Projection‐based techniques for high‐dimensional optimal transport problems
Sign Up to like & getrecommendations! Published in 2022 at "Wiley Interdisciplinary Reviews: Computational Statistics"
DOI: 10.1002/wics.1587
Abstract: Optimal transport (OT) methods seek a transformation map (or plan) between two probability measures, such that the transformation has the minimum transportation cost. Such a minimum transport cost, with a certain power transform, is called… read more here.
Keywords: optimal transport; projection based; transport; based techniques ... See more keywords
Computation of optimal transport on discrete metric measure spaces
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DOI: 10.1007/s00211-019-01077-z
Abstract: In this paper we investigate the numerical approximation of an analogue of the Wasserstein distance for optimal transport on graphs that is defined via a discrete modification of the Benamou–Brenier formula. This approach involves the… read more here.
Keywords: computation optimal; optimal transport; transport discrete; measure ... See more keywords
A fast approach to optimal transport: the back-and-forth method
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DOI: 10.1007/s00211-020-01154-8
Abstract: We present an iterative method to efficiently solve the optimal transportation problem for a class of strictly convex costs which includes quadratic and p-power costs. Given two probability measures supported on a discrete grid with… read more here.
Keywords: transport back; optimal transport; method; fast approach ... See more keywords
Population Games and Discrete Optimal Transport
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DOI: 10.1007/s00332-018-9507-5
Abstract: We propose an evolutionary dynamics for population games with discrete strategy sets, inspired by optimal transport theory and mean field games. The proposed dynamics is the Smith dynamics with strategy graph structure, in which payoffs… read more here.
Keywords: population games; games discrete; optimal transport; transport ... See more keywords
A Geometric Perspective on Regularized Optimal Transport
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DOI: 10.1007/s10884-018-9684-9
Abstract: We present new geometric intuition on dynamical versions of regularized optimal transport. We introduce two families of variational problems on Riemannian manifolds which contain analogues of the Schrödinger bridge problem and the Yasue problem. We… read more here.
Keywords: perspective regularized; regularized optimal; geometric perspective; optimal transport ... See more keywords
Quantum Optimal Transport is Cheaper
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DOI: 10.1007/s10955-020-02571-7
Abstract: We compare bipartite (Euclidean) matching problems in classical and quantum mechanics. The quantum case is treated in terms of a quantum version of the Wasserstein distance. We show that the optimal quantum cost can be… read more here.
Keywords: quantum; optimal transport; transport cheaper; quantum optimal ... See more keywords
Sharp boundary ε-regularity of optimal transport maps
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DOI: 10.1016/j.aim.2021.107603
Abstract: Abstract In this paper we develop a boundary e-regularity theory for optimal transport maps between bounded open sets with C 1 , α -boundary. Our main result asserts sharp C 1 , α -regularity of… read more here.
Keywords: boundary regularity; transport; regularity; sharp boundary ... See more keywords
Peacock geodesics in Wasserstein space
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DOI: 10.1016/j.difgeo.2021.101764
Abstract: Abstract Martingale optimal transport has attracted much attention due to its application in pricing and hedging in mathematical finance. The essential notion which makes martingale optimal transport different from optimal transport is peacock. A peacock… read more here.
Keywords: peacock; peacock geodesics; martingale optimal; optimal transport ... See more keywords
Convex duality in nonlinear optimal transport
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DOI: 10.1016/j.jfa.2019.04.010
Abstract: This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and… read more here.
Keywords: nonlinear optimal; convex duality; problem; duality nonlinear ... See more keywords
On the convergence of augmented Lagrangian method for optimal transport between nonnegative densities
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DOI: 10.1016/j.jmaa.2019.123811
Abstract: The dynamical formulation of the optimal transport problem, introduced by J. D. Benamou and Y. Brenier, corresponds to the time-space search of a density and a momentum minimizing a transport energy between two densities. In… read more here.
Keywords: augmented lagrangian; transport; convergence augmented; saddle point ... See more keywords
Compactness criterion for semimartingale laws and semimartingale optimal transport
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DOI: 10.1090/tran/7663
Abstract: We provide a compactness criterion for the set of laws $\mathfrak{P}^{ac}_{sem}(\Theta)$ on the Skorokhod space for which the canonical process $X$ is a semimartingale having absolutely continuous characteristics with differential characteristics taking values in some… read more here.
Keywords: transport; theta; mathfrak sem; compactness criterion ... See more keywords