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Computing optimal transport (OT) between measures in high dimensions is doomed by the curse of dimensionality.
The speed of mean glivenko-cantelli convergence
R. Dudley · 1969
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On a formula for the l2 Wasserstein metric between measures on Euclidean and Hilbert spaces
M. Gelbrich · 1990
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Gradient Flows in Metric Spaces and in the Space of Probability Measures
L. Ambrosio, N. Gigli, and G. Savare · 2005
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Optimal transport: old and new
C. Villani · 2008
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From knothe’s transport to brenier’s map and a continuation method for optimal transport
G. Carlier, A. Galichon, and F. Santambrogio · 2009
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Wasserstein barycenter and its application to texture mixing
J. Rabin, G. Peyré, J. Delon, and M. Bernot · 2011
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Sinkhorn distances: Lightspeed computation of optimal transport
M. Cuturi · 2013
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Optimal transport for domain adaptation
N. Courty, R. Flamary, A. Rakotomamonjy, and D. Tuia · 2014
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Regularized discrete optimal transport
S. Ferradans, N. Papadakis, G. Peyré, and J.-F. Aujol · 2014
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Generative adversarial nets
I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio · 2014
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Auto-encoding variational bayes
D. P. Kingma and M. Welling · 2014
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Adaptive color transfer with relaxed optimal transport
J. Rabin, S. Ferradans, and N. Papadakis · 2014
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Sliced and Radon Wasserstein Barycenters of Measures
N. Bonneel, J. Rabin, G. Peyré, and H. Pfister · 2015
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On the rate of convergence in wasserstein distance of the empirical measure
N. Fournier and A. Guillin · 2015
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Optimal transport for applied mathematicians, 2015
F. Santambrogio · 2015
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Wasserstein generative adversarial networks
M. Arjovsky, S. Chintala, and L. Bottou · 2017
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Joint distribution optimal transportation for domain adaptation
N. Courty, R. Flamary, A. Habrard, and A. Rakotomamonjy · 2017
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Learning generative models with sinkhorn divergences
A. Genevay, G. Peyre, and M. Cuturi · 2018
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Generalizing point embeddings using the wasserstein space of elliptical distributions
B. Muzellec and M. Cuturi · 2018
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Large-scale optimal transport and mapping estimation
V. Seguy, B. B. Damodaran, R. Flamary, N. Courty, A. Rolet, and M. Blondel · 2018
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Wasserstein auto-encoders
I. Tolstikhin, O. Bousquet, S. Gelly, and B. Scholkopf · 2018
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Optimal transport for gaussian mixture models
Y. Chen, T. T. Georgiou, and A. Tannenbaum · 2019
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Sample complexity of sinkhorn divergences
A. Genevay, L. Chizat, F. Bach, M. Cuturi, and G. Peyré · 2019
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Deep hashing network for unsupervised domain adaptation
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Generative modeling using the sliced wasserstein distance
I. Deshpande, Z. Zhang, and A. G. Schwing · 2018
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Mémoire sur la théorie des déblais et des remblais
G. Monge
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Subspace robust Wasserstein distances
F.-P. Paty and M. Cuturi · 2019
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Regularity as regularization: Smooth and strongly convex brenier potentials in optimal transport
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Orthogonal estimation of wasserstein distances
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Optimal-transport analysis of single-cell gene expression identifies developmental trajectories in reprogramming
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Sliced wasserstein generative models
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