2018年3月5日 · $$ H(Y \mid X) = -\sum_{x\in \mathcal X}\sum_{y\in \mathcal Y}p(x,y)log_2p(y\mid x)\tag{2}\label{eq2} $$ With the chain rule of probability, the theorem: $$ H(X,Y) = H(X)+H(Y \mid X)\tag{3}\label{eq3} $$ is another interpretation of the joint entropy for $(X,Y)$. A corollary of this theorem is: $$ H(X,Y \mid Z) = H(X \mid Z)+H(Y \mid X,Z) $$ Proof:

Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2018年7月31日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2022年5月12日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2020年3月24日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2019年4月7日 · I read in my textbook the following Corollary that follows from the chain rule for entropy: H(X, Y) >= H(X) or H(X, Y) >= H(Y) I was wondering what the necessary condition is for equality? If X and Y are random variables of course.

2016年7月14日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2019年10月6日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.