Conditional Entropy

Definition

$H(Y|X)=H(X,Y)-H(X)=-E_{(X,Y)\sim p(x,y)}\left[\log \left(\frac{p(x,y)}{p(x)}\right)\right]=-{\int }_{X,Y}p(x,y)\log p(y|x)dxdy$

Conditional entropy quantifies the amount of information needed to describe the outcome of a Random Variable $Y$ given that the value of another Random Variable $X$ is known.