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...

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

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

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...

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...

distance) Hellinger distance Lévy–Prokhorov metric Wasserstein metric: also known as the Kantorovich metric, or earth mover's distance Mahalanobis distance...

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

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...

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...

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

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

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

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

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

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...

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

|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...

test Shapiro–Wilk test Anderson–Darling test Cramér–von Mises test Wasserstein metric Naaman, Michael (2021). "On the tight constant in the multivariate...

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...

transport flow is to construct a probability path minimizing the Wasserstein metric. The distribution on which we condition is the optimal transport plan...

Lipschitz constant. Wasserstein metric Acoustic metric Apophysis (software) Complete metric Fractal image compression Image differencing Metric tensor Multifractal...

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 (...

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

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

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

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...

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

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

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...