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Optimal transport (OT) is a versatile framework for comparing probability measures, with many applications to statistics, machine learning, and applied mathematics.
Sergey G. Bobkov, Isoperimetric and Analytic Inequalities for Log-Concave Probability Measures , The Annals of Probability 27
1921
Earlier work this paper cites.
Erwin Schrödinger, Über die umkehrung der naturgesetze , Akad. Wiss. Berlin. Phys. Math. 144
1931
Earlier work this paper cites.
Leonid V. Kantorovich, On the translocation of masses , Doklady Akademii Nauk USSR, vol. 37, 1942, pp. 199–201
1942
Earlier work this paper cites.
Jason Altschuler, Jonathan Weed, and Philippe Rigollet, Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration , Proceedings of the 31st International Conference on Neural Information Processing Systems, 2017, pp. 1961–1971
1971
Earlier work this paper cites.
Masashi Okamoto, Distinctness of the Eigenvalues of a Quadratic form in a Multivariate Sample , The Annals of Statistics 1
1973
Earlier work this paper cites.
T. Byczkowski, Gaussian measures on L p L_{p} spaces 0 ≤ p < ∞ 0\leq p<\infty , Studia Math. 59
1977
Earlier work this paper cites.
Shlomo Levental, Uniform limit theorems for harris recurrent markov chains , Probability theory and related fields 80
1988
Earlier work this paper cites.
Evarist Giné and Joel Zinn, Bootstrapping general empirical measures , The Annals of Probability (1990), 851–869
1990
Earlier work this paper cites.
Alexander Shapiro, On concepts of directional differentiability , Journal of Optimization Theory and Applications 66
1990
Earlier work this paper cites.
Michel Ledoux and Michel Talagrand, Probability in banach spaces: isoperimetry and processes , vol. 23, Springer Science & Business Media, 1991
1991
Earlier work this paper cites.
Alexander Shapiro, Asymptotic analysis of stochastic programs , Annals of Operations Research 30
1991
Earlier work this paper cites.
Aad W van der Vaart, Efficiency and hadamard differentiability , Scandinavian Journal of Statistics 18
1991
Earlier work this paper cites.
Lutz Dümbgen, On nondifferentiable functions and the bootstrap , Probability Theory and Related Fields 95
1993
Earlier work this paper cites.
Donald WK Andrews and David Pollard, An introduction to functional central limit theorems for dependent stochastic processes , International Statistical Review/Revue Internationale de Statistique (1994), 119–132
1994
Earlier work this paper cites.
Miguel Angel Arcones and Bin Yu, Central limit theorems for empirical andu-processes of stationary mixing sequences , Journal of Theoretical Probability 7
1994
Earlier work this paper cites.
Jongsig Bae and Shlomo Levental, Uniform clt for markov chains and its invariance principle: a martingale approach , Journal of Theoretical Probability 8
1995
Earlier work this paper cites.
Paul Doukhan, Pascal Massart, and Emmanuel Rio, Invariance principles for absolutely regular empirical processes , Annales de l’IHP Probabilités et statistiques 31
1995
Earlier work this paper cites.
Paul Malliavin, Hélène Airault, Leslie Kay, and Gérard Letac, Integration and probability , vol. 157, Springer Science & Business Media, 1995
1995
Earlier work this paper cites.
Aad var der Vaart, New Donsker classes , The Annals of Probability 24
1996
Earlier work this paper cites.
Aad W van der Vaart and Jon A Wellner, Weak convergence , Weak convergence and empirical processes, Springer, 1996, pp. 16–28
1996
Earlier work this paper cites.
Bernhard Schölkopf, Alexander Smola, and Klaus-Robert Müller, Nonlinear component analysis as a kernel eigenvalue problem , Neural computation 10
1998
Earlier work this paper cites.
Aad W van der Vaart, Asymptotic statistics , Cambridge University Press, Cambridge, UK, 1998
1998
Earlier work this paper cites.
Eustasio del Barrio, Evarist Giné, and Carlos Matrán, Central limit theorems for the Wasserstein distance between the empirical and the true distributions , The Annals of Probability 27
1999
Earlier work this paper cites.
Yoichi Nishiyama, Weak convergence of some classes of martingales with jumps , The Annals of Probability 28
2000
Earlier work this paper cites.
Yossi Rubner, Carlo Tomasi, and Leonidas J. Guibas, The earth mover’s distance as a metric for image retrieval , International Journal of Computer Vision 40
2000
Earlier work this paper cites.
R. M. Dudley, Real analysis and probability , Cambridge University Press, 2002
2002
Earlier work this paper cites.
Robert A Adams and John JF Fournier, Sobolev spaces , Elsevier, 2003
2003
Earlier work this paper cites.
Lars Hörmander, The analysis of linear partial differential operators i: Distribution theory and fourier analysis , Springer, 2003
2003
Earlier work this paper cites.
Cédric Villani, Topics in optimal transportation , no. 58, American Mathematical Soc., 2003
2003
Earlier work this paper cites.
Werner Römisch, Delta method, infinite dimensional , Encyclopedia of Statistical Sciences, Wiley, 2004
2004
Earlier work this paper cites.
Holger Wendland, Scattered data approximation , vol. 17, Cambridge university press, 2004
2004
Earlier work this paper cites.
Eustasio del Barrio, Evarist Giné, and Frederic Utzet, Asymptotics for L 2 L_{2} functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances , Bernoulli 11
2005
Earlier work this paper cites.
Francis Narcowich, Joseph Ward, and Holger Wendland, Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting , Mathematics of Computation 74
2005
Earlier work this paper cites.
Charalambos D Aliprantis and Kim C Border, Infinite dimensional analysis: A hitchhiker’s guide , Springer Science & Business Media, 2006
2006
Earlier work this paper cites.
László Lovász and Santosh Vempala, The geometry of logconcave functions and sampling algorithms , Random Structures & Algorithms 30
2007
Earlier work this paper cites.
Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré, Gradient flows: in metric spaces and in the space of probability measures , Springer Science & Business Media, 2008
2008
Earlier work this paper cites.
Cédric Villani, Optimal transport: Old and new , Springer, 2008
2008
Earlier work this paper cites.
J.H. van Zanten and Aad W van der Vaart, Reproducing kernel hilbert spaces of gaussian priors , Pushing the limits of contemporary statistics: contributions in honor of Jayanta K. Ghosh, Institute of Mathematical Statistics, 2008, pp. 200–222
2008
Earlier work this paper cites.
Emanuel Milman, On the role of convexity in isoperimetry, spectral gap and concentration , Inventiones mathematicae 177
2009
Cited alongside, same era.
Daniel W Stroock, Probability theory: an analytic view , Cambridge university press, 2010
2010
Cited alongside, same era.
Julien Rabin, Gabriel Peyré, Julie Delon, and Marc Bernot, Wasserstein barycenter and its application to texture mixing , International Conference on Scale Space and Variational Methods in Computer Vision, Springer, 2011, pp. 435–446
2011
Cited alongside, same era.
Roman Sandler and Michael Lindenbaum, Nonnegative matrix factorization with earth mover’s distance metric for image analysis , IEEE Transactions on Pattern Analysis and Machine Intelligence 33
2011
Cited alongside, same era.
Nicolas Bonnotte, Unidimensional and evolution methods for optimal transportation , Ph.D. thesis, Paris 11, 2013
Gonzalo Mena and Jonathan Niles-Weed, Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem , Advances in Neural Information Processing Systems 32
2019
Later among the works it cites.
Kimia Nadjahi, Alain Durmus, Umut Simsekli, and Roland Badeau, Asymptotic guarantees for learning generative models with the sliced-wasserstein distance , Advances in Neural Information Processing Systems 32
2019
Later among the works it cites.
Carla Tameling, Max Sommerfeld, and Axel Munk, Empirical optimal transport on countable metric spaces: Distributional limits and statistical applications , The Annals of Applied Probability 29
2019
Later among the works it cites.
Eric Wong, Frank Schmidt, and Zico Kolter, Wasserstein adversarial examples via projected sinkhorn iterations , Proceedings of the 36th International Conference on Machine Learning, 2019, pp. 6808–6817
2019
Later among the works it cites.
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2013
Cited alongside, same era.
Victor Chernozhukov, Sokbae Lee, and Adam M Rosen, Intersection bounds: estimation and inference , Econometrica 81
2013
Cited alongside, same era.
Marco Cuturi, Sinkhorn distances: lightspeed computation of optimal transport , Proceedings of the 26th International Conference on Neural Information Processing Systems, 2013, pp. 2292–2300
2013
Cited alongside, same era.
Peihua Li, Qilong Wang, and Lei Zhang, A novel earth mover’s distance methodology for image matching with gaussian mixture models , Proceedings of the IEEE International Conference on Computer Vision, 2013, pp. 1689–1696
2013
Cited alongside, same era.
Guido De Philippis and Alessio Figalli, The monge–ampère equation and its link to optimal transportation , Bulletin of the American Mathematical Society 51
2014
Cited alongside, same era.
Richard M Dudley, Uniform central limit theorems , vol. 142, Cambridge university press, 2014
2014
Cited alongside, same era.
Herbert Federer, Geometric measure theory , Springer, 2014
2014
Cited alongside, same era.
Christian Léonard, A survey of the Schrödinger problem and some of its connections with optimal transport , Discrete & Continuous Dynamical Systems 34
2014
Cited alongside, same era.
Javier Cárcamo, Antonio Cuevas, and Luis-Alberto Rodríguez, Directional differentiability for supremum-type functionals: statistical applications , Bernoulli 26
2020
Later among the works it cites.
Ziv Goldfeld and Kristjan Greenewald, Gaussian-smoothed optimal transport: Metric structure and statistical efficiency , Proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS-2020), 2020, pp. 3327–3337
2020
Later among the works it cites.
Ziv Goldfeld, Kristjan Greenewald, and Kengo Kato, Asymptotic guarantees for generative modeling based on the smooth Wasserstein distance , Proceedings of the International Conference on Neural Information Processing Systems (NeurIPS-2020), 2020, pp. 2527–2539
2020
Later among the works it cites.
Ziv Goldfeld, Kristjan Greenewald, Jonathan Niles-Weed, and Yury Polyanskiy, Convergence of smoothed empirical measures with applications to entropy estimation , IEEE Transactions on Information Theory 66
2020
Later among the works it cites.
Ziv Goldfeld and Kengo Kato, Limit distribution for smooth total variation and χ 2 \chi^{2} -divergence in high dimensions , Proceedings of the IEEE International Symposium on Information Theory (ISIT-2020), 2020
2020
Later among the works it cites.
Marcel Klatt, Carla Tameling, and Axel Munk, Empirical regularized optimal transport: Statistical theory and applications , SIAM Journal on Mathematics of Data Science 2
2020
Later among the works it cites.
Kimia Nadjahi, Alain Durmus, Lénaïc Chizat, Soheil Kolouri, Shahin Shahrampour, and Umut Simsekli, Statistical and topological properties of sliced probability divergences , Advances in Neural Information Processing Systems 33
2020
Later among the works it cites.
2020
Later among the works it cites.
Erhan Bayraktar and Gaoyue Guo, Strong equivalence between metrics of Wasserstein type , Electronic Communications in Probability 26
2021
Later among the works it cites.
Yao Chen, Qingyi Gao, and Xiao Wang, Inferential Wasserstein generative adversarial networks , Journal of the Royal Statistical Society: Series B (Statistical Methodology), to appear (2021)
2021
Later among the works it cites.
Hong-Bin Chen and Jonathan Niles-Weed, Asymptotics of smoothed wasserstein distances , Potential Analysis (2021), 1–25
2021
Later among the works it cites.
2021
Later among the works it cites.
Laurent Davezies, Xavier D’Haultfœuille, and Yannick Guyonvarch, Empirical process results for exchangeable arrays , The Annals of Statistics 49
2021
Later among the works it cites.
Promit Ghosal and Bodhisattva Sen, Multivariate ranks and quantiles using optimal transport: Consistency, rates, and nonparametric testing , The Annals of Statistics, to appear (2021)
2021
Later among the works it cites.
Marc Hallin, Eustasio del Barrio, Juan Cuesta-Albertos, and Carlos Matrán, Distribution and quantile functions, ranks and signs in dimension d: A measure transportation approach , The Annals of Statistics 49
2021
Later among the works it cites.
2021
Later among the works it cites.
Tianyi Lin, Zeyu Zheng, Elynn Y. Chen, Marco Cuturi, and Michael I. Jordan, On projection robust optimal transport: Sample complexity and model misspecification , Proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS-2021), 2021, pp. 262–270
2021
Later among the works it cites.
Tudor Manole, Sivaraman Balakrishnan, Jonathan Niles-Weed, and Larry Wasserman, Plugin estimation of smooth optimal transport maps , arXiv preprint: arXiv 2107.12364 (2021)
2021
Later among the works it cites.
Boris Muzellec, Adrien Vacher, Francis Bach, François-Xavier Vialard, and Alessandro Rudi, Near-optimal estimation of smooth transport maps with kernel sums-of-squares , 2021
2021
Later among the works it cites.
Sloan Nietert, Ziv Goldfeld, and Kengo Kato, Smooth p p -Wasserstein distance: Structure, empirical approximation, and statistical applications , Proceedings of the International Conference on Machine Learning (ICML-2021), PMLR, 2021, pp. 8172–8183
2021
Later among the works it cites.
Marcel Nutz and Johannes Wiesel, Entropic optimal transport: Convergence of potentials , Probability Theory and Related Fields (2021), 1–24
2021
Later among the works it cites.
Jonathan Niles-Weed and Philippe Rigollet, Estimation of Wasserstein distances in the spiked transport model , Bernoulli, to appear (2021)
2021
Later among the works it cites.
2021
Later among the works it cites.
2021
Later among the works it cites.
Adrien Vacher, Boris Muzellec, Alessandro Rudi, Francis Bach, and Francois-Xavier Vialard, A dimension-free computational upper-bound for smooth optimal transport estimation , Proceedings of the Conference on Learning Theory (COLT-2021), 2021, pp. 4143–4173
2021
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2021
Later among the works it cites.
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Tudor Manole, Sivaraman Balakrishnan, and Larry Wasserman, Minimax confidence intervals for the sliced wasserstein distance , Electronic Journal of Statistics 16
2022
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Dimitris N Politis and Joseph P Romano, Large sample confidence regions based on subsamples under minimal assumptions , The Annals of Statistics (1994), 2031–2050
2050
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