p(y|x,z)=p(x,y,z)/p(x,z)的解释

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         p(y|x,z)=p(x,y,z)/p(x,z)这个式子的本意是在x,z发生的条件下，y发生的概率。

更多的内容参考http://math.stackexchange.com/questions/301207/why-is-px-yz-pyx-zpxz，下面截取的一个回答。

        From

P(X,Y|Z)=P(X,Y,Z)P(Z)

P(Y|X,Z)=P(X,Y,Z)P(X,Z)

P(X|Z)=P(X,Z)P(Z)

      we have

P(Y|X,Z)P(X|Z)=P(X,Y,Z)P(X,Z)P(X,Z)P(Z)=P(X,Y,Z)P(Z)=P(X,Y|Z).

This is also intuitive: The probability that  X  and  Y  happen if we know that  Z  happens is the same as the probability that  X  happens when we know that  Z  happens and that then  Y  happens when we know that  X  and  Z  happen.

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