M. Arjovsky, S. Chintala, and L. Bottou, , 2017.

F. Bassetti, A. Bodini, R. , and E. , On minimum Kantorovich distance estimators. Statistics & probability letters, vol.76, pp.1298-1302, 2006.
DOI : 10.1016/j.spl.2006.02.001

N. Bonneel, G. Peyré, C. , and M. , Wasserstein barycentric coordinates: Histogram regression using optimal transport, ACM Transactions on Graphics, vol.35, issue.4, 2016.
DOI : 10.1145/2897824.2925918

URL : https://hal.archives-ouvertes.fr/hal-01303148

L. M. Bregman, The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming, USSR computational mathematics and mathematical physics, vol.7, issue.3, pp.200-217, 1967.

B. Charlier, J. Feydy, G. , and J. , Kernel operations on the gpu, with autodiff, without memory overflows, pp.2018-2028, 2018.

M. Cuturi, Sinkhorn distances: Lightspeed computation of optimal transport, Adv. in Neural Information Processing Systems, pp.2292-2300, 2013.

G. K. Dziugaite, D. M. Roy, G. , and Z. , Training generative neural networks via maximum mean discrepancy optimization, Proceedings of the Thirty-First Conference on Uncertainty in Artificial Intelligence, pp.258-267, 2015.

J. Franklin and J. Lorenz, On the scaling of multidimensional matrices, Linear Algebra and its applications, vol.114, pp.717-735, 1989.

C. Frogner, C. Zhang, H. Mobahi, M. Araya, and T. A. Poggio, Learning with a Wasserstein loss, Advances in Neural Information Processing Systems, pp.2053-2061, 2015.

A. Galichon and B. Salanié, Matching with trade-offs: Revealed preferences over competing characteristics, 2010.
DOI : 10.2139/ssrn.1487307

URL : http://spire.sciencespo.fr/hdl:/2441/1293p84sf58s482v2dpn0gsd67/resources/matching-with-trade-offs.pdf

A. Genevay, G. Peyré, C. , and M. , Learning generative models with sinkhorn divergences, International Conference on Artificial Intelligence and Statistics, pp.1608-1617, 2018.

J. Glaunes, A. Trouvé, Y. , and L. , Diffeomorphic matching of distributions: A new approach for unlabelled point-sets and sub-manifolds matching, Proceedings of the 2004 IEEE Computer Society Conference on, vol.2, pp.II-II, 2004.

I. Goodfellow, J. Pouget-abadie, M. Mirza, B. Xu, D. Warde-farley et al., Generative adversarial nets, Advances in neural information processing systems, pp.2672-2680, 2014.

A. Gretton, K. M. Borgwardt, M. Rasch, B. Schölkopf, and A. J. Smola, A kernel method for the two-sample-problem, Advances in neural information processing systems, pp.513-520, 2007.

I. Kaltenmark, B. Charlier, C. , and N. , A general framework for curve and surface comparison and registration with oriented varifolds, Computer Vision and Pattern Recognition (CVPR), 2017.
DOI : 10.1109/cvpr.2017.487

URL : https://hal.archives-ouvertes.fr/hal-01817514

L. Kantorovich, On the transfer of masses (in Russian), Doklady Akademii Nauk, vol.37, issue.2, pp.227-229, 1942.

C. Léonard, A survey of the Schrödinger problem and some of its connections with optimal transport, 2013.

Y. Li, K. Swersky, and R. Zemel, Generative moment matching networks, Proceedings of the 32nd International Conference on Machine Learning (ICML-15), pp.1718-1727, 2015.

C. A. Micchelli, Y. Xu, and H. Zhang, Universal kernels, Journal of Machine Learning Research, vol.7, pp.2651-2667, 2006.

G. Montavon, K. Müller, C. , and M. , Wasserstein training of restricted boltzmann machines, Advances in Neural Information Processing Systems, pp.3718-3726, 2016.

A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang et al., Automatic differentiation in pytorch, 2017.

G. Peyré and M. Cuturi, , 2017.

A. Ramdas, N. G. Trillos, C. , and M. , On wasserstein two-sample testing and related families of nonparametric tests, Entropy, vol.19, issue.2, 2017.

Y. Rubner, C. Tomasi, and L. J. Guibas, The earth mover's distance as a metric for image retrieval, International Journal of Computer Vision, vol.40, issue.2, pp.99-121, 2000.

T. Salimans, H. Zhang, A. Radford, and D. Metaxas, Improving GANs using optimal transport, 2018.

M. Sanjabi, J. Ba, M. Razaviyayn, and J. D. Lee, On the convergence and robustness of training GANs with regularized optimal transport, 2018.

F. Santambrogio, Optimal Transport for applied mathematicians, of Progress in Nonlinear Differential Equations and their applications, vol.87, 2015.