In information theory, the conditional entropy quantifies the amount of information needed to describe the outcome of a random variable $${\displaystyle Y}$$ given that the value of another random variable $${\displaystyle X}$$ is known. Here, information is measured in shannons, nats, or hartleys. The entropy of See more The conditional entropy of $${\displaystyle Y}$$ given $${\displaystyle X}$$ is defined as where $${\displaystyle {\mathcal {X}}}$$ and $${\displaystyle {\mathcal {Y}}}$$ denote the See more Let $${\displaystyle \mathrm {H} (Y X=x)}$$ be the entropy of the discrete random variable $${\displaystyle Y}$$ conditioned on the discrete random variable $${\displaystyle X}$$ taking a certain value $${\displaystyle x}$$. Denote the support sets of See more In quantum information theory, the conditional entropy is generalized to the conditional quantum entropy. The latter can take negative … See more • Entropy (information theory) • Mutual information • Conditional quantum entropy • Variation of information See more Conditional entropy equals zero $${\displaystyle \mathrm {H} (Y X)=0}$$ if and only if the value of $${\displaystyle Y}$$ is completely determined by the value of See more Definition The above definition is for discrete random variables. The continuous version of discrete conditional entropy is called conditional differential (or continuous) entropy. Let $${\displaystyle X}$$ and $${\displaystyle Y}$$ be … See more
Lecture 8: Information Theory and Maximum Entropy
WebApr 23, 2024 · The new estimates of the conditional Shannon entropy are introduced in the framework of the model describing a discrete response variable depending on a vector of d factors having a density w.r.t. the Lebesgue measure in R^d. Namely, the mixed-pair model (X,Y) is considered where X and Y take values in R^d and an arbitrary finite set, … http://www.science4all.org/article/shannons-information-theory/ case vacanze ikaria
Multivariate Dependence beyond Shannon Information
WebDec 8, 2024 · Moving on to the comma notation, it denotes joint probability and thus joint entropy. In other words, P X, Y ( x, y) can also be written as P ( X = x, Y = y). Combining these two concepts, P X, Y Z ( x, y z) denotes the probability of ( X, Y) taking the value ( x, y), knowing Z. The conditional entropy H ( X, Y Z) makes use of this ... WebOct 6, 2024 · Shannon entropy is the natural choice among this family. In addition to other facts, entropy is maximal for uniform distributions (property #1), additive for independent events (#2), increasing in the number of outcomes with non-zero probabilities (#3 and #5), continuous (#4), non-negative (#6), zero for certain outcomes (#7) and permutation ... WebJun 10, 2013 · Eq. (9) states that the Shannon entropy per particle can be approximated as the conditional entropy of each particle with respect to a variable representing the state of its neighbourhood. In the following, we will employ Eq. (9) as a measure of disorder in multi-component systems. case vacanze aosta booking