In probability theory, an f {\displaystyle f} -divergence is a certain type of function D f ( P ‖ Q ) {\displaystyle D_{f}(P\|Q)} that measures the difference...

mathematical statistics, the Kullback–Leibler (KL) divergence (also called relative entropy and I-divergence), denoted D KL ( P ∥ Q ) {\displaystyle D_{\text{KL}}(P\parallel...

divergence), which is central to information theory. There are numerous other specific divergences and classes of divergences, notably f-divergences and...

divergence of a continuously differentiable vector field F = F x i + F y j + F z k {\displaystyle \mathbf {F} =F_{x}\mathbf {i} +F_{y}\mathbf {j} +F_{z}\mathbf...

In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through...

below, are summarized as: Gradient: grad ⁡ f = ∇ f {\displaystyle \operatorname {grad} f=\nabla f} Divergence: div ⁡ v = ∇ ⋅ v {\displaystyle \operatorname...

mathematics, specifically statistics and information geometry, a Bregman divergence or Bregman distance is a measure of difference between two points, defined...

In electromagnetics, especially in optics, beam divergence is an angular measure of the increase in beam diameter or radius with distance from the optical...

theory Divergence (statistics), a measure of dissimilarity between probability measures Bregman divergence f-divergence Jensen–Shannon divergence Kullback–Leibler...

the similarity between two probability distributions. It is a type of f-divergence. The Hellinger distance is defined in terms of the Hellinger integral...

(which could be infinite), it defines an f-divergence D f {\displaystyle D_{f}} . Then if f {\displaystyle f} is strictly convex at 1 {\displaystyle 1}...

One major difference between f-divergences and most IPMs is that when P and Q have disjoint support, all f-divergences take on a constant value; by contrast...

distance is an f-divergence and an integral probability metric. The total variation distance is related to the Kullback–Leibler divergence by Pinsker’s...

The Great Divergence or European miracle is the socioeconomic shift in which the Western world (i.e. Western Europe and the parts of the New World where...

distance, as it violates the triangle inequality) f-divergence: generalizes several distances and divergences Discriminability index, specifically the Bayes...

Genetic divergence is the process in which two or more populations of an ancestral species accumulate independent genetic changes (mutations) through time...

divergence of a continuously differentiable vector field F = F x i + F y j + F z k {\displaystyle \mathbf {F} =F_{x}\mathbf {i} +F_{y}\mathbf {j} +F_{z}\mathbf...

J_{F,\alpha }(\theta :\theta ')=\alpha F(\theta )+(1-\alpha )F(\theta ')-F(\alpha \theta +(1-\alpha )\theta ')} is a Jensen difference divergence. The...

In the field of information retrieval, divergence from randomness (DFR), is a generalization of one of the very first models, Harter's 2-Poisson indexing-model...

_{2}}}.} Any f-divergence between two Cauchy distributions is symmetric and can be expressed as a function of the chi-squared divergence. Closed-form...

from the 1948 to the 1952 model years. The introduction of the F-Series marked the divergence of Ford car and truck design, developing a chassis intended...

In probability theory and statistics, the Jensen–Shannon divergence, named after Johan Jensen and Claude Shannon, is a method of measuring the similarity...

an f-divergence and a Bregman divergence (and in fact the only example which is both). Statistical manifolds corresponding to Bregman divergences are...

is the (Riemannian) divergence of the (Riemannian) gradient: Δ f = d i v ( ∇ f ) . {\displaystyle \Delta f={\rm {div}}(\nabla f).} An explicit formula...

Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean space. It is usually...

Bhattacharyya angle Kullback–Leibler divergence Hellinger distance Mahalanobis distance Chernoff bound Rényi entropy F-divergence Fidelity of quantum states Dodge...

conditional convergence, absolute convergence, interval of convergence or divergence of an infinite series ∑ n = 1 ∞ a n {\displaystyle \sum _{n=1}^{\infty...

concept of information projection can be extended to arbitrary f-divergences and other divergences. Sanov's theorem Cover, Thomas M.; Thomas, Joy A. (2006)...

loads. Aircraft are designed to avoid the following aeroelastic problems: divergence where the aerodynamic forces increase the twist of a wing which further...

In mathematics, the nth-term test for divergence is a simple test for the divergence of an infinite series: If lim n → ∞ a n ≠ 0 {\displaystyle \lim _{n\to...