A class of Wasserstein metrics for probability distributions.

By C. Givens, R. Shortt. 1984

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Citations in the corpus

Generalized Zero- and Few-Shot Learning via Aligned Variational Autoencoders (2018, methodology): “In the case of multivariate Gaussians, a closed-form solution of the 2-Wasserstein distance [8] between two distributions i and j is given as:”
Contractions in the 2-Wasserstein Length Space and Thermalization of Granular Media (2006, background): “Here, we have used well-known properties of the Wasserstein distance with respect to weak-∗ limits one can see in e.g. Givens and Shortt [32]: namely, weak-∗ lower semicontinuity in both arguments and continuity when weak-∗ convergence is augmented by convergence of second order moments (5.6).”
Rethinking Rotated Object Detection with Gaussian Wasserstein Distance Loss (2021, unknown): “(10) This formula interested several works [14, 40, 22, 9].”
Regret in the Newsvendor Model with Demand and Yield Randomness (2021, unknown): “…balls of the form F ρ ð θ Þ ≜ f  ∈ P ð W Þ j d ρ ð  ,  Þ ≤ θ g ; here, for any ﬁnite ρ ∈ [1, ∞ ), the type-ρ Wasser-stein distance is deﬁned as It is intuitive that the type-ρ Wasserstein distance converges to the type-∞ Wasserstein distance as ρ approaches inﬁnity (Givens and Shortt 1984).”
The derivation of swarming models: Mean-field limit and Wasserstein distances (2013, background): “The set of probability measures with bounded moments of order p , denoted by P p ( R d ), 1 ≤ p < ∞ , is a complete metric space endowed with the p -Wassertein distance d p , see [80]. to We refer [41, 61] for more details in the case of the d ∞ distance.”
A spectral notion of Gromov–Wasserstein distance and related methods (2011, background): “These distances are known as Wasserstein–Kantorovich–Rubinstein distances between measures [56,59,60].”
A Convexity Principle for Interacting Gases (1997, background): “3 shows that only one can be positive; it is 4= 7(1) 2 1 (7 1 2 1 707 1 2 1 ) &1 2 7(1) 2 1 , as has previously been noted by several authors [7, 18, 9, 11].”
Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning (2019, background): “In its between normal distributions has been discovered earlier in [30, 43, 72].”
Statistical Aspects of Wasserstein Distances (2018, background): “For the Gaussian case, see Olkin & Pukelsheim (1982) or Givens & Shortt (1984) in ﬁnite dimensions, and Gelbrich (1990) and Cuesta-Albertos et al. (1996) for an inﬁnite-dimensional extension.”
Optimal-order bounds on the rate of convergence to normality in the multivariate delta method (2009, background): “[49, 16, 23] (as noted by Dudley in his review MR0752258 on MathSciNet, the normality assumption is not actually needed there).”
THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION (2001, background): “We found the few results on d we need in [41] or [27].”
Scenario tree modeling for multistage stochastic programs (2009, background): “and sometimes also called Wasserstein metrics of order r [9].”
t-Closeness: Privacy Beyond k-Anonymity and l-Diversity (2007, background): “This requirement leads us to the the Earth Mover’s distance (EMD) [14], which is actually a Monge-Kantorovich transportation distance [5] in disguise.”