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→条件互信息 Conditional mutual information
Sometimes it is useful to express the mutual information of two random variables conditioned on a third.
Sometimes it is useful to express the mutual information of two random variables conditioned on a third.
有时度量两个随机变量在以第三个随机变量为条件的情况下的相互信息也是有意义的。
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
第三个随机变量的条件作用可能增加或减少互信息，但下式始终是成立的：
:<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<math>X,Y,Z</math>。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 ===