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We revisit the question of characterizing the convergence rate of plug-in estimators of optimal transport costs.
1908
Earlier work this paper cites.
Vapnik, V. N
1968
Earlier work this paper cites.
[author] Dudley, Richard MansfieldR. M. (1969). The Speed of Mean Glivenko-Cantelli Convergence. The Annals of Mathematical Statistics 40 40–50
1969
Earlier work this paper cites.
[author] Bronshtein, E. M.E. M. (1976). ϵ \epsilon -Entropy of Convex Sets and Functions. Siberian Mathematical Journal 17 393–398
1976
Earlier work this paper cites.
[author] Gangbo, WilfridW. and McCann, Robert J.R. J. (1996). The Geometry of Optimal Transportation. Acta Mathematica 177 113–161
1996
Earlier work this paper cites.
[author] van der Vaart, Aad W.A. W. and Wellner, Jon A.J. A. (1996). Weak Convergence and Empirical Processes. Springer Series in Statistics. Springer-Verlag, New York
1996
Earlier work this paper cites.
[author] Munk, AxelA. and Czado, ClaudiaC. (1998). Nonparametric Validation of Similar Distributions and Assessment of Goodness of Fit. Journal of the Royal Statistical Society: Series B 60 223–241
1998
Earlier work this paper cites.
[author] Rubner, YossiY., Tomasi, CarloC. and Guibas, Leonidas J.L. J. (2000). The Earth Mover’s Distance as a Metric for Image Retrieval. International Journal of Computer Vision 40 99–121
2000
Earlier work this paper cites.
[author] van de Geer, SaraS. (2000). Empirical Processes in M-estimation. Cambridge UP
2000
Earlier work this paper cites.
[author] Villani, CédricC. (2003). Topics in Optimal Transportation. American Mathematical Soc
2003
Earlier work this paper cites.
[author] Hiriart-Urruty, Jean-BaptisteJ.-B. and Lemaréchal, ClaudeC. (2004). Fundamentals of Convex Analysis. Springer Science & Business Media
2004
Earlier work this paper cites.
[author] von Luxburg, UlrikeU. and Bousquet, OlivierO. (2004). Distance-Based Classification with Lipschitz Functions. Journal of Machine Learning Research 5 669–695
2004
Earlier work this paper cites.
[author] Freitag, GudrunG. and Munk, AxelA. (2005). On Hadamard Differentiability in K K -Sample Semiparametric Models—with Applications to the Assessment of Structural Relationships. Journal of Multivariate Analysis 94 123–158
2005
Earlier work this paper cites.
[author] Ma, Xi-NanX.-N., Trudinger, Neil S.N. S. and Wang, Xu-JiaX.-J. (2005). Regularity of Potential Functions of the Optimal Transportation Problem. Archive for Rational Mechanics and Analysis 177 151–183
2005
Earlier work this paper cites.
[author] Carlier, G.G., Jimenez, C.C. and Santambrogio, F.F. (2008). Optimal transportation with traffic congestion and Wardrop equilibria. SIAM J. Control Optim. 47 1330–1350
2008
Earlier work this paper cites.
[author] Villani, CédricC. (2008). Optimal Transport: Old and New 338. Springer Science & Business Media
2008
Earlier work this paper cites.
[author] Brasco, LorenzoL., Carlier, GuillaumeG. and Santambrogio, FilippoF. (2010). Congested traffic dynamics, weak flows and very degenerate elliptic equations. J. Math. Pures Appl. (9) 93 163–182. 10.1016/j.matpur.2009.06.003
2009
Cited alongside, same era.
Guntuboyina, A
2012
Cited alongside, same era.
[author] Boucheron, StéphaneS., Lugosi, GáborG. and Massart, PascalP. (2013). Concentration Inequalities: A Nonasymptotic Theory of Independence. Oxford University Press
2013
Cited alongside, same era.
Boissard, E
2014
Cited alongside, same era.
[author] Dudley, Richard M.R. M. (2014). Uniform Central Limit Theorems 142. Cambridge University Press
2014
Cited alongside, same era.
[author] Peyré, GabrielG. and Cuturi, MarcoM. (2019). Computational Optimal Transport. Foundations and Trends® in Machine Learning 11 355–607
2019
Later among the works it cites.
2019
Later among the works it cites.
[author] Tameling, CarlaC., Sommerfeld, MaxM. and Munk, AxelA. (2019). Empirical Optimal Transport on Countable Metric Spaces: Distributional Limits and Statistical Applications. The Annals of Applied Probability 29 2744–2781
2019
Later among the works it cites.
[author] Wainwright, Martin J.M. J. (2019). High-Dimensional Statistics: A Non-Asymptotic Viewpoint 48. Cambridge University Press
2019
Later among the works it cites.
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[author] Li, Qi-RuiQ.-R., Santambrogio, FilippoF. and Wang, Xu-JiaX.-J. (2014). Regularity in Monge’s Mass Transfer Problem. Journal de Mathématiques Pures et Appliquées 102 1015–1040
2014
Cited alongside, same era.
[author] Fournier, NicolasN. and Guillin, ArnaudA. (2015). On the Rate of Convergence in Wasserstein Distance of the Empirical Measure. Probability Theory and Related Fields 162 707–738
2015
Cited alongside, same era.
[author] Santambrogio, FilippoF. (2015). Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling 87. Birkhäuser
2015
Cited alongside, same era.
[author] Orlova, Darya Y.D. Y., Zimmerman, NoahN., Meehan, StephenS., Meehan, ConnorC., Waters, JeffreyJ., Ghosn, Eliver E. B.E. E. B., Filatenkov, AlexanderA., Kolyagin, Gleb A.G. A., Gernez, YaelY., Tsuda, ShanelS., Moore, WayneW., Moss, Richard B.R. B., Herzenberg, Leonore A.L. A. and Walther, GuentherG. (2016). Earth Mover’s Distance (EMD): A True Metric for Comparing Biomarker Expression Levels in Cell Populations. PLoS ONE 11
2016
Cited alongside, same era.
[author] Polyanskiy, Y.Y. and Wu, Y.Y. (2016). Wasserstein Continuity of Entropy and Outer Bounds for Interference Channels. IEEE Transactions on Information Theory 62 3992–4002
2016
Cited alongside, same era.
Arjovsky, M
2017
Cited alongside, same era.
Singh, S
2018
Cited alongside, same era.
2019
Later among the works it cites.
[author] Chizat, LenaicL., Roussillon, PierreP., Léger, FlavienF., Vialard, François-XavierF.-X. and Peyré, GabrielG. (2020). Faster Wasserstein Distance Estimation with the Sinkhorn Divergence. Advances in Neural Information Processing Systems 33 2257–2269
2020
Later among the works it cites.
[author] Lei, JingJ. (2020). Convergence and Concentration of Empirical Measures under Wasserstein Distance in Unbounded Functional Spaces. Bernoulli 26 767–798
2020
Later among the works it cites.
[author] Vladimirova, MariiaM., Girard, StephaneS., Nguyen, HienH. and Arbel, JulyanJ. (2020). Sub-Weibull Distributions: Generalizing Sub-Gaussian and Sub-Exponential Properties to Heavier-Tailed Distributions. Stat 9
2020
Later among the works it cites.
[author] Colombo, MariaM. and Fathi, MaxM. (2021). Bounds on Optimal Transport Maps onto Log-Concave Measures. Journal of Differential Equations 271 1007–1022
2021
Closest in time.
[author] Hütter, Jan-ChristianJ.-C. and Rigollet, PhilippeP. (2021). Minimax Rates of Estimation for Smooth Optimal Transport Maps. The Annals of Statistics 49 1166–1194
2021
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[author] Liang, TengyuanT. (2021). How Well Generative Adversarial Networks Learn Distributions. Journal of Machine Learning Research 22 1–41
2021
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[author] Kuchibhotla, Arun KumarA. K. and Chakrabortty, AbhishekA. (2022). Moving beyond sub-Gaussianity in high-dimensional statistics: Applications in covariance estimation and linear regression. Information and Inference: A Journal of the IMA 11 1389–1456
2022
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[author] Niles-Weed, JonathanJ. and Rigollet, PhilippeP. (2022). Estimation of Wasserstein distances in the spiked transport model. Bernoulli 28 2663–2688
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