Fetching the paper…
Reading the bibliography…
This work studies an explicit embedding of the set of probability measures into a Hilbert space, defined using optimal transport maps from a reference probability density.
Polar factorization and monotone rearrangement of vector-valued functions
Yann Brenier · 1991
Earlier work this paper cites.
Generalised lagrangian solutions for atmospheric and oceanic flows
MJP Cullen, J Norbury, and RJ Purser · 1991
Earlier work this paper cites.
The geometry of optimal transportation
Wilfrid Gangbo and Robert J McCann · 1996
Earlier work this paper cites.
Minkowski-type theorems and least-squares clustering
Franz Aurenhammer, Friedrich Hoffmann, and Boris Aronov · 1998
Earlier work this paper cites.
Problem of reflector design with given far-field scattering data
Luis A Caffarelli, Sergey A Kochengin, and Vladimir I Oliker · 1999
Earlier work this paper cites.
Finite volume methods
Robert Eymard, Thierry Gallouët, and Raphaèle Herbin · 2000
Earlier work this paper cites.
The geometry of dissipative evolution equations: the porous medium equation
Felix Otto · 2001
Earlier work this paper cites.
Topics in optimal transportation
Cédric Villani · 2003
Earlier work this paper cites.
Principal geodesic analysis for the study of nonlinear statistics of shape
Thomas P. Fletcher, Conglin Lu, Stephen M Pizer, and Sarang Joshi · 2004
Earlier work this paper cites.
k-means++: The advantages of careful seeding
David Arthur and Sergei Vassilvitskii · 2007
Earlier work this paper cites.
Gradient flows: in metric spaces and in the space of probability measures
Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré · 2008
Earlier work this paper cites.
MNIST handwritten digit database
Yann LeCun and Corinna Cortes · 2010
Earlier work this paper cites.
On hölder continuity-in-time of the optimal transport map towards measures along a curve
Nicola Gigli · 2011
Earlier work this paper cites.
A multiscale approach to optimal transport
Quentin Mérigot · 2011
Cited alongside, same era.
Learning probability measures with respect to optimal transport metrics
Guillermo Canas and Lorenzo Rosasco · 2012
Cited alongside, same era.
Blue noise through optimal transport
Fernando De Goes, Katherine Breeden, Victor Ostromoukhov, and Mathieu Desbrun · 2012
Cited alongside, same era.
Sinkhorn distances: Lightspeed computation of optimal transport
Marco Cuturi · 2013
Cited alongside, same era.
A linear optimal transportation framework for quantifying and visualizing variations in sets of images
Wei Wang, Dejan Slepčev, Saurav Basu, John A. Ozolek, and Gustavo K. Rohde · 2013
Cited alongside, same era.
A numerical algorithm for l2 semi-discrete optimal transport in 3d
Bruno Lévy · 2015
Cited alongside, same era.
Monge–Kantorovich depth, quantiles, ranks and signs
Victor Chernozhukov, Alfred Galichon, Marc Hallin, and Marc Henry · 2017
Later among the works it cites.
Unsupervised hyperalignment for multilingual word embeddings
Jean Alaux, Edouard Grave, Marco Cuturi, and Armand Joulin · 2018
Later among the works it cites.
Convergence rates for discretized monge-ampère equations and quantitative stability of optimal transport
Robert J. Berman · 2018
Later among the works it cites.
Wasserstein Discriminant Analysis
Rémi Flamary, Marco Cuturi, Nicolas Courty, and Alain Rakotomamonjy · 2018
Later among the works it cites.
Learning generative models with sinkhorn divergences
Aude Genevay, Gabriel Peyre, and Marco Cuturi · 2018
Later among the works it cites.
Central limit theorems for entropy-regularized optimal transport on finite spaces and statistical applications
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
On wasserstein two sample testing and related families of nonparametric tests
Aaditya Ramdas, Nicolas Garcia, and Marco Cuturi · 2015
Cited alongside, same era.
Optimal transport for applied mathematicians
Filippo Santambrogio · 2015
Cited alongside, same era.
Discretization of functionals involving the monge–ampère operator
Jean-David Benamou, Guillaume Carlier, Quentin Mérigot, and Edouard Oudet · 2016
Cited alongside, same era.
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.
Log-pca versus geodesic pca of histograms in the wasserstein space
Elsa Cazelles, Vivien Seguy, Jérémie Bigot, Marco Cuturi, and Nicolas Papadakis · 2017
Cited alongside, same era.
Jérémie Bigot, Elsa Cazelles, and Nicolas Papadakis · 2019
Closest in time.
Obtaining fairness using optimal transport theory
Paula Gordaliza, Eustasio Del Barrio, Gamboa Fabrice, and Jean-Michel Loubes · 2019
Closest in time.
Minimax rates of estimation for smooth optimal transport maps
Jan-Christian Hütter and Philippe Rigollet · 2019
Closest in time.
Convergence of a newton algorithm for semi-discrete optimal transport
Jun Kitagawa, Quentin Mérigot, and Boris Thibert · 2019
Closest in time.
Pointwise rates of convergence for the oliker–prussner method for the monge–ampère equation
Ricardo H Nochetto and Wujun Zhang · 2019
Closest in time.
Computational optimal transport
Gabriel Peyré and Marco Cuturi · 2019
Closest in time.
Estimation of smooth densities in wasserstein distance, 2019
Jonathan Weed and Quentin Berthet · 2019
Closest in time.