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In information theory, the conditional entropy quantifies the amount of information needed to describe the outcome of a random variable given that the value of another random variable is known. Here, information is measured in shannons, nats, or hartleys.
31 Ιαν 2021 · 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: $$ H(X|Y) = \mathbb{E}_{p(y)} [H(X|Y=y)] = \sum_y p(y) H(X|Y=y) $$
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.
entropy. There are a few ways to measure entropy for multiple variables; we’ll use two, Xand Y. De nition 8.2 (Conditional entropy) The conditional entropy of a random variable is the entropy of one random variable conditioned on knowledge of another random variable, on average.
conditional information, and relative entropy (discrimination, Kullback-Leibler information), along with the limiting normalized versions of these quantities such as entropy rate and information rate.
In this lecture, we will introduce certain key measures of information, that play crucial roles in theoretical and operational characterizations throughout the course. These include the entropy, the mutual information, and the relative entropy.
The joint entropy \(H(X, Y)\) of a pair of discrete random variables \((X, Y)\) with a joint distribution \(p(x, y)\) is defined as \[H(X, Y) = - \sum_{x \in \mathcal{X}} \sum_{y \in \mathcal{Y}} p(x, y) \log p(x, y) = - E \log p(X, Y)\]
