= 조건부상호정보의 연쇄법칙 chain rule for conditional mutual information =
chain rule이 있음. curr goto [[연쇄법칙,chain_rule#s-5]]

tmp from [[https://www.di.univr.it/documenti/OccorrenzaIns/matdid/matdid648405.pdf this slide]] page1 slide2
{
Conditional Mutual Information

We define the conditional mutual information of random variable X and Y given Z as:
 $I(X;Y|Z)$
 $=H(X|Z)-H(X|Y,Z)$
 $=E_{p(x,y,z)}\log\frac{p(X,Y|Z)}{p(X|Z)p(Y|Z)}$

Mutual information also satisfy a chain rule([[연쇄법칙,chain_rule#s-5.2]]):
 $I(X_1,X_2,\cdots,X_n;Y)=\sum_{i=1}^{n}I(X_i;Y|X_{i-1},X_{i-2},\cdots,X_1)$
}

----
Up: [[조건부,conditional]] [[상호정보,mutual_information]]