Results 11 to 20 of about 32,144 (182)
Matricial Wasserstein-1 Distance [PDF]
IEEE Control Systems Letters, 2017 In this note, we propose an extension of the Wasserstein 1-metric ($W_1$) for matrix probability densities, matrix-valued density measures, and an unbalanced interpretation of mass transport. The key is using duality theory, in particular, a "dual of the
Chen, Yongxin +3 more
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Asymptotics of Smoothed Wasserstein Distances [PDF]
Potential Analysis, 2021 We investigate contraction of the Wasserstein distances on $\mathbb{R}^d$ under Gaussian smoothing. It is well known that the heat semigroup is exponentially contractive with respect to the Wasserstein distances on manifolds of positive curvature; however, on flat Euclidean space---where the heat semigroup corresponds to smoothing the measures by ...
Hong-Bin Chen, Jonathan Niles-Weed
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Wasserstein distance to independence models [PDF]
Journal of Symbolic Computation, 2021 An independence model for discrete random variables is a Segre-Veronese variety in a probability simplex. Any metric on the set of joint states of the random variables induces a Wasserstein metric on the probability simplex. The unit ball of this polyhedral norm is dual to the Lipschitz polytope.
Celik T. O. +4 more
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Hyperbolic Wasserstein Distance for Shape Indexing. [PDF]
IEEE Trans Pattern Anal Mach Intell, 2020 Shape space is an active research topic in computer vision and medical imaging fields. The distance defined in a shape space may provide a simple and refined index to represent a unique shape. This work studies the Wasserstein space and proposes a novel framework to compute the Wasserstein distance between general topological surfaces by integrating ...
Shi J, Wang Y.
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Donsker’s theorem in Wasserstein-1 distance [PDF]
Electronic Communications in Probability, 2020 We compute the Wassertein-1 (or Kolmogorov-Rubinstein) distance between a random walk in $R^d$ and the Brownian motion. The proof is based on a new estimate of the Lipschitz modulus of the solution of the Stein's equation. As an application, we can evaluate the rate of convergence towards the local time at 0 of the Brownian motion.
Coutin, Laure, Decreusefond, Laurent
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Entropy-Regularized Optimal Transport on Multivariate Normal and q-normal Distributions
Entropy, 2021 The distance and divergence of the probability measures play a central role in statistics, machine learning, and many other related fields. The Wasserstein distance has received much attention in recent years because of its distinctions from other ...
Qijun Tong, Kei Kobayashi
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Multimedia Analysis and Fusion via Wasserstein Barycenter
International Journal of Networked and Distributed Computing (IJNDC), 2020 Optimal transport distance, otherwise known as Wasserstein distance, recently has attracted attention in music signal processing and machine learning as powerful discrepancy measures for probability distributions.
Cong Jin +7 more
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Fused Gromov-Wasserstein Distance for Structured Objects
Algorithms, 2020 Optimal transport theory has recently found many applications in machine learning thanks to its capacity to meaningfully compare various machine learning objects that are viewed as distributions.
Titouan Vayer +4 more
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The Ultrametric Gromov–Wasserstein Distance
Discrete & Computational Geometry, 2023 In this paper, we investigate compact ultrametric measure spaces which form a subset $\mathcal{U}^w$ of the collection of all metric measure spaces $\mathcal{M}^w$. Similar as for the ultrametric Gromov-Hausdorff distance on the collection of ultrametric spaces $\mathcal{U}$, we define ultrametric versions of two metrics on $\mathcal{U}^w$, namely of ...
Facundo Mémoli +3 more
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Convolutional wasserstein distances [PDF]
ACM Transactions on Graphics, 2015 This paper introduces a new class of algorithms for optimization problems involving optimal transportation over geometric domains. Our main contribution is to show that optimal transportation can be made tractable over large domains used in graphics, such as images and triangle meshes, improving performance by orders of magnitude compared to previous ...
Solomon, Justin +7 more
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