mathematics, the Wasserstein distance or Kantorovich–Rubinstein metric is a distance function defined between probability distributions on a given metric space M...

the main page on Wasserstein metric. By the Kantorovich-Rubenstein duality, the definition of Wasserstein GAN is clear: A Wasserstein GAN game is defined...

metrics, including the Wasserstein-1 distance and the total variation distance. In addition to theoretical importance, integral probability metrics are...

instead, as the cost of changing from one state to another (as with Wasserstein metrics on spaces of measures) or the degree of difference between two objects...

name: Wasserstein metric, a mathematical distance measure Dresdner Kleinwort Wasserstein, an investment bank, part of Dresdner Bank Wasserstein Perella...

the Wasserstein metric with p ≥ 1 {\displaystyle p\geq 1} and μ , ν {\displaystyle \mu ,\nu } have finite p {\displaystyle p} th moment. Lévy metric Prokhorov's...

Lévy–Prokhorov metric Wasserstein metric: also known as the Kantorovich metric, or earth mover's distance Mahalanobis distance Integral probability metrics generalize...

Alternate forms of the last name: Vaseršteĭn, Vasershtein, Wasserstein. The Wasserstein metric was named after him by R.L. Dobrushin in 1970. Leonid Vaserstein...

mover's distance is also known as the Wasserstein metric W 1 {\displaystyle W_{1}} , Kantorovich–Rubinstein metric, or Mallows's distance. It is the solution...

{\displaystyle Q} , respectively. Total variation Kolmogorov–Smirnov test Wasserstein metric Chatterjee, Sourav. "Distances between probability measures" (PDF)...

Radon metric, which presents difficulties in certain applications. On the other hand, if X is a compact metric space, then the Wasserstein metric turns...

transport flow is to construct a probability path minimizing the Wasserstein metric. The distribution on which we condition is an approximation of the...

{\displaystyle Y} ). (Compare this formulation with the definition of the Wasserstein metric W p {\displaystyle W_{p}} on the space of probability measures.) A...

is the Wasserstein-Fréchet mean, or simply the Wasserstein mean, which is the Fréchet mean with the L 2 {\displaystyle L^{2}} -Wasserstein metric d W 2...

functions from X to [−1, 1]. This is in contrast, for example, to the Wasserstein metric, where the definition is of the same form, but the supremum is taken...

L(F_{n},F)\to 0} . Càdlàg Lévy–Prokhorov metric Wasserstein metric V.M. Zolotarev (2001) [1994], "Lévy metric", Encyclopedia of Mathematics, EMS Press...

test Shapiro–Wilk test Anderson–Darling test Cramér–von Mises test Wasserstein metric Stephens, M. A. (1974). "EDF Statistics for Goodness of Fit and Some...

probability distribution Joint probability distribution Marginal likelihood Wasserstein metric Conditional distribution Trumpler, Robert J. & Harold F. Weaver (1962)...

distributions on R d {\displaystyle \mathbb {R} ^{d}} equipped with the Wasserstein metric W 2 {\displaystyle W_{2}} and M d ( R ) {\displaystyle {\mathcal {M}}_{d}(\mathbb...

is that D p {\displaystyle D_{p}} is complete and separable in the Wasserstein metric W p ( u , v ) = ( inf γ ∈ Γ ( u , v ) ∫ X × X ρ p ( x , y ) d γ (...

distance performed better in ordinal regression than KL distance or the Wasserstein metric. While CRPS is widely used for evaluating probabilistic forecasts...

distribution Total variation distance Hellinger distance Wasserstein metric Lévy–Prokhorov metric Lévy metric Continuity correction Heavy-tailed distribution Truncated...

|P-Q|_{\pi }} is commonly known as the earth mover's distance or Wasserstein metric. Similarly, define | log ⁡ P : Q | π = sup p ∈ P ′ | log ⁡ p − log...

dimensional Riemannian manifold by interpreting the Wasserstein distance as if it was a Riemannian metric. It is named after Felix Otto, who developed it...

metric space structure of a Riemannian manifold, together with its volume form. This established a deep link between Ricci curvature and Wasserstein geometry...

The Fréchet inception distance (FID) is a metric used to assess the quality of images created by a generative model, like a generative adversarial network...

enjoy Wasserstein convergence control, meaning that D P ( Q n ) → 0 {\displaystyle D_{P}(Q_{n})\rightarrow 0} implies that the Wasserstein metric between...

His name is associated to the Kantorovich–Rubinstein metric, also commonly known as the Wasserstein distance, used in optimal transport. Alternate form...

a certain "entropy" functional along geodesics of the associated Wasserstein metric space. In 2009, Lott and Cédric Villani capitalized upon this equivalence...

D {\displaystyle F\in \mathbb {D} } under the Kolmogorov, Lévy or Wasserstein metric. A p-box is a crude but computationally convenient kind of credal...