
@article{WassersteinGAN,
  title={Wasserstein {GAN}},
  author={Arjovsky, Martin and Chintala, Soumith and Bottou, L{\'e}on},
  journal={arXiv preprint arXiv:1701.07875},
  year={2017}
}


@article{bassetti2006minimum,
  title={On minimum {Kantorovich} distance estimators},
  author={Bassetti, Federico and Bodini, Antonella and Regazzini, Eugenio},
  journal={Statistics \& probability letters},
  volume={76},
  number={12},
  pages={1298--1302},
  year={2006},
  publisher={Elsevier}
}


@article{bonneel2016wasserstein,
  title={Wasserstein barycentric coordinates: Histogram regression using optimal transport},
  author={Bonneel, Nicolas and Peyr{\'e}, Gabriel and Cuturi, Marco},
  journal={ACM Transactions on Graphics},
  volume={35},
  number={4},
  year={2016}
}


@article{bregman1967relaxation,
  title={The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming},
  author={Bregman, Lev M},
  journal={USSR computational mathematics and mathematical physics},
  volume={7},
  number={3},
  pages={200--217},
  year={1967},
  publisher={Elsevier}
}


@misc{keops,
  title = {Kernel Operations on the GPU, with autodiff, without memory overflows},
  author={Charlier, Benjamin and Feydy, Jean and Glaun\`es, Joan},
  howpublished = {\url{http://www.kernel-operations.io}},
  year={2018},
  note = {Accessed: 2019-04-01}
}



@inproceedings{CuturiSinkhorn,
  title={Sinkhorn distances: Lightspeed computation of optimal transport},
  author={Cuturi, Marco},
  booktitle={Adv. in Neural Information Processing Systems},
  pages={2292--2300},
  year={2013}
}


@inproceedings{MMD-GAN,
  title={Training generative neural networks via maximum mean discrepancy optimization},
  author={Dziugaite, Gintare Karolina and Roy, Daniel M and Ghahramani, Zoubin},
  booktitle={Proceedings of the Thirty-First Conference on Uncertainty in Artificial Intelligence},
  pages = "258--267",
  year={2015}
}


@article{franklin1989scaling,
  title={On the scaling of multidimensional matrices},
  author={Franklin, Joel and Lorenz, Jens},
  journal={Linear Algebra and its applications},
  volume={114},
  pages={717--735},
  year={1989},
  publisher={Elsevier}
}


@inproceedings{2015-Frogner,
  title={Learning with a {W}asserstein loss},
  author={Frogner, Charlie and Zhang, Chiyuan and Mobahi, Hossein and Araya, Mauricio and Poggio, Tomaso A},
  booktitle={Advances in Neural Information Processing Systems},
  pages={2053--2061},
  year={2015}
}


%% Galichon
@article{galichon2010matching,
  title={Matching with trade-offs: Revealed preferences over competing characteristics},
  author={Galichon, Alfred and Salani{\'e}, Bernard},
  journal={Preprint hal-00473173},
  year={2010}
}


@inproceedings{genevay2018learning,
  title={Learning generative models with sinkhorn divergences},
  author={Genevay, Aude and Peyr{\'e}, Gabriel and Cuturi, Marco},
  booktitle={International Conference on Artificial Intelligence and Statistics},
  pages={1608--1617},
  year={2018}
}


@inproceedings{glaunes2004diffeomorphic,
  title={Diffeomorphic matching of distributions: A new approach for unlabelled point-sets and sub-manifolds matching},
  author={Glaunes, Joan and Trouv{\'e}, Alain and Younes, Laurent},
  booktitle={Computer Vision and Pattern Recognition, 2004. CVPR 2004. Proceedings of the 2004 IEEE Computer Society Conference on},
  volume={2},
  pages={II--II},
  year={2004},
  organization={Ieee}
}


@inproceedings{goodfellow2014generative,
  title={Generative adversarial nets},
  author={Goodfellow, Ian and Pouget-Abadie, Jean and Mirza, Mehdi and Xu, Bing and Warde-Farley, David and Ozair, Sherjil and Courville, Aaron and Bengio, Yoshua},
  booktitle={Advances in neural information processing systems},
  pages={2672--2680},
  year={2014}
}


@inproceedings{gretton2007kernel,
  title={A kernel method for the two-sample-problem},
  author={Gretton, Arthur and Borgwardt, Karsten M and Rasch, Malte and Sch{\"o}lkopf, Bernhard and Smola, Alex J},
  booktitle={Advances in neural information processing systems},
  pages={513--520},
  year={2007}
}

@inproceedings{varifold,
  title={A general framework for curve and surface comparison and registration with oriented varifolds},
  author={Kaltenmark, Irene and Charlier, Benjamin and Charon, Nicolas},
  booktitle={Computer Vision and Pattern Recognition (CVPR)},
  year={2017}
}


@article{Kantorovich42,
	Address = {Hingham, MA, USA},
	Author = {Leonid Kantorovich},
	Journal = {Doklady Akademii Nauk},
	Number = {2},
	Optannote = {Translated in Management Science, Vol. 5, pp. 1--4, 1959},
	Pages = {227-229},
	Title = {On the transfer of masses (in {R}ussian)},
	Volume = {37},
	Year = {1942}}


@article{leonard2013survey,
  title={A survey of the {Schr{\"o}dinger} problem and some of its connections with optimal transport},
  author={L{\'e}onard, Christian},
  journal={arXiv preprint arXiv:1308.0215},
  year={2013}
}


@inproceedings{li2015generative,
  title={Generative moment matching networks},
  author={Li, Yujia and Swersky, Kevin and Zemel, Rich},
  booktitle={Proceedings of the 32nd International Conference on Machine Learning (ICML-15)},
  pages={1718--1727},
  year={2015}
}


@article{micchelli2006universal,
  title={Universal kernels},
  author={Micchelli, Charles A and Xu, Yuesheng and Zhang, Haizhang},
  journal={Journal of Machine Learning Research},
  volume={7},
  number={Dec},
  pages={2651--2667},
  year={2006}
}


@inproceedings{montavon2016wasserstein,
  title={Wasserstein training of restricted Boltzmann machines},
  author={Montavon, Gr{\'e}goire and M{\"u}ller, Klaus-Robert and Cuturi, Marco},
  booktitle={Advances in Neural Information Processing Systems},
  pages={3718--3726},
  year={2016}
}


@article{pytorch,
  title={Automatic differentiation in pytorch},
  author={Paszke, Adam and Gross, Sam and Chintala, Soumith and Chanan, Gregory and Yang, Edward and DeVito, Zachary and Lin, Zeming and Desmaison, Alban and Antiga, Luca and Lerer, Adam},
  year={2017}
}


@ARTICLE{peyre2017computational,
  title={Computational Optimal Transport},
  author={Peyr{\'e}, Gabriel and Cuturi, Marco},
  journal = {arXiv:1610.06519},  
  year={2017}
}


@Article{ramdas,
AUTHOR = {Ramdas, Aaditya and Trillos, Nicolas Garcia and Cuturi, Marco},
TITLE = {On Wasserstein Two-Sample Testing and Related Families of Nonparametric Tests},
JOURNAL = {Entropy},
VOLUME = {19},
YEAR = {2017},
NUMBER = {2},
}


@article{rubner-2000,
 author = {Rubner, Yossi and Tomasi, Carlo and Guibas, Leonidas J.},
 title = {The Earth Mover's Distance As a Metric for Image Retrieval},
 journal = {International Journal of Computer Vision},
 volume = {40},
 number = {2},
 month = nov,
 year = {2000},
 pages = {99--121},
} 



@inproceedings{OTGAN,
title={Improving {GAN}s Using Optimal Transport},
author={Tim Salimans and Han Zhang and Alec Radford and Dimitris Metaxas},
booktitle={International Conference on Learning Representations},
year={2018},
url={https://openreview.net/forum?id=rkQkBnJAb}
}


@article{SanjabiSinkhGAN,
    title = "On the Convergence and Robustness of Training {GANs} with Regularized Optimal Transport", 
    author = "Maziar Sanjabi and Jimmy Ba and Meisam Razaviyayn and Jason D. Lee", 
  journal={arXiv preprint arXiv:1802.08249},
  year={2018}
}



@book{santambrogio2015optimal,
  title={Optimal Transport for applied mathematicians},
  author={Santambrogio, Filippo},
  series={Progress in Nonlinear Differential Equations and their applications},
  volume={87},
  year={2015},
  publisher={Springer}
}


% energy distance
@article{szekely2004testing,
  title={Testing for equal distributions in high dimension},
  author={Sz{\'e}kely, G{\'a}bor J and Rizzo, Maria L},
  journal={InterStat},
  volume={5},
  number={16.10},
  year={2004}
}



@article{thibault2017overrelaxed,
  title={Overrelaxed Sinkhorn-Knopp Algorithm for Regularized Optimal Transport},
  author={Thibault, Alexis and Chizat, L{\'e}na{\"\i}c and Dossal, Charles and Papadakis, Nicolas},
  journal={arXiv preprint arXiv:1711.01851},
  year={2017}
}


@inproceedings{vaillant2005surface,
  title={Surface matching via currents},
  author={Vaillant, Marc and Glaun{\`e}s, Joan},
  booktitle={Biennial International Conference on Information Processing in Medical Imaging},
  pages={381--392},
  year={2005},
  organization={Springer}
}



@article{bernhard,
  title={Stabilized sparse scaling algorithms for entropy regularized transport problems},
  author={Schmitzer, Bernhard},
  journal={arXiv preprint arXiv:1610.06519},
  year={2016}
}



@article{chuiraganajan,
  title={A new point matching algorithm for non-rigid registration},
  author={Chui, Haili and Rangarajan, Anand},
  journal={Computer Vision and Image Understanding},
  volume={89},
  number={2-3},
  pages={114--141},
  year={2003},
  publisher={Elsevier}
}



@article{yuille,
  title={The invisible hand algorithm: {Solving} the assignment problem with statistical physics},
  author={Kosowsky, JJ and Yuille, Alan L},
  journal={Neural networks},
  volume={7},
  number={3},
  pages={477--490},
  year={1994},
  publisher={Elsevier}
}


@inproceedings{schrodinger1932theorie,
  title={Sur la th{\'e}orie relativiste de l'{\'e}lectron et l'interpr{\'e}tation de la m{\'e}canique quantique},
  author={Schr{\"o}dinger, Erwin},
  booktitle={Annales de l'institut Henri Poincar{\'e}},
  volume={2},
  number={4},
  pages={269--310},
  year={1932}
}

@article{wilson1969use,
  title={The use of entropy maximising models, in the theory of trip distribution, mode split and route split},
  author={Wilson, Alan Geoffrey},
  journal={Journal of Transport Economics and Policy},
  pages={108--126},
  year={1969},
  publisher={JSTOR}
}



