
%%% OT GENERAL %%%

@book{villani2003,
  title={Topics in C. Transportation},
  author={Villani, Cedric},
  series={Graduate studies in Math.},
  year={2003},
  publisher={AMS}
}

@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}
}


@article{Monge1781,
	    author = {Monge, G.},
	    journal = {Histoire de l'Acad{\'e}mie Royale des Sciences},
	    pages = {666--704},
	    title = {M{\'e}moire sur la th{\'e}orie des d{\'e}blais et des remblais},
	    year = {1781}
}

@article{berman2017sinkhorn,
  title={The sinkhorn algorithm, parabolic optimal transport and geometric Monge-Amp$\backslash$ere equations},
  author={Berman, Robert J},
  journal={arXiv preprint arXiv:1712.03082},
  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{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}
}

@book{lemmens2012nonlinear,
  title={Nonlinear Perron-Frobenius Theory},
  author={Lemmens, Bas and Nussbaum, Roger},
  volume={189},
  year={2012},
  publisher={Cambridge University Press}
}

@article{benamou2000computational,
	Author = {Benamou, J-D. and Brenier, Y.},
	Date-Added = {2015-02-08 20:05:54 +0000},
	Date-Modified = {2015-06-21 09:48:07 +0000},
	Journal = {Numerische Mathematik},
	Keywords = {optimal transport},
	Number = {3},
	Pages = {375--393},
	Publisher = {Springer},
	Title = {A computational fluid mechanics solution to the {M}onge-{K}antorovich mass transfer problem},
	Volume = {84},
	Year = {2000},}


@article{Brenier91,
    AUTHOR = {Brenier, Y.},
     TITLE = {Polar factorization and monotone rearrangement of
              vector-valued functions},
   JOURNAL = {Comm. Pure Appl. Math.},
  FJOURNAL = {Communications on Pure and Applied Mathematics},
    VOLUME = {44},
      YEAR = {1991},
    NUMBER = {4},
     PAGES = {375--417},
}


@article{agueh-2011,
author = {M. Agueh and G. Carlier},
title = {Barycenters in the {W}asserstein Space},
journal = {SIAM Journal on Mathematical Analysis},
volume = {43},
number = {2},
pages = {904--924},
year = {2011},
}


@BOOK{Burkard09,
  title = {Assignment Problems},
  publisher = {Society for Industrial and Applied Mathematics},
  year = {2009},
  author = {Burkard, R. and Dell'Amico, M. and Martello, S.},
  address = {Philadelphia, PA, USA},
  isbn = {0898716632, 9780898716634}
}

@book{rockafellar-convex,
  title={Convex analysis},
  author={Rockafellar, Ralph Tyrell},
  year={1970},
  publisher={Princeton University Press}
}



%%% OT ENTROPY %%%%

@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{cuturidoucet14,
  title={Fast computation of Wasserstein barycenters},
  author={Cuturi, Marco and Doucet, Arnaud},
  booktitle={International Conference on Machine Learning},
  pages={685--693},
  year={2014}
}

@article{Benamou2015,
  title={Iterative Bregman projections for regularized transportation problems},
  author={Benamou, Jean-David and Carlier, Guillaume and Cuturi, Marco and Nenna, Luca and Peyr{\'e}, Gabriel},
  journal={SIAM Journal on Scientific Computing},
  volume={37},
  number={2},
  pages={A1111--A1138},
  year={2015},
  publisher={SIAM}
}


@article{solomon2015convolutional,
  title={Convolutional {Wasserstein} distances: Efficient optimal transportation on geometric domains},
  author={Solomon, Justin and De Goes, Fernando and Peyr{\'e}, Gabriel and Cuturi, Marco and Butscher, Adrian and Nguyen, Andy and Du, Tao and Guibas, Leonidas},
  journal={ACM Transactions on Graphics (TOG)},
  volume={34},
  number={4},
  pages={66},
  year={2015},
  publisher={ACM}
}

@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}
}

@ARTICLE{Sinkhorn64,
  author={Sinkhorn, Richard},
  title = {A relationship between arbitrary positive matrices and doubly stochastic
	matrices},
  journal = {Ann. Math. Statist.},
  year = {1964},
  volume = {35},
  pages = {876--879}
}

@ARTICLE{Schroedinger31,
  author = {E. Schr\"odinger},
  title = {{\"U}ber die {U}mkehrung der {N}aturgesetze},
  journal = {Sitzungsberichte Preuss. Akad. Wiss. Berlin. Phys. Math.},
  year = {1931},
  volume = {144},
  pages = {144--153}
}

@ARTICLE{Schmitzer2016,
  author = {B. Schmitzer},
  title = {Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems},
  journal = {arXiv:1610.06519},
  year = {2016},
}

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

@article{chizat2016scaling,
  title={Scaling algorithms for unbalanced transport problems},
  author={Chizat, Lenaic and Peyr{\'e}, Gabriel and Schmitzer, Bernhard and Vialard, Fran{\c{c}}ois-Xavier},
  journal={to appear in Mathematics of Computation},
  year={2018}
}


@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}
}

@article{Carlier2017,
  title={Convergence of entropic schemes for optimal transport and gradient flows},
  author={Carlier, Guillaume and Duval, Vincent and Peyr{\'e}, Gabriel and Schmitzer, Bernhard},
  journal={SIAM Journal on Mathematical Analysis},
  volume={49},
  number={2},
  pages={1385--1418},
  year={2017},
  publisher={SIAM}
}

@article{leonard2012schrodinger,
  title={From the {Schr{\"o}dinger} problem to the {Monge--Kantorovich} problem},
  author={L{\'e}onard, Christian},
  journal={Journal of Functional Analysis},
  volume={262},
  number={4},
  pages={1879--1920},
  year={2012},
  publisher={Elsevier}
}


@Article{RamdasSinkhAsymptotics,
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{amari2017information,
  title={Information Geometry Connecting Wasserstein Distance and Kullback-Leibler Divergence via the Entropy-Relaxed Transportation Problem},
  author={Amari, Shun-ichi and Karakida, Ryo and Oizumi, Masafumi},
  journal={arXiv preprint arXiv:1709.10219},
  year={2017}
}

%%%% kernels

@book{scholkopf2002learning,
  title={Learning with kernels: support vector machines, regularization, optimization, and beyond},
  author={Sch{\"o}lkopf, Bernhard and Smola, Alexander J},
  year={2002},
  publisher={MIT press}
}



%%%% OT for ML %%%%%

@inproceedings{kusner2015word,
  title={From Word Embeddings To Document Distances},
  author={Kusner, Matt and Sun, Yu and Kolkin, Nicholas and Weinberger, Kilian Q},
  booktitle={Proc. of the 32nd Intern. Conf. on Machine Learning},
  pages={957--966},
  year={2015}
}


@incollection{NIPS2016_6139,
title = {Supervised Word Mover's Distance},
author = {Huang, Gao and Guo, Chuan and Kusner, Matt J and Sun, Yu and Sha, Fei and Weinberger, Kilian Q},
booktitle = {Advances in Neural Information Processing Systems 29},
editor = {D. D. Lee and M. Sugiyama and U. V. Luxburg and I. Guyon and R. Garnett},
pages = {4862--4870},
year = {2016},
publisher = {Curran Associates, Inc.},
url = {http://papers.nips.cc/paper/6139-supervised-word-movers-distance.pdf}
}

@inproceedings{2016-genevay-nips,
  title={Stochastic optimization for large-scale optimal transport},
  author={Genevay, Aude and Cuturi, Marco and Peyr{\'e}, Gabriel and Bach, Francis},
  booktitle={Advances in Neural Information Processing Systems},
  pages={3440--3448},
  year={2016}
}

@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}
}
%
@article{salimans2018improving,
  title={Improving {GANs} using optimal transport},
  author={Salimans, Tim and Zhang, Han and Radford, Alec and Metaxas, Dimitris},
  journal={arXiv preprint arXiv:1803.05573},
  year={2018}
}

@inproceedings{altschuler2017near,
  title={Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration},
  author={Altschuler, Jason and Weed, Jonathan and Rigollet, Philippe},
  booktitle={Advances in Neural Information Processing Systems},
  pages={1961--1971},
  year={2017}
}

@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}
}

@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{Feydy2017,
  url = { https://hal.archives-ouvertes.fr/hal-01540455 },
  year = { 2017 },
  booktitle = { Proc. MICCAI'17 },
  author = { Jean Feydy and Benjamin Charlier and Francois-Xavier Vialard and Gabriel Peyr{\'e} },
  title = { Optimal Transport for Diffeomorphic Registration },
}

%%%% OT APPLICATIONS %%%

@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},
} 

@article{bonneel-2011,
 author = {Bonneel, N. and van de Panne, M. and Paris, S. and Heidrich, W.},
 title = {Displacement Interpolation Using {L}agrangian Mass Transport},
 journal = {ACM Trans. Graph.},
  volume = {30},
 number = {6},
 month = dec,
 year = {2011},
 pages = {158:1--158:12},
 } 


@article{deGoes-2012,
 author = {de Goes, F. and Breeden, K. and Ostromoukhov, V. and Desbrun, M.},
 title = {Blue Noise Through Optimal Transport},
 journal = {ACM Trans. Graph.},
 volume = {31},
 number = {6},
 month = nov,
 year = {2012},
 pages = {171:1--171:11},
} 


@article{solomon-2014,
 author = {Solomon, J. and Rustamov, R. and Guibas, L. and Butscher, A.},
 title = {Earth Mover's Distances on Discrete Surfaces},
 journal = {ACM Trans. Graph.},
 volume = {33},
 number = {4},
 month = jul,
 year = {2014},
 pages = {67:1--67:12},
} 

@article{solomon2016entropic,
  title={Entropic Metric Alignment for Correspondence Problems},
  author={Solomon, J. and Peyr{\'e}, G. and Kim, V. and Sra, S.},
  year={2016},
 journal={ACM Transactions on Graphics (TOG)},
  volume={35},
  number={4},
  publisher={ACM}
 }






%% OT Fidelity

@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}
}

@INPROCEEDINGS{CuturiDoucet,
  author = {M. Cuturi and A. Doucet},
  title = {Fast Computation of {Wasserstein} Barycenters},
  booktitle = {Proceedings of the 31st International Conference on Machine Learning
	(ICML), JMLR W\&CP},
  year = {2014},
  volume = {32}
}

@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{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{metivier2016optimal,
  title={An optimal transport approach for seismic tomography: Application to 3D full waveform inversion},
  author={M{\'e}tivier, L and Brossier, R and M{\'e}rigot, Q and Oudet, E and Virieux, J},
  journal={Inverse Problems},
  volume={32},
  number={11},
  pages={115008},
  year={2016},
  publisher={IOP Publishing}
}

@article{theano2016,
  author    = {Rami Al{-}Rfou and
               Guillaume Alain and
               Amjad Almahairi and
               Christof Angerm{\"{u}}ller and
               Dzmitry Bahdanau and
               Nicolas Ballas and
               ... and
               Ying Zhang},
  title     = {Theano: {A} Python framework for fast computation of mathematical
               expressions},
  journal   = {CoRR},
  volume    = {abs/1605.02688},
  year      = {2016},
  timestamp = {Wed, 28 Dec 2016 11:28:29 +0100},
  biburl    = {http://dblp.uni-trier.de/rec/bib/journals/corr/Al-RfouAAa16},
  bibsource = {dblp computer science bibliography, http://dblp.org}
}


%% Neural Networks

@inproceedings{GoodfellowGAN,
  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{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{VAE,
  title={Auto-encoding variational bayes},
  author={Kingma, Diederik P and Welling, Max},
  journal={arXiv preprint arXiv:1312.6114},
  year={2013}
}

@inproceedings{Xavier,
  title={Understanding the difficulty of training deep feedforward neural networks},
  author={Glorot, Xavier and Bengio, Yoshua},
  booktitle={Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics},
  pages={249--256},
  year={2010}
}

@incollection{CanasRosasco,
title = {Learning Probability Measures with respect to Optimal Transport Metrics},
author = {Guillermo Canas and Rosasco, Lorenzo},
booktitle = {Advances in Neural Information Processing Systems 25},
editor = {F. Pereira and C. J. C. Burges and L. Bottou and K. Q. Weinberger},
pages = {2492--2500},
year = {2012},
publisher = {Curran Associates, Inc.},
url = {http://papers.nips.cc/paper/4651-learning-probability-measures-with-respect-to-optimal-transport-metrics.pdf}
}


@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{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}
}

@article{MMDGAN,
  title={{MMD GAN}: Towards Deeper Understanding of Moment Matching Network},
  author={Li, Chun-Liang and Chang, Wei-Cheng and Cheng, Yu and Yang, Yiming and P{\'o}czos, Barnab{\'a}s},
  journal={arXiv preprint arXiv:1705.08584},
  year={2017}
}


@article{gulrajani2017improved,
  title={Improved training of {Wasserstein} {GAN}s},
  author={Gulrajani, Ishaan and Ahmed, Faruk and Arjovsky, Martin and Dumoulin, Vincent and Courville, Aaron},
  journal={arXiv preprint arXiv:1704.00028},
  year={2017}
}


@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}
}

@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}
}

@inproceedings{courty2014domain,
  title={Domain adaptation with regularized optimal transport},
  author={Courty, Nicolas and Flamary, R{\'e}mi and Tuia, Devis},
  booktitle={Joint European Conference on Machine Learning and Knowledge Discovery in Databases},
  pages={274--289},
  year={2014},
  organization={Springer}
}

@ARTICLE{7586038, 
author={N. Courty and R. Flamary and D. Tuia and A. Rakotomamonjy}, 
journal={IEEE Transactions on Pattern Analysis and Machine Intelligence}, 
title={Optimal Transport for Domain Adaptation}, 
year={2016}, 
volume={PP}, 
number={99}, 
pages={1-1}, 
keywords={Data analysis;Feature extraction;Kernel;Probability density function;Probability distribution;Training;Transportation;Classification;Optimal Transport;Transfer Learning;Unsupervised Domain Adaptation;Visual Adaptation}, 
doi={10.1109/TPAMI.2016.2615921}, 
ISSN={0162-8828}, 
month={},}

@article{sriperumbudur2012empirical,
  title={On the empirical estimation of integral probability metrics},
  author={Sriperumbudur, Bharath K and Fukumizu, Kenji and Gretton, Arthur and Sch{\"o}lkopf, Bernhard and Lanckriet, Gert RG and others},
  journal={Electronic Journal of Statistics},
  volume={6},
  pages={1550--1599},
  year={2012},
  publisher={The Institute of Mathematical Statistics and the Bernoulli Society}
}


@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{pmlr-v51-rolet16,
  title = 	 {Fast Dictionary Learning with a Smoothed Wasserstein Loss},
  author = 	 {Antoine Rolet and Marco Cuturi and Gabriel Peyr{\'e}},
  booktitle = 	 {Proceedings of the 19th International Conference on Artificial Intelligence and Statistics},
  pages = 	 {630--638},
  year = 	 {2016},
  editor = 	 {Arthur Gretton and Christian C. Robert},
  volume = 	 {51},
  series = 	 {Proceedings of Machine Learning Research},
  address = 	 {Cadiz, Spain},
  month = 	 {09--11 May},
  publisher = 	 {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v51/rolet16.pdf},
  url = 	 {http://proceedings.mlr.press/v51/rolet16.html},
}

@article{CramerGAN,
  title={The {Cramer} Distance as a Solution to Biased {Wasserstein} Gradients},
  author={Bellemare, Marc G and Danihelka, Ivo and Dabney, Will and Mohamed, Shakir and Lakshminarayanan, Balaji and Hoyer, Stephan and Munos, R{\'e}mi},
  journal={arXiv preprint arXiv:1705.10743},
  year={2017}
}

@inproceedings{inception,
  title={Improved techniques for training {GAN}s},
  author={Salimans, Tim and Goodfellow, Ian and Zaremba, Wojciech and Cheung, Vicki and Radford, Alec and Chen, Xi},
  booktitle={Advances in Neural Information Processing Systems},
  pages={2234--2242},
  year={2016}
}

%% Bayesian Stuff

@article{K2ABC,
  title={K2-ABC: Approximate Bayesian Computation with Kernel Embeddings},
  author={Park, Mijung and Jitkrittum, Wittawat and Sejdinovic, Dino},
  journal={arXiv preprint arXiv:1502.02558},
  year={2015}
}

@article{bernton2017inference,
  title={Inference in generative models using the Wasserstein distance},
  author={Bernton, Espen and Jacob, Pierre E and Gerber, Mathieu and Robert, Christian P},
  journal={arXiv preprint arXiv:1701.05146},
  year={2017}
}

@article{ABC,
  title={Approximate Bayesian computation in population genetics},
  author={Beaumont, Mark A and Zhang, Wenyang and Balding, David J},
  journal={Genetics},
  volume={162},
  number={4},
  pages={2025--2035},
  year={2002},
  publisher={Genetics Soc America}
}

%% Other

@article{kingma2014adam,
  title={Adam: A method for stochastic optimization},
  author={Kingma, Diederik and Ba, Jimmy},
  journal={arXiv preprint arXiv:1412.6980},
  year={2014}
}

@article{diggle1984monte,
  title={Monte Carlo methods of inference for implicit statistical models},
  author={Diggle, Peter J and Gratton, Richard J},
  journal={Journal of the Royal Statistical Society. Series B (Methodological)},
  pages={193--227},
  year={1984},
  publisher={JSTOR}
}


@article{Bousquet2017,
  title={From optimal transport to generative modeling: the {VEGAN} cookbook},
  author={Olivier Bousquet and Sylvain Gelly and Ilya Tolstikhin and Carl-Johann Simon-Gabriel and Bernhard Schoelkopf},
  journal={arXiv preprint arXiv:1705.07642},
  year={2017}
}

@article{weed2017sharp,
  title={Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance},
  author={Weed, Jonathan and Bach, Francis},
  journal={arXiv preprint arXiv:1707.00087},
  year={2017}
}

@article{muandet2017kernel,
  title={Kernel mean embedding of distributions: A review and beyond},
  author={Muandet, Krikamol and Fukumizu, Kenji and Sriperumbudur, Bharath and Sch{\"o}lkopf, Bernhard},
  journal={Foundations and Trends{\textregistered} in Machine Learning},
  volume={10},
  number={1-2},
  pages={1--141},
  year={2017},
  publisher={Now Publishers, Inc.}
}

% 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{SR05,
  title = {Hierarchical clustering via joint between-within distances: Extending Ward’s minimum variance method},
  author = {Sz{\'e}kely, G{\'a}bor J and Rizzo, Maria L},
  journal={J. Classification},
  volume={22},
  pages={151--183},
  year={2004}
}
%%% shapes 

@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}
}



%% 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}
}

%% Bregman divergences

@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}
}

@article{frigyik2008functional,
  title={Functional Bregman divergence and Bayesian estimation of distributions},
  author={Frigyik, B{\'e}la A and Srivastava, Santosh and Gupta, Maya R},
  journal={IEEE Transactions on Information Theory},
  volume={54},
  number={11},
  pages={5130--5139},
  year={2008},
  publisher={IEEE}
}

@article{liero2015optimal,
  title={Optimal entropy-transport problems and a new Hellinger--Kantorovich distance between positive measures},
  author={Liero, Matthias and Mielke, Alexander and Savar{\'e}, Giuseppe},
  journal={Inventiones mathematicae},
  pages={1--149},
  year={2015},
  publisher={Springer}
}

@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{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}
}
@Misc{numpy,
  author =    {Travis Oliphant},
  title =     {A guide to NumPy},
  year =      {2006},
  publisher={USA: Trelgol Publishing},
}
@inproceedings{ot-miccai,
  title={Optimal transport for diffeomorphic registration},
  author={Feydy, Jean and Charlier, Benjamin and Vialard, Fran{\c{c}}ois-Xavier and Peyr{\'e}, Gabriel},
  booktitle={International Conference on Medical Image Computing and Computer-Assisted Intervention},
  pages={291--299},
  year={2017},
  organization={Springer}
}
@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: 2018-10-04}
}

@inproceedings{hausdorff,
  title={Mesh: Measuring errors between surfaces using the hausdorff distance},
  author={Aspert, Nicolas and Santa-Cruz, Diego and Ebrahimi, Touradj},
  booktitle={Multimedia and Expo, 2002. ICME'02. Proceedings. 2002 IEEE International Conference on},
  volume={1},
  pages={705--708},
  year={2002},
  organization={IEEE}
}
@unpublished{global-divergences,
  TITLE = {{Global divergences between measures: from Hausdorff distance to Optimal Transport}},
  AUTHOR = {Feydy, Jean and Trouv{\'e}, Alain},
  URL = {https://hal.archives-ouvertes.fr/hal-01827184},
  NOTE = {working paper or preprint},
  YEAR = {2018},
  MONTH = Jul,
  PDF = {https://hal.archives-ouvertes.fr/hal-01827184/file/ShapeMI_2018_submission.pdf},
  HAL_ID = {hal-01827184},
  HAL_VERSION = {v1},
}
@article{sharp_sinkhorn,
  title={Differential Properties of Sinkhorn Approximation for Learning with Wasserstein Distance},
  author={Luise, Giulia and Rudi, Alessandro and Pontil, Massimiliano and Ciliberto, Carlo},
  journal={arXiv preprint arXiv:1805.11897},
  year={2018}
}
@article{lenaic,
  title={Unbalanced optimal transport: geometry and Kantorovich formulation},
  author={Chizat, Lenaic and Peyr{\'e}, Gabriel and Schmitzer, Bernhard and Vialard, Fran{\c{c}}ois-Xavier},
  journal={arXiv preprint arXiv:1508.05216},
  year={2015}
}


% kernels

@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{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}
}

@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{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={Pergamon}
}

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


@inproceedings{TPSRPM,
  title={A new algorithm for non-rigid point matching},
  author={Chui, Haili and Rangarajan, Anand},
  booktitle={Computer Vision and Pattern Recognition, 2000. Proceedings. IEEE Conference on},
  volume={2},
  pages={44--51},
  year={2000},
  organization={IEEE}
}

@article{sriperumbudur2010hilbert,
  title={Hilbert space embeddings and metrics on probability measures},
  author={Sriperumbudur, Bharath K and Gretton, Arthur and Fukumizu, Kenji and Sch{\"o}lkopf, Bernhard and Lanckriet, Gert RG},
  journal={Journal of Machine Learning Research},
  volume={11},
  number={Apr},
  pages={1517--1561},
  year={2010}
}

@inproceedings{electrostatic,
  title={Electrostatic halftoning},
  author={Schmaltz, Christian and Gwosdek, Pascal and Bruhn, Andr{\'e}s and Weickert, Joachim},
  booktitle={Computer Graphics Forum},
  volume={29},
  number={8},
  pages={2313--2327},
  year={2010},
  organization={Wiley Online Library}
}
