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Distribution comparison plays a central role in many machine learning tasks like data classification and generative modeling.
Convergence with Hilbert’s space-filling curve
Arthur R Butz · 1969
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Alternative algorithm for Hilbert’s space-filling curve
Arthur R Butz · 1971
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A comparative analysis of some two-dimensional orderings
David J Abel and David M Mark · 1990
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Hilbert R-tree: An improved R-tree using fractals
Ibrahim Kamel and Christos Faloutsos · 1993
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A homogenized model for vortex sheets
Yann Brenier · 1997
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The earth mover’s distance, multi-dimensional scaling, and color-based image retrieval
Yossi Rubner, Leonidas J Guibas, and Carlo Tomasi · 1997
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Gradient-based learning applied to document recognition
Yann LeCun, Léon Bottou, Yoshua Bengio, and Patrick Haffner · 1998
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Analysis of the clustering properties of the Hilbert space-filling curve
Bongki Moon, Hosagrahar V Jagadish, Christos Faloutsos, and Joel H. Saltz · 2001
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Study on a fast ordering of high dimensional data to spatial index
A Tanaka · 2001
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The Monge–Kantorovitch mass transfer and its computational fluid mechanics formulation
J-D Benamou, Yann Brenier, and Kevin Guittet · 2002
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Programming the Hilbert curve
John Skilling · 2004
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Parallel space-filling curve generation through sorting
Justin Luitjens, Martin Berzins, and Tom Henderson · 2007
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Compact Hilbert indices: Space-filling curves for domains with unequal side lengths
Chris H Hamilton and Andrew Rau-Chaplin · 2008
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Optimal transport: old and new
Cédric Villani · 2009
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Fast and robust earth mover’s distances
Ofir Pele and Michael Werman · 2009
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CGAL: The computational geometry algorithms library
Andreas Fabri and Sylvain Pion · 2009
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Gromov–Wasserstein distances and the metric approach to object matching
Facundo Mémoli · 2011
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Barycenters in the Wasserstein space
Martial Agueh and Guillaume Carlier · 2011
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A kernel two-sample test
Arthur Gretton, Karsten M Borgwardt, Malte J Rasch, Bernhard Schölkopf, and Alexander Smola · 2012
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Space-filling curves: an introduction with applications in scientific computing
Michael Bader · 2012
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Parallel multilevel methods: adaptive mesh refinement and loadbalancing
Gerhard Zumbusch · 2012
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Sinkhorn distances: Lightspeed computation of optimal transport
Marco Cuturi · 2013
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Distributed representations of words and phrases and their compositionality
Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S Corrado, and Jeff Dean · 2013
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Unidimensional and evolution methods for optimal transportation
Nicolas Bonnotte · 2013
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Generative adversarial nets
Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio · 2014
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Auto-encoding variational bayes
Diederik P Kingma and Max Welling · 2014
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Bregman alternating direction method of multipliers
Huahua Wang and Arindam Banerjee · 2014
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Adaptive color transfer with relaxed optimal transport
Julien Rabin, Sira Ferradans, and Nicolas Papadakis · 2014
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Generalized Wasserstein distance and its application to transport equations with source
Benedetto Piccoli and Francesco Rossi · 2014
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From word embeddings to document distances
Matt Kusner, Yu Sun, Nicholas Kolkin, and Kilian Weinberger · 2015
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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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Learning with a Wasserstein loss
Charlie Frogner, Chiyuan Zhang, Hossein Mobahi, Mauricio Araya, and Tomaso A Poggio · 2015
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3d shapenets: A deep representation for volumetric shapes
Zhirong Wu, Shuran Song, Aditya Khosla, Fisher Yu, Linguang Zhang, Xiaoou Tang, and Jianxiong Xiao · 2015
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Adam: A method for stochastic optimization
Diederik P Kingma and Jimmy Ba · 2015
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Multi-marginal optimal transport: theory and applications
Brendan Pass · 2015
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Supervised word mover’s distance
Gao Huang, Chuan Guo, Matt J Kusner, Yu Sun, Fei Sha, and Kilian Q Weinberger · 2016
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Stochastic optimization for large-scale optimal transport
Aude Genevay, Marco Cuturi, Gabriel Peyré, and Francis Bach · 2016
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Extensible grids: uniform sampling on a space filling curve
Zhijian He and Art B Owen · 2016
Cited alongside, same era.
Gromov-Wasserstein learning for graph matching and node embedding
Hongteng Xu, Dixin Luo, Hongyuan Zha, and Lawrence Carin Duke · 2019
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Scalable Gromov-Wasserstein learning for graph partitioning and matching
Hongteng Xu, Dixin Luo, and Lawrence Carin · 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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Hierarchical optimal transport for document representation
Mikhail Yurochkin, Sebastian Claici, Edward Chien, Farzaneh Mirzazadeh, and Justin M Solomon · 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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Statistical aspects of Wasserstein distances
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Fast Hilbert sort algorithm without using Hilbert indices
Yasunobu Imamura, Takeshi Shinohara, Kouichi Hirata, and Tetsuji Kuboyama · 2016
Cited alongside, same era.
Unsupervised representation learning with deep convolutional generative adversarial networks
Alec Radford, Luke Metz, and Soumith Chintala · 2016
Cited alongside, same era.
Gromov-Wasserstein averaging of kernel and distance matrices
Gabriel Peyré, Marco Cuturi, and Justin Solomon · 2016
Cited alongside, same era.
Wasserstein generative adversarial networks
Martin Arjovsky, Soumith Chintala, and Léon Bottou · 2017
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Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration
Jason Altschuler, Jonathan Niles-Weed, and Philippe Rigollet · 2017
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Pavel Dvurechensky, Alexander Gasnikov, Sergey Omelchenko, and Alexander Tiurin · 2017
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Victor M Panaretos and Yoav Zemel · 2019
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Computational optimal transport: With applications to data science
Gabriel Peyré and Marco Cuturi · 2019
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Approximate Bayesian computation with the Wasserstein distance
Espen Bernton, Pierre E Jacob, Mathieu Gerber, and Christian P Robert · 2019
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One-dimensional empirical measures, order statistics, and Kantorovich transport distances
Sergey Bobkov and Michel Ledoux · 2019
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Fast algorithms for computational optimal transport and Wasserstein barycenter
Wenshuo Guo, Nhat Ho, and Michael Jordan · 2020
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A fast proximal point method for computing exact Wasserstein distance
Yujia Xie, Xiangfeng Wang, Ruijia Wang, and Hongyuan Zha · 2020
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Distributional sliced-Wasserstein and applications to generative modeling
Khai Nguyen, Nhat Ho, Tung Pham, and Hung Bui · 2020
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Projection robust Wasserstein distance and Riemannian optimization
Tianyi Lin, Chenyou Fan, Nhat Ho, Marco Cuturi, and Michael Jordan · 2020
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Learning autoencoders with relational regularization
Hongteng Xu, Dixin Luo, Ricardo Henao, Svati Shah, and Lawrence Carin · 2020
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Sufficient dimension reduction for classification using principal optimal transport direction
Cheng Meng, Jun Yu, Jingyi Zhang, Ping Ma, and Wenxuan Zhong · 2020
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Learning with minibatch Wasserstein: asymptotic and gradient properties
Kilian Fatras, Younes Zine, Rémi Flamary, Remi Gribonval, and Nicolas Courty · 2020
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Robust optimal transport with applications in generative modeling and domain adaptation
Yogesh Balaji, Rama Chellappa, and Soheil Feizi · 2020
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On unbalanced optimal transport: An analysis of Sinkhorn algorithm
Khiem Pham, Khang Le, Nhat Ho, Tung Pham, and Hung Bui · 2020
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Overrelaxed Sinkhorn–Knopp algorithm for regularized optimal transport
Alexis Thibault, Lénaïc Chizat, Charles Dossal, and Nicolas Papadakis · 2021
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On projection robust optimal transport: Sample complexity and model misspecification
Tianyi Lin, Zeyu Zheng, Elynn Chen, Marco Cuturi, and Michael I Jordan · 2021
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Outlier-robust optimal transport
Debarghya Mukherjee, Aritra Guha, Justin M Solomon, Yuekai Sun, and Mikhail Yurochkin · 2021
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On robust optimal transport: Computational complexity and barycenter computation
Khang Le, Huy Nguyen, Quang M Nguyen, Tung Pham, Hung Bui, and Nhat Ho · 2021
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Multi-marginal optimal transport and probabilistic graphical models
Isabel Haasler, Rahul Singh, Qinsheng Zhang, Johan Karlsson, and Yongxin Chen · 2021
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Fast Sinkhorn I: An O ( N ) {O(N)} algorithm for the Wasserstein-1 metric
Qichen Liao, Jing Chen, Zihao Wang, Bo Bai, Shi Jin, and Hao Wu · 2022
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Representing graphs via Gromov-Wasserstein factorization
Hongteng Xu, Jiachang Liu, Dixin Luo, and Lawrence Carin · 2022
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Revisiting sliced Wasserstein on images: From vectorization to convolution
Khai Nguyen and Nhat Ho · 2022
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Amortized projection optimization for sliced Wasserstein generative models
Khai Nguyen and Nhat Ho · 2022
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Distributional convergence of the sliced Wasserstein process
Jiaqi Xi and Jonathan Niles-Weed · 2022
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Importance sparsification for Sinkhorn algorithm
Mengyu Li, Jun Yu, Tao Li, and Cheng Meng · 2023
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Efficient approximation of Gromov-Wasserstein distance using importance sparsification
Mengyu Li, Jun Yu, Hongteng Xu, and Cheng Meng · 2023
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Unbalanced optimal transport meets sliced-Wasserstein
Thibault Séjourné, Clément Bonet, Kilian Fatras, Kimia Nadjahi, and Nicolas Courty · 2023
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