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The Sliced-Wasserstein distance (SW) is being increasingly used in machine learning applications as an alternative to the Wasserstein distance and offers significant computational and statistical benefits.
Computational Optimal Transport: With Applications to Data Science
Gabriel Peyré and Marco Cuturi · 1935
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The speed of mean Glivenko-Cantelli convergence
Richard M. Dudley · 1969
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Typical distributions of linear functionals in finite dimensional spaces of high dimension
Vladimir Nikolaevich Sudakov · 1978
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The Fréchet distance between multivariate normal distributions
D.C Dowson and B.V Landau · 1982
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Gamma function derivation of n-sphere volumes
Greg Huber · 1982
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Asymptotics of Graphical Projection Pursuit
Persi Diaconis and David Freedman · 1984
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On almost Linearity of Low Dimensional Projections from High Dimensional Data
Peter Hall and Ker-Chau Li · 1993
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Sudakov’s typical marginals, random linear functionals and a conditional central limit theorem
Heinrich von Weizsäcker · 1997
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Mass Transportation Problems: Volume I: Theory , volume 1
Svetlozar T Rachev and Ludger Rüschendorf · 1998
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A new weak dependence condition and applications to moment inequalities
Paul Doukhan and Sana Louhichi · 1999
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The Central Limit Problem for Convex Bodies
Milla Anttila, Keith Ball, and Irini Perissinaki · 2003
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On concentration of distributions of random weighted sums
Sergey G. Bobkov · 2003
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Probability and moment inequalities for sums of weakly dependent random variables, with applications
Paul Doukhan and Michael H. Neumann · 2006
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A central limit theorem for convex sets
Bo’az Klartag · 2007
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The notion of
Paul Doukhan and Michael H. Neumann · 2008
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Approximation of Projections of Random Vectors
Elizabeth Meckes · 2010
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MNIST handwritten digit database
Yann LeCun and Corinna Cortes · 2010
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Wasserstein Barycenter and Its Application to Texture Mixing
Julien Rabin, Gabriel Peyré, Julie Delon, and Marc Bernot · 2012
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Unidimensional and Evolution Methods for Optimal Transportation
Nicolas Bonnotte · 2013
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On low-dimensional projections of high-dimensional distributions
Lutz Dümbgen and Perla Del Conte-Zerial · 2013
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On the conditional distributions of low-dimensional projections from high-dimensional data
Hannes Leeb · 2013
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Sliced Wasserstein distance for Learning Gaussian Mixture Models
Soheil Kolouri, Gustavo K Rohde, and Heiko Hoffmann · 2018
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Generative Modeling using the Sliced Wasserstein Distance
Ishan Deshpande, Ziyu Zhang, and Alexander Schwing · 2018
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Sliced Wasserstein Generative Models
Jiqing Wu, Zhiwu Huang, Dinesh Acharya, Wen Li, Janine Thoma, Danda Pani Paudel, and Luc Van Gool · 2019
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Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusions
Antoine Liutkus, Umut Simsekli, Szymon Majewski, Alain Durmus, and Fabian-Robert Stöter · 2019
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Asymptotic Guarantees for Learning Generative Models with the Sliced-Wasserstein distance
Kimia Nadjahi, Alain Durmus, Umut Simsekli, and Roland Badeau · 2019
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Strong equivalence between metrics of Wasserstein type, 2019
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Sliced and Radon Wasserstein barycenters of measures
Nicolas Bonneel, Julien Rabin, Gabriel Peyré, and Hanspeter Pfister · 2015
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On the rate of convergence in Wasserstein distance of the empirical measure
Nicolas Fournier and Arnaud Guillin · 2015
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Deep Learning Face Attributes in the Wild
Ziwei Liu, Ping Luo, Xiaogang Wang, and Xiaoou Tang · 2015
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Adam: A Method for Stochastic Optimization
Diederik P. Kingma and Jimmy Ba · 2015
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Sliced-Wasserstein Kernels for Probability distributions
Soheil Kolouri, Yang Zou, and Gustavo K Rohde · 2016
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Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks
Alec Radford, Luke Metz, and Soumith Chintala · 2016
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Erhan Bayraktar and Gaoyue Guo · 2019
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Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance
Jonathan Weed and Francis Bach · 2019
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Large-scale optimal transport map estimation using projection pursuit
Cheng Meng, Yuan Ke, Jingyi Zhang, Mengrui Zhang, Wenxuan Zhong, and Ping Ma · 2019
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Max-Sliced Wasserstein distance and its use for GANs
Ishan Deshpande, Yuan-Ting Hu, Ruoyu Sun, Ayis Pyrros, Nasir Siddiqui, Sanmi Koyejo, Zhizhen Zhao, David Forsyth, and Alexander G Schwing · 2019
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Approximate Bayesian Computation with the Sliced-Wasserstein distance
Kimia Nadjahi, Valentin Bortoli, Alain Durmus, Roland Badeau, and Umut Simsekli · 2020
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Sliced Multi-Marginal Optimal Transport, 2021
Samuel Cohen, K S Sesh Kumar, and Marc Peter Deisenroth · 2021
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Sliced Iterative Normalizing Flows, 2021
Biwei Dai and Uros Seljak · 2021
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Distributional Sliced-Wasserstein and Applications to Generative Modeling
Khai Nguyen, Nhat Ho, Tung Pham, and Hung Bui · 2021
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The Gaussian equivalence of generative models for learning with shallow neural networks
Sebastian Goldt, Bruno Loureiro, Galen Reeves, Florent Krzakala, Marc Mézard, and Lenka Zdeborová · 2021
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