Measure of information in probability and information theory
Information theory
Entropy
Differential entropy
Conditional entropy
Joint entropy
Mutual information
Directed information
Conditional mutual information
Relative entropy
Entropy rate
Limiting density of discrete points
Asymptotic equipartition property
Rate–distortion theory
Shannon's source coding theorem
Channel capacity
Noisy-channel coding theorem
Shannon–Hartley theorem
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A misleading[1] Venn diagram showing additive, and subtractive relationships between various information measures associated with correlated variables X and Y. The area contained by both circles is the joint entropy H(X,Y). The circle on the left (red and violet) is the individual entropy H(X), with the red being the conditional entropy H(X|Y). The circle on the right (blue and violet) is H(Y), with the blue being H(Y|X). The violet is the mutual information I(X;Y).
In information theory, joint entropy is a measure of the uncertainty associated with a set of variables.[2]
^D.J.C. Mackay (2003). Information theory, inferences, and learning algorithms. Bibcode:2003itil.book.....M.: 141
^Theresa M. Korn; Korn, Granino Arthur (January 2000). Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review. New York: Dover Publications. ISBN 0-486-41147-8.
information theory, jointentropy is a measure of the uncertainty associated with a set of variables. The joint Shannon entropy (in bits) of two discrete...
The joint quantum entropy generalizes the classical jointentropy to the context of quantum information theory. Intuitively, given two quantum states...
p(x,y)\,} Despite similar notation, jointentropy should not be confused with cross-entropy. The conditional entropy or conditional uncertainty of X given...
In information theory, the conditional entropy quantifies the amount of information needed to describe the outcome of a random variable Y {\displaystyle...
then the jointentropy is simply the sum of their individual entropies. (Note: The jointentropy should not be confused with the cross entropy, despite...
sequence of its jointentropies H n ( X 1 , X 2 , … X n ) {\displaystyle H_{n}(X_{1},X_{2},\dots X_{n})} . If the limit exists, the entropy rate is defined...
The mathematical expressions for thermodynamic entropy in the statistical thermodynamics formulation established by Ludwig Boltzmann and J. Willard Gibbs...
theorem implies that the joint information (negative of the jointentropy) of the distribution remains constant in time. The joint information is equal to...
information-theoretic jointentropy) is constant in time. This jointentropy is equal to the marginal entropy (entropy assuming no correlations) plus the entropy of correlation...
relationships among Shannon's basic measures of information: entropy, jointentropy, conditional entropy and mutual information. Information diagrams are a useful...
jointentropy (the entropy of the random variable representing the pair X 1 , X 2 {\displaystyle X_{1},X_{2}} ) is at most the sum of the entropies of...
In physics, the von Neumann entropy, named after John von Neumann, is an extension of the concept of Gibbs entropy from classical statistical mechanics...
in the symbol for jointentropy, since the jointentropy of any number of random variables is the same as the entropy of their joint distribution.) It...
content of random variables and a measure over sets. Namely the jointentropy, conditional entropy, and mutual information can be considered as the measure of...
Differential entropy (also referred to as continuous entropy) is a concept in information theory that began as an attempt by Claude Shannon to extend...
the calculation of entropy. A deep neural network (DNN) can be used to estimate the jointentropy and called Neural JointEntropy Estimator (NJEE). Practically...
neural networks can be used to estimate the entropy of a stochastic process and called Neural JointEntropy Estimator (NJEE). Such an estimation provides...
correlation is bounded by the sum entropies of the n elements, the dual total correlation is bounded by the joint-entropy of the n elements. Although well...
Neumann entropy, which will simply be called "entropy". Given a bipartite quantum state ρ A B {\displaystyle \rho ^{AB}} , the entropy of the joint system...
In physics, the Tsallis entropy is a generalization of the standard Boltzmann–Gibbs entropy. It is proportional to the expectation of the q-logarithm...
distances through past distances, use of move-to-front queue in entropy code selection, joint-entropy coding of literal and copy lengths, the use of graph algorithms...
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