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E. Giné and J. Zinn, “Empirical processes indexed by lipschitz functions,” The Annals of Probability , pp. 1329–1338, 1986
1986
Earlier work this paper cites.
M. Ledoux and M. Talagrand, Probability in Banach Spaces: isoperimetry and processes . Springer Science & Business Media, 1991, vol. 23
1991
Earlier work this paper cites.
A. Van Der Vaart, “New donsker classes,” The Annals of Probability , vol. 24, no. 4, pp. 2128–2140, 1996
1996
Earlier work this paper cites.
A. W. Van Der Vaart, A. W. van der Vaart, A. van der Vaart, and J. Wellner, Weak convergence and empirical processes: with applications to statistics . Springer Science & Business Media, 1996
1996
Earlier work this paper cites.
E. del Barrio, E. Giné, and C. Matrán, “Central limit theorems for the wasserstein distance between the empirical and the true distributions,” Annals of Probability , pp. 1009–1071, 1999
1999
Earlier work this paper cites.
M. Ledoux, The concentration of measure phenomenon . American Mathematical Soc., 2001, no. 89
2001
Earlier work this paper cites.
U. von Luxburg and O. Bousquet, “Distance-based classification with lipschitz functions.” J. Mach. Learn. Res. , vol. 5, no. Jun, pp. 669–695, 2004
2004
Earlier work this paper cites.
L. Baringhaus and C. Franz, “On a new multivariate two-sample test,” Journal of multivariate analysis , vol. 88, no. 1, pp. 190–206, 2004
2004
Earlier work this paper cites.
E. Del Barrio, E. Giné, and F. Utzet, “Asymptotics for l2 functionals of the empirical quantile process, with applications to tests of fit based on weighted wasserstein distances,” Bernoulli , vol. 11, no. 1, pp. 131–189, 2005
2005
Earlier work this paper cites.
R. Adamczak, “A tail inequality for suprema of unbounded empirical processes with applications to markov chains,” Electronic Journal of Probability , vol. 13, pp. 1000–1034, 2008
2008
Earlier work this paper cites.
J. Rabin, G. Peyré, J. Delon, and M. Bernot, “Wasserstein barycenter and its application to texture mixing,” in International Conference on Scale Space and Variational Methods in Computer Vision . Springer, 2011, pp. 435–446
2011
Earlier work this paper cites.
N. Bonnotte, “Unidimensional and evolution methods for optimal transportation,” Ph.D. dissertation, Paris 11, 2013
2013
Earlier work this paper cites.
M. Cuturi, “Sinkhorn distances: Lightspeed computation of optimal transport,” Advances in neural information processing systems , vol. 26, 2013
2013
Earlier work this paper cites.
S. Dereich, M. Scheutzow, and R. Schottstedt, “Constructive quantization: Approximation by empirical measures,” in Annales de l’IHP Probabilités et statistiques , vol. 49, no. 4, 2013, pp. 1183–1203
2013
Earlier work this paper cites.
S. Bobkov and M. Ledoux, “One-dimensional empirical measures, order statistics and kantorovich transport distances,” preprint , vol. 7127347, 2014
2014
Earlier work this paper cites.
R. Van Handel, “Probability in high dimension,” PRINCETON UNIV NJ, Tech. Rep., 2014
2014
Earlier work this paper cites.
J. Solomon, F. De Goes, G. Peyré, M. Cuturi, A. Butscher, A. Nguyen, T. Du, and L. Guibas, “Convolutional wasserstein distances: Efficient optimal transportation on geometric domains,” ACM Transactions on Graphics (ToG) , vol. 34, no. 4, pp. 1–11, 2015
2015
Earlier work this paper cites.
N. Fournier and A. Guillin, “On the rate of convergence in wasserstein distance of the empirical measure,” Probability Theory and Related Fields , vol. 162, no. 3, pp. 707–738, 2015
2015
Earlier work this paper cites.
I. Gulrajani, F. Ahmed, M. Arjovsky, V. Dumoulin, and A. C. Courville, “Improved training of wasserstein gans,” Advances in neural information processing systems , vol. 30, 2017
2017
Earlier work this paper cites.
M. Arjovsky, S. Chintala, and L. Bottou, “Wasserstein generative adversarial networks,” in International conference on machine learning . PMLR, 2017, pp. 214–223
2017
Cited alongside, same era.
M. Carriere, M. Cuturi, and S. Oudot, “Sliced wasserstein kernel for persistence diagrams,” in International conference on machine learning . PMLR, 2017, pp. 664–673
2017
Cited alongside, same era.
P. Rigollet and J. Weed, “Entropic optimal transport is maximum-likelihood deconvolution,” Comptes Rendus Mathematique , vol. 356, no. 11-12, pp. 1228–1235, 2018
2018
Cited alongside, same era.
R. Flamary, M. Cuturi, N. Courty, and A. Rakotomamonjy, “Wasserstein discriminant analysis,” Machine Learning , vol. 107, no. 12, pp. 1923–1945, 2018
2018
Cited alongside, same era.
H. Lavenant, S. Claici, E. Chien, and J. Solomon, “Dynamical optimal transport on discrete surfaces,” ACM Transactions on Graphics (TOG) , vol. 37, no. 6, pp. 1–16, 2018
G. Mena and J. Niles-Weed, “Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem,” Advances in Neural Information Processing Systems , vol. 32, 2019
2019
Later among the works it cites.
J. Weed and F. Bach, “Sharp asymptotic and finite-sample rates of convergence of empirical measures in wasserstein distance,” Bernoulli , vol. 25, no. 4A, pp. 2620–2648, 2019
2019
Later among the works it cites.
M. J. Wainwright, High-dimensional statistics: A non-asymptotic viewpoint . Cambridge University Press, 2019, vol. 48
2019
Later among the works it cites.
2019
Later among the works it cites.
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2018
Cited alongside, same era.
I. Deshpande, Z. Zhang, and A. G. Schwing, “Generative modeling using the sliced wasserstein distance,” in Proceedings of the IEEE conference on computer vision and pattern recognition , 2018, pp. 3483–3491
2018
Cited alongside, same era.
S. Kolouri, P. E. Pope, C. E. Martin, and G. K. Rohde, “Sliced wasserstein auto-encoders,” in International Conference on Learning Representations , 2018
2018
Cited alongside, same era.
M. Sommerfeld and A. Munk, “Inference for empirical wasserstein distances on finite spaces,” Journal of the Royal Statistical Society: Series B (Statistical Methodology) , vol. 80, no. 1, pp. 219–238, 2018
2018
Cited alongside, same era.
J. Weed and Q. Berthet, “Estimation of smooth densities in wasserstein distance,” in Conference on Learning Theory . PMLR, 2019, pp. 3118–3119
2019
Cited alongside, same era.
Y. Zemel and V. M. Panaretos, “Fréchet means and procrustes analysis in wasserstein space,” Bernoulli , vol. 25, no. 2, pp. 932–976, 2019
2019
Cited alongside, same era.
E. Del Barrio, P. Gordaliza, H. Lescornel, and J.-M. Loubes, “Central limit theorem and bootstrap procedure for wasserstein’s variations with an application to structural relationships between distributions,” Journal of Multivariate Analysis , vol. 169, pp. 341–362, 2019
2019
Cited alongside, same era.
P. Gordaliza, E. Del Barrio, G. Fabrice, and J.-M. Loubes, “Obtaining fairness using optimal transport theory,” in International Conference on Machine Learning . PMLR, 2019, pp. 2357–2365
2019
Cited alongside, same era.
K. Nadjahi, A. Durmus, L. Chizat, S. Kolouri, S. Shahrampour, and U. Simsekli, “Statistical and topological properties of sliced probability divergences,” Advances in Neural Information Processing Systems , vol. 33, pp. 20 802–20 812, 2020
2020
Later among the works it cites.
P. Berthet, J. Dedecker, and F. Merlevède, “Central limit theorem and almost sure results for bivariate empirical w 1 distances,” 2020
2020
Later among the works it cites.
M. Klatt, C. Tameling, and A. Munk, “Empirical regularized optimal transport: Statistical theory and applications,” SIAM Journal on Mathematics of Data Science , vol. 2, no. 2, pp. 419–443, 2020
2020
Later among the works it cites.
J. Lei, “Convergence and concentration of empirical measures under wasserstein distance in unbounded functional spaces,” Bernoulli , vol. 26, no. 1, pp. 767–798, 2020
2020
Later among the works it cites.
J. Cárcamo, A. Cuevas, and L.-A. Rodríguez, “Directional differentiability for supremum-type functionals: statistical applications,” Bernoulli , vol. 26, no. 3, pp. 2143–2175, 2020
2020
Later among the works it cites.
Z. Goldfeld and K. Kato, “Limit distributions for smooth total variation and χ \chi 2-divergence in high dimensions,” in 2020 IEEE International Symposium on Information Theory (ISIT) . IEEE, 2020, pp. 2640–2645
2020
Later among the works it cites.
2021
Later among the works it cites.
S. Nietert, Z. Goldfeld, and K. Kato, “Smooth p p -wasserstein distance: Structure, empirical approximation, and statistical applications,” in International Conference on Machine Learning . PMLR, 2021, pp. 8172–8183
2021
Later among the works it cites.
2021
Later among the works it cites.
K. Nadjahi, A. Durmus, P. E. Jacob, R. Badeau, and U. Simsekli, “Fast approximation of the sliced-wasserstein distance using concentration of random projections,” Advances in Neural Information Processing Systems , vol. 34, 2021
2021
Later among the works it cites.
T. Lin, Z. Zheng, E. Chen, M. Cuturi, and M. I. Jordan, “On projection robust optimal transport: Sample complexity and model misspecification,” in International Conference on Artificial Intelligence and Statistics . PMLR, 2021, pp. 262–270
2021
Later among the works it cites.
E. Giné and R. Nickl, Mathematical foundations of infinite-dimensional statistical models . Cambridge university press, 2021
2021
Later among the works it cites.
2022
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