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→条件互信息 Conditional mutual information
有时表达两个以第三个为条件的随机变量的相互信息是有用的。
有时表达两个以第三个为条件的随机变量的相互信息是有用的。
For jointly discrete random variables this takes the form
For jointly discrete random variables this takes the form
对于联合离散随机变量，这采用以下形式：
:<math>
:<math>
For jointly continuous random variables this takes the form
For jointly continuous random variables this takes the form
对于联合连续的随机变量，其形式为：
:<math>
:<math>
Conditioning on a third random variable may either increase or decrease the mutual information, but it is always true that
Conditioning on a third random variable may either increase or decrease the mutual information, but it is always true that
对第三个随机变量的条件作用可能增加或减少互信息，但它始终是正确的
:<math>\operatorname{I}(X;Y|Z) \ge 0</math>
:<math>\operatorname{I}(X;Y|Z) \ge 0</math>
for discrete, jointly distributed random variables <math>X,Y,Z</math>. This result has been used as a basic building block for proving other inequalities in information theory.
for discrete, jointly distributed random variables <math>X,Y,Z</math>. This result has been used as a basic building block for proving other inequalities in information theory.
对于离散的、联合分布的随机变量𝑋，𝑌，𝑍。这一结果被用作证明信息论中其他不等式的基本组成部分。
=== 多元互信息 Multivariate mutual information ===
=== 多元互信息 Multivariate mutual information ===