Αποτελέσματα Αναζήτησης
31 Ιαν 2021 · $$ H(X|Y) = 0 \iff Y=f(X) $$ Where $H(X|Y)$ is the average conditional entropy of the discrete random variable $X$ over all values of the discrete random variable $Y$, and $f$ is an arbitrary invertible function. $H(X|Y)$ is defined as: $$ H(X|Y) = \mathbb{E}_{p(y)} [H(X|Y=y)] = \sum_y p(y) H(X|Y=y) $$
- information theory - Conditional Entropy: if $H[y|x]=0$, then there ...
Suppose that the conditional entropy H[Y|X] between two...
- Zero conditional entropy - Mathematics Stack Exchange
According to the relevant solution manual, assume that there...
- information theory - Conditional Entropy: if $H[y|x]=0$, then there ...
Conditional entropy equals zero [ edit ] H ( Y | X ) = 0 {\displaystyle \mathrm {H} (Y|X)=0} if and only if the value of Y {\displaystyle Y} is completely determined by the value of X {\displaystyle X} .
Definition The conditional entropy of X given Y is. H(X|Y ) = −. p(x, y) log p(x|y) = −E[ log(p(x|y)) ] (5) The conditional entropy is a measure of how much uncertainty remains about the random variable.
6 Οκτ 2019 · Suppose that the conditional entropy H[Y|X] between two discrete random variables x and y is zero. Show that, for all values of x such that p(x)> 0, the variable y must be a function of x, in other words, for each x there is only one value of y such that p(y|x) ≠ 0.
20 Μαρ 2016 · Let $X,Y$ be iid fair Bernoulli $(p=1/2)$, let $T= X \oplus Y$ (XOR, or sum in modulus 2). Then $T$ is independent from $X$ and from $Y$ (each taken alone), but it's a deterministic function of the pair $X,Y$.
21 Αυγ 2015 · According to the relevant solution manual, assume that there exists an $x$, say $x_0$ and two different values of $y$, say $y_1$ and $y_2$ such that $P_{X,Y}(x_0,y_1)>0$ and $P_{X,Y}(x_0,y_2)>0$. Then $$ P_X(x_0)\geqslant P_{X,Y}(x_0,y_1)+P_{X,Y}(x_0,y_2) $$ and $P_{X,Y}(x_0,y_1)$ and $P_{X,Y}(x_0,y_2)$ are not equal to $0$ or $1$ .
if X = Y , or if X = f(Y ) (so we know X given Y ), the conditional entropy is 0. On the other hand, if X and Y are independent, the conditional entropy is just H(X).
