of possibilities $X$ can be seen as representing an implicit probability distribution $q(x\_i)\; =\; 2^$ over $X$, where $l\_i$ is the length of the code for $x\_i$ in bits. Therefore, cross entropy can be interpreted as the expected message-length per datum when a wrong distribution $Q$ is assumed, however the data actually follows a distribution $P$ — that is why the expectation is taken over the probability distribution $P$ and not $Q$. :$H(p,\; q)\; =\; \backslash operatorname\_p()\; =\; \backslash operatorname\_p\backslash left(\backslash frac\backslash right)$ :$H(p,\; q)\; =\; \backslash sum\_\; p(x\_i)\backslash ,\; \backslash log\; \backslash frac\; \backslash !$ :$H(p,\; q)\; =\; -\backslash sum\_x\; p(x)\backslash ,\; \backslash log\; q(x).\; \backslash !$ 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「Cross 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.