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→多元互信息 Multivariate mutual information
Several generalizations of mutual information to more than two random variables have been proposed, such as total correlation (or multi-information) and interaction information. The expression and study of multivariate higher-degree mutual-information was achieved in two seemingly independent works: McGill (1954) who called these functions “interaction information”, and Hu Kuo Ting (1962) who also first proved the possible negativity of mutual-information for degrees higher than 2 and justified algebraically the intuitive correspondence to Venn diagrams
Several generalizations of mutual information to more than two random variables have been proposed, such as total correlation (or multi-information) and interaction information. The expression and study of multivariate higher-degree mutual-information was achieved in two seemingly independent works: McGill (1954) who called these functions “interaction information”, and Hu Kuo Ting (1962) who also first proved the possible negativity of mutual-information for degrees higher than 2 and justified algebraically the intuitive correspondence to Venn diagrams
提出了将互信息推广到两个以上随机变量的方法，如全相关（或多信息）和交互信息。多元高阶互信息的表达和研究是在两部看似独立的著作中实现的：McGill（1954）称这些函数为“交互信息”，胡国亭（1962）也首次证明了大于2度的互信息可能是负的，并用代数证明了维恩图的直观对应关系
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and for <math>n > 1,</math>
and for <math>n > 1,</math>
and for 𝑛>1,
而对于𝑛>1，有：
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where (as above) we define
where (as above) we define
在（如上所述）我们定义：
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:<math>
(This definition of multivariate mutual information is identical to that of interaction information except for a change in sign when the number of random variables is odd.)
(This definition of multivariate mutual information is identical to that of interaction information except for a change in sign when the number of random variables is odd.)
（这个多元互信息的定义与互信息的定义相同，随机变量的数目为奇数时符号的变化除外。）