Fetching the paper…
Reading the bibliography…
The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base divergence' between one-dimensional random projections of the two measures.
On the composition of elementary errors
Harald Cramér · 1928
Earlier work this paper cites.
On the scaling of multidimensional matrices
Joel Franklin and Jens Lorenz · 1989
Earlier work this paper cites.
Integral probability metrics and their generating classes of functions
Alfred Müller · 1997
Earlier work this paper cites.
Foundations of modern probability
O. Kallenberg · 1997
Earlier work this paper cites.
Convergence of probability measures
Patrick Billingsley · 1999
Earlier work this paper cites.
Real analysis
G. B. Folland · 1999
Earlier work this paper cites.
On choosing and bounding probability metrics
Alison L. Gibbs and Francis Edward Su · 2002
Earlier work this paper cites.
The empirical distribution function for dependent variables: asymptotic and nonasymptotic results in
Jérôme Dedecker and Florence Merlevède · 2007
Earlier work this paper cites.
Measure Theory
V.I. Bogachev · 2007
Earlier work this paper cites.
Optimal transport: old and new
Cédric Villani · 2008
Earlier work this paper cites.
Gradient Flows: In Metric Spaces and in the Space of Probability Measures
L. Ambrosio, N. Gigli, and G. Savare · 2008
Earlier work this paper cites.
On integral probability metrics,
Bharath K. Sriperumbudur, Kenji Fukumizu, Arthur Gretton, Bernhard Schölkopf, and Gert R. G. Lanckriet · 2009
Earlier work this paper cites.
Learning multiple layers of features from tiny images
Alex Krizhevsky · 2009
Earlier work this paper cites.
MNIST handwritten digit database
Yann LeCun and Corinna Cortes · 2010
Earlier work this paper cites.
A kernel two-sample test
Arthur Gretton, Karsten M. Borgwardt, Malte J. Rasch, Bernhard Schölkopf, and Alexander Smola · 2012
Earlier work this paper cites.
Unidimensional and Evolution Methods for Optimal Transportation
Nicolas Bonnotte · 2013
Earlier work this paper cites.
Sinkhorn distances: Lightspeed computation of optimal transport
Marco Cuturi · 2013
Cited alongside, same era.
Generative adversarial nets
Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio · 2014
Cited alongside, same era.
Auto-encoding variational bayes
Diederik P Kingma and Max Welling · 2014
Cited alongside, same era.
Sliced and Radon Wasserstein barycenters of measures
Nicolas Bonneel, Julien Rabin, Gabriel Peyré, and Hanspeter Pfister · 2015
Cited alongside, same era.
On the rate of convergence in Wasserstein distance of the empirical measure
Nicolas Fournier and Arnaud Guillin · 2015
Cited alongside, same era.
Directional statistics in machine learning: a brief review, 2016
Suvrit Sra · 2016
Cited alongside, same era.
Maximum mean discrepancy gradient flow
Michael Arbel, Anna Korba, Adil Salim, and Arthur Gretton · 2019
Later among the works it cites.
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 Schwing · 2019
Later among the works it cites.
Subspace robust Wasserstein distances
François-Pierre Paty and Marco Cuturi · 2019
Later among the works it cites.
Sliced Wasserstein auto-encoders
Soheil Kolouri, Phillip E. Pope, Charles E. Martin, and Gustavo K. Rohde · 2019
Later among the works it cites.
Generalized sliced Wasserstein distances
Soheil Kolouri, Kimia Nadjahi, Umut Simsekli, Roland Badeau, and Gustavo Rohde · 2019
Later among the works it cites.
Sliced Gromov-Wasserstein
Titouan Vayer, Rémi Flamary, Romain Tavenard, Laetitia Chapel, and Nicolas Courty · 2019
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Stochastic optimization for large-scale optimal transport
Aude Genevay, Marco Cuturi, Gabriel Peyré, and Francis Bach · 2016
Cited alongside, same era.
Wasserstein generative adversarial networks
Martin Arjovsky, Soumith Chintala, and Léon Bottou · 2017
Cited alongside, same era.
From optimal transport to generative modeling: the VEGAN cookbook
Olivier Bousquet, Sylvain Gelly, Ilya Tolstikhin, Carl-Johann Simon-Gabriel, and Bernhard Schoelkopf · 2017
Cited alongside, same era.
Improved training of Wasserstein GANs
Ishaan Gulrajani, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron C Courville · 2017
Cited alongside, same era.
Near-linear time approximation algorithms for optimal transport via sinkhorn iteration
Jason Altschuler, Jonathan Niles-Weed, and Philippe Rigollet · 2017
Cited alongside, same era.
The Cramer distance as a solution to biased Wasserstein gradients
Marc G Bellemare, Ivo Danihelka, Will Dabney, Shakir Mohamed, Balaji Lakshminarayanan, Stephan Hoyer, and Rémi Munos · 2017
Cited alongside, same era.
Strong equivalence between metrics of Wasserstein type, 2019
Erhan Bayraktar and Gaoyue Guo · 2019
Later among the works it cites.
Interpolating between optimal transport and MMD using Sinkhorn divergences
Jean Feydy, Thibault Séjourné, François-Xavier Vialard, Shun-ichi Amari, Alain Trouve, and Gabriel Peyré · 2019
Later among the works it cites.
Sample complexity of Sinkhorn divergences
Aude Genevay, Lénaïc Chizat, Francis Bach, Marco Cuturi, and Gabriel Peyré · 2019
Later among the works it cites.
Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem
Gonzalo Mena and Jonathan Niles-Weed · 2019
Later among the works it cites.
Sliced-Wasserstein flows: Nonparametric generative modeling via optimal transport and diffusions
Antoine Liutkus, Umut Şimşekli, Szymon Majewski, Alain Durmus, and Fabian-Robert Stoter · 2019
Later among the works it cites.
Sliced wasserstein generative models
Jiqing Wu, Zhiwu Huang, Wen Li, Janine Thoma, and Luc Van Gool · 2019
Later among the works it cites.
Minimax confidence intervals for the sliced Wasserstein distance, 2019
Tudor Manole, Sivaraman Balakrishnan, and Larry Wasserman · 2019
Later among the works it cites.
Computational optimal transport
Gabriel Peyré, Marco Cuturi, et al · 2019
Later among the works it cites.
High-dimensional statistics: A non-asymptotic viewpoint
Martin J Wainwright · 2019
Later among the works it cites.
Sliced Cramer synaptic consolidation for preserving deeply learned representations
Soheil Kolouri, Nicholas A. Ketz, Andrea Soltoggio, and Praveen K. Pilly · 2020
Closest in time.