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Optimal Transport to a Variety [PDF]
, 2020 We study the problem of minimizing the Wasserstein distance between a probability distribution and an algebraic variety. We consider the setting of finite state spaces and describe the solution depending on the choice of the ground metric and the given distribution.
Celik T. O. +4 more
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On the Degeneracy of Optimal Transportation [PDF]
Communications in Partial Differential Equations, 2014 We extend a dimensional upper bound on how much an optimal transport map can degenerate for the quadratic transportation cost, originally due to Caffarelli, to cost functions that satisfy the curvature condition of Ma, Trudinger, and Wang.
Kim, Young-Heon, Kitagawa, Jun
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Mathematical Physics, Analysis and Geometry, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sam Cole +3 more
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The directional optimal transport
The Annals of Applied Probability, 2022 Forthcoming in 'Annals of Applied Probability'
Nutz, Marcel, Wang, Ruodu
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CoRR, 2020 Optimal transport (OT) is a powerful geometric and probabilistic tool for finding correspondences and measuring similarity between two distributions. Yet, its original formulation relies on the existence of a cost function between the samples of the two distributions, which makes it impractical when they are supported on different spaces. To circumvent
Titouan Vayer +3 more
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Unbalanced CO-optimal Transport
Proceedings of the AAAI Conference on Artificial Intelligence, 2023 Optimal transport (OT) compares probability distributions by computing a meaningful alignment between their samples. CO-optimal transport (COOT) takes this comparison further by inferring an alignment between features as well. While this approach leads to better alignments and generalizes both OT and Gromov-Wasserstein distances, we provide a ...
Tran, Quang Huy +6 more
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Immiscible color flows in optimal transport networks for image classification
Frontiers in Physics, 2023 In classification tasks, it is crucial to meaningfully exploit the information contained in the data. While much of the work in addressing these tasks is focused on building complex algorithmic infrastructures to process inputs in a black-box fashion ...
Alessandro Lonardi +2 more
doaj +1 more source
Constrained Optimal Transport [PDF]
Archive for Rational Mechanics and Analysis, 2017 The classical duality theory of Kantorovich and Kellerer for the classical optimal transport is generalized to an abstract framework and a characterization of the dual elements is provided. This abstract generalization is set in a Banach lattice $\cal{X}$ with a order unit.
Ibrahim Ekren, H. Mete Soner
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Quantum Optimal Transport is Cheaper [PDF]
Journal of Statistical Physics, 2020 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 introduced in [F. Golse, C. Mouhot, T. Paul, Commun. Math. Phys. 343 (2016), 165-205]. We show that the optimal quantum cost can be cheaper than the classical one.
Caglioti E., Golse F., Paul T.
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