Results 11 to 20 of about 24,886 (258)
Wasserstein distance and metric trees [PDF]
L’Enseignement Mathématique, 2021 We study the Wasserstein (or earthmover) metric on the space P(X) of probability measures on a metric space X . We show that, if a finite metric space
Maxime Mathey-Prevot, Alain Valette
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The Wasserstein Metric between a Discrete Probability Measure and a Continuous One
MathematicsThis paper examines the Wasserstein metric between the empirical probability measure of n discrete random variables and a continuous uniform measure in the d-dimensional ball, providing an asymptotic estimation of their expectations as n approaches ...
Weihua Yang, Xu Zhang, Xia Wang
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A prelude to statistics in Wasserstein metric spaces [PDF]
Asian Journal of Economics and Banking, 2023 PurposeThis paper aims mainly at introducing applied statisticians and econometricians to the current research methodology with non-Euclidean data sets. Specifically, it provides the basis and rationale for statistics in Wasserstein space, where the metric on probability measures is taken as a Wasserstein metric arising from optimal transport theory ...
Chon Van Le, Uyen Pham
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Ensemble Riemannian data assimilation over the Wasserstein space [PDF]
Nonlinear Processes in Geophysics, 2021 In this paper, we present an ensemble data assimilation paradigm over a Riemannian manifold equipped with the Wasserstein metric. Unlike the Euclidean distance used in classic data assimilation methodologies, the Wasserstein metric can capture the ...
S. K. Tamang +6 more
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Nonembeddability of Persistence Diagrams with $p>2$ Wasserstein Metric [PDF]
Proceedings of the American Mathematical Society, 2019 Persistence diagrams do not admit an inner product structure compatible with any Wasserstein metric. Hence, when applying kernel methods to persistence diagrams, the underlying feature map necessarily causes distortion. We prove that persistence diagrams with the
A. Wagner
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Wasserstein model reduction approach for parametrized flow problems in porous media [PDF]
ESAIM: Proceedings and Surveys, 2023 The aim of this work is to build a reduced order model for parametrized porous media equations. The main challenge of this type of problems is that the Kolmogorov width of the solution manifold typically decays quite slowly and thus makes usual linear ...
Battisti Beatrice +5 more
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Constrained deepest descent in the 2-Wasserstein metric [PDF]
Annals of Mathematics, 2003 We study several constrained variational problem in the 2-Wasserstein metric for which the set of probability densities satisfying the constraint is not closed. For example, given a probability density $F_0$ on $\R^d$ and a time-step $h>0$, we seek to minimize $I(F) = hS(F) + W_2^2(F_0,F)$ over all of the probability densities $F$ that have the same
Eric A. Carlen, Wilfrid Gangbo
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Notes on the Wasserstein Metric in Hilbert Spaces [PDF]
The Annals of Probability, 1989 Let $(X, Y)$ be a pair of Hilbert-valued random variables for which the Wasserstein distance between the marginal distributions is reached. We prove that the mapping $\omega \rightarrow (X(\omega), Y(\omega))$ is increasing in a certain sense. Moreover, if $Y$ satisfies a nondegeneration condition, we can take $X = T(Y)$ with $T$ monotone in the sense ...
Juan A. Cuesta‐Albertos +1 more
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Free complete Wasserstein algebras [PDF]
Logical Methods in Computer Science, 2018 We present an algebraic account of the Wasserstein distances $W_p$ on complete metric spaces, for $p \geq 1$. This is part of a program of a quantitative algebraic theory of effects in programming languages.
Radu Mardare +2 more
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Deconvolution for the Wasserstein metric and geometric inference [PDF]
Electronic Journal of Statistics, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Caillerie, Claire +3 more
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