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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 Multivariate mutual information ： ウィキペディア英語版 Multivariate mutual information In information theory there have been various attempts over the years to extend the definition of mutual information to more than two random variables. These attempts have met with a great deal of confusion and a realization that interactions among many random variables are poorly understood. ==Definition== The conditional mutual information can be used to inductively define a multivariate mutual information (MMI) in a set- or measure-theoretic sense in the context of information diagrams. In this sense we define the multivariate mutual information as follows: :$I(X\_1;\backslash ldots;X\_)\; =\; I(X\_1;\backslash ldots;X\_n)\; -\; I(X\_1;\backslash ldots;X\_n|X\_),$ where :$I(X\_1;\backslash ldots;X\_n|X\_)\; =\; \backslash mathbb\; E\_\backslash big).$ This definition is identical to that of interaction information except for a change in sign in the case of an odd number of random variables. Alternatively, the multivariate mutual information may be defined in measure-theoretic terms as the intersection of the individual entropies $\backslash mu(\backslash tilde\_i)$: :$$ I(X_1;X_2;...;X_)=\mu\left(\bigcap_^\tilde_i\right) Defining $\backslash tilde=\backslash bigcap\_^n\backslash tilde\_i$, the set-theoretic identity $\backslash tilde=(\backslash tilde\backslash cap\backslash tilde)\backslash cup(\backslash tilde\backslash backslash\backslash tilde)$ which corresponds to the measure-theoretic statement $\backslash mu(\backslash tilde)=\backslash mu(\backslash tilde\backslash cap\; \backslash tilde)+\backslash mu(\backslash tilde\backslash backslash\backslash tilde)$, allows the above to be rewritten as: :$$ I(X_1;X_2;...;X_)=\mu(\tilde\cap\tilde_)=\mu(\tilde)-\mu(\tilde\backslash\tilde_) which is identical to the first definition. 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「Multivariate mutual information」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.