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...

that entropy should be a measure of how informative the average outcome of a variable is. For a continuous random variable, differential entropy is analogous...

In information theory, the conditional entropy quantifies the amount of information needed to describe the outcome of a random variable Y {\displaystyle...

in which case we say that the differential entropy is not defined. As in the discrete case the joint differential entropy of a set of random variables...

the discrete entropy. It is known since then that the differential entropy may differ from the infinitesimal limit of the discrete entropy by an infinite...

with probability density p ( x ) {\displaystyle p(x)} , then the differential entropy of X {\displaystyle X} is defined as H ( X ) = − ∫ − ∞ ∞ p ( x )...

_{x})-S(p_{x})\,} where S ( φ x ) {\displaystyle S(\varphi _{x})} is the differential entropy of the Gaussian density with the same mean and variance as p x {\displaystyle...

d-dimensional entropy does not necessarily exist there. Finally, dimensional-rate bias generalizes the Shannon's entropy and differential entropy, as one could...

In information theory, the cross-entropy between two probability distributions p {\displaystyle p} and q {\displaystyle q} , over the same underlying...

properties; for example, differential entropy may be negative. The differential analogies of entropy, joint entropy, conditional entropy, and mutual information...

with finite differential entropy, R ( D ) ≥ h ( X ) − h ( D ) {\displaystyle R(D)\geq h(X)-h(D)\,} where h(D) is the differential entropy of a Gaussian...

learning, and time delay estimation it is useful to estimate the differential entropy of a system or process, given some observations. The simplest and...

{\displaystyle \operatorname {erf} (z)} is the error function. The differential entropy is given by[citation needed] H = 1 + ln ⁡ ( σ 2 ) + γ 2 {\displaystyle...

entropy states that the probability distribution which best represents the current state of knowledge about a system is the one with largest entropy,...

vector, it is distributed as a generalized chi-squared variable. The differential entropy of the multivariate normal distribution is h ( f ) = − ∫ − ∞ ∞ ∫...

its time series X1, ..., Xn is i.i.d. with entropy H(X) in the discrete-valued case and differential entropy in the continuous-valued case. The Source...

Shannon for differential entropy. It was formulated by Edwin Thompson Jaynes to address defects in the initial definition of differential entropy. Shannon...

distributions, for which Shannon entropy ceases to be so useful (see differential entropy), but the relative entropy continues to be just as relevant...

mathematical theory of probability, the entropy rate or source information rate is a function assigning an entropy to a stochastic process. For a strongly...

V, Gilson MK (March 2010). "Thermodynamic and Differential Entropy under a Change of Variables". Entropy. 12 (3): 578–590. Bibcode:2010Entrp..12..578H...

quantities include the Rényi entropy and the Tsallis entropy (generalizations of the concept of entropy), differential entropy (a generalization of quantities...

Entropy (information theory), also called Shannon entropy, a measure of the unpredictability or information content of a message source Differential entropy...

variable. The concept of mutual information is intimately linked to that of entropy of a random variable, a fundamental notion in information theory that quantifies...

the new distribution. The differential entropy of the half-normal distribution is exactly one bit less the differential entropy of a zero-mean normal distribution...

I ( X ; Y ) {\displaystyle I(X;Y)} , writing it in terms of the differential entropy: I ( X ; Y ) = h ( Y ) − h ( Y ∣ X ) = h ( Y ) − h ( X + Z ∣ X )...

Boltzmann equation, which is a partial differential equation) is a probability equation relating the entropy S {\displaystyle S} , also written as S...

distribution with λ = 1/μ has the largest differential entropy. In other words, it is the maximum entropy probability distribution for a random variate...

Clausius named the concept of "the differential of a quantity which depends on the configuration of the system", entropy (Entropie) after the Greek word...

Entropy is one of the few quantities in the physical sciences that require a particular direction for time, sometimes called an arrow of time. As one...

whereas for continuous random variables the related concept of differential entropy, written h ( X ) {\displaystyle h(X)} , is used (see Cover and Thomas...