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...
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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...
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divergence), which is central to information theory. There are numerous other specific divergences and classes of divergences, notably f-divergences and...
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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...
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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...
31 KB (4,586 words) - 17:25, 23 April 2024
Del (redirect from Divergence operator)
below, are summarized as: Gradient: grad f = ∇ f {\displaystyle \operatorname {grad} f=\nabla f} Divergence: div v = ∇ ⋅ v {\displaystyle \operatorname...
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mathematics, specifically statistics and information geometry, a Bregman divergence or Bregman distance is a measure of difference between two points, defined...
26 KB (4,434 words) - 13:48, 23 June 2024
In electromagnetics, especially in optics, beam divergence is an angular measure of the increase in beam diameter or radius with distance from the optical...
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theory Divergence (statistics), a measure of dissimilarity between probability measures Bregman divergence f-divergence Jensen–Shannon divergence Kullback–Leibler...
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Hellinger distance (category F-divergences)
the similarity between two probability distributions. It is a type of f-divergence. The Hellinger distance is defined in terms of the Hellinger integral...
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Fisher information (section F-divergence)
(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}...
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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...
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Total variation distance of probability measures (category F-divergences)
distance is an f-divergence and an integral probability metric. The total variation distance is related to the Kullback–Leibler divergence by Pinsker’s...
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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...
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Statistical distance (section Divergences)
distance, as it violates the triangle inequality) f-divergence: generalizes several distances and divergences Discriminability index, specifically the Bayes...
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Genetic divergence is the process in which two or more populations of an ancestral species accumulate independent genetic changes (mutations) through time...
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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...
34 KB (5,570 words) - 17:25, 27 September 2024
Rényi entropy (redirect from Renyi divergence)
J_{F,\alpha }(\theta :\theta ')=\alpha F(\theta )+(1-\alpha )F(\theta ')-F(\alpha \theta +(1-\alpha )\theta ')} is a Jensen difference divergence. The...
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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...
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_{2}}}.} Any f-divergence between two Cauchy distributions is symmetric and can be expressed as a function of the chi-squared divergence. Closed-form...
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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...
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In probability theory and statistics, the Jensen–Shannon divergence, named after Johan Jensen and Claude Shannon, is a method of measuring the similarity...
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an f-divergence and a Bregman divergence (and in fact the only example which is both). Statistical manifolds corresponding to Bregman divergences are...
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is the (Riemannian) divergence of the (Riemannian) gradient: Δ f = d i v ( ∇ f ) . {\displaystyle \Delta f={\rm {div}}(\nabla f).} An explicit formula...
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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...
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Bhattacharyya angle Kullback–Leibler divergence Hellinger distance Mahalanobis distance Chernoff bound Rényi entropy F-divergence Fidelity of quantum states Dodge...
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Convergence tests (redirect from Divergence test)
conditional convergence, absolute convergence, interval of convergence or divergence of an infinite series ∑ n = 1 ∞ a n {\displaystyle \sum _{n=1}^{\infty...
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concept of information projection can be extended to arbitrary f-divergences and other divergences. Sanov's theorem Cover, Thomas M.; Thomas, Joy A. (2006)...
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Aeroelasticity (section Divergence)
loads. Aircraft are designed to avoid the following aeroelastic problems: divergence where the aerodynamic forces increase the twist of a wing which further...
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Nth-term test (redirect from Nth term test for divergence)
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...
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