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→In terms of pdf's for continuous distributions
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==In terms of pdf's for continuous distributions==
== In terms of pdf's for continuous distributions 关于连续分布的概率密度函数 ==
For (absolutely) continuous random variables <math>X</math>, <math>Y</math>, and <math>Z</math> with [[Support (mathematics)|support sets]] <math>\mathcal{X}</math>, <math>\mathcal{Y}</math> and <math>\mathcal{Z}</math>, the conditional mutual information <math>I(X;Y|Z)</math> is as follows
For (absolutely) continuous random variables <math>X</math>, <math>Y</math>, and <math>Z</math> with [[Support (mathematics)|support sets]] <math>\mathcal{X}</math>, <math>\mathcal{Y}</math> and <math>\mathcal{Z}</math>, the conditional mutual information <math>I(X;Y|Z)</math> is as follows
对于具有支持集<math>X</math>, <math>Y</math>, 和 <math>Z</math>的（绝对）连续随机变量<math>\mathcal{X}</math>, <math>\mathcal{Y}</math> 和 <math>\mathcal{Z}</math>，条件交互信息<math>I(X;Y|Z)</math>如下
:<math>
:<math>
I(X;Y|Z) = \int_{\mathcal{Z}} \bigg( \int_{\mathcal{Y}} \int_{\mathcal{X}}
I(X;Y|Z) = \int_{\mathcal{Z}} \bigg( \int_{\mathcal{Y}} \int_{\mathcal{X}}
\log \left(\frac{p_{X,Y|Z}(x,y|z)}{p_{X|Z}(x|z)p_{Y|Z}(y|z)}\right) p_{X,Y|Z}(x,y|z) dx dy \bigg) p_Z(z) dz
\log \left(\frac{p_{X,Y|Z}(x,y|z)}{p_{X|Z}(x|z)p_{Y|Z}(y|z)}\right) p_{X,Y|Z}(x,y|z) dx dy \bigg) p_Z(z) dz
</math>
</math>
where the marginal, joint, and/or conditional [[probability density function]]s are denoted by <math>p</math> with the appropriate subscript. This can be simplified as
where the marginal, joint, and/or conditional [[probability density function]]s are denoted by <math>p</math> with the appropriate subscript. This can be simplified as
其中边缘概率密度函数，联合概率密度函数，和（或）条件概率密度函数可以由p加上适当的下标表示。这可以简化为
{{Equation box 1
{{Equation box 1