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→Chain rule 链式法则
:<math>\Eta(Y|X)\, = \, \Eta(X,Y)- \Eta(X).</math><ref name=cover1991 />{{rp|17}}
:<math>H(Y|X)\, = \, H(X,Y)- H(X).</math><ref name=cover1991 />{{rp|17}}
:<math>\begin{align}
:<math>\begin{align}
H(Y|X) &= \sum_{x\in\mathcal X, y\in\mathcal Y}p(x,y)\log \left(\frac{p(x)}{p(x,y)} \right) \\[4pt]
&= \sum_{x\in\mathcal X, y\in\mathcal Y}p(x,y)(\log (p(x))-\log (p(x,y))) \\[4pt]
&= \sum_{x\in\mathcal X, y\in\mathcal Y}p(x,y)(\log (p(x))-\log (p(x,y))) \\[4pt]
&= -\sum_{x\in\mathcal X, y\in\mathcal Y}p(x,y)\log (p(x,y)) + \sum_{x\in\mathcal X, y\in\mathcal Y}{p(x,y)\log(p(x))} \\[4pt]
&= -\sum_{x\in\mathcal X, y\in\mathcal Y}p(x,y)\log (p(x,y)) + \sum_{x\in\mathcal X, y\in\mathcal Y}{p(x,y)\log(p(x))} \\[4pt]
& = \Eta(X,Y) + \sum_{x \in \mathcal X} p(x)\log (p(x) ) \\[4pt]
& = H(X,Y) + \sum_{x \in \mathcal X} p(x)\log (p(x) ) \\[4pt]
& = \Eta(X,Y) - \Eta(X).
& = H(X,Y) - \Eta(X).
\end{align}</math>
\end{align}</math>
:<math> \Eta(X_1,X_2,\ldots,X_n) =
:<math> H(X_1,X_2,\ldots,X_n) =
\sum_{i=1}^n \Eta(X_i | X_1, \ldots, X_{i-1}) </math><ref name=cover1991 />{{rp|22}}
\sum_{i=1}^n H(X_i | X_1, \ldots, X_{i-1}) </math><ref name=cover1991 />{{rp|22}}
除了使用加法而不是乘法之外，它具有与概率论中的链式法则类似的形式。
除了使用加法而不是乘法之外，它具有与概率论中的链式法则类似的形式。
===Bayes' rule===
===Bayes' rule===