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Optimal transport (OT) distances are increasingly used as loss functions for statistical inference, notably in the learning of generative models or supervised learning.
The minimum distance method
J. Wolfowitz · 1957
Earlier work this paper cites.
The speed of mean Glivenko-Cantelli convergence
R. M. Dudley · 1969
Earlier work this paper cites.
Measurable selections of extrema
L. D. Brown and R. Purves · 1973
Earlier work this paper cites.
The minimum distance method of testing
D. Pollard · 1980
Earlier work this paper cites.
Transportation cost for Gaussian and other product measures
M. Talagrand · 1996
Earlier work this paper cites.
Mass Transportation Problems: Volume I: Theory , volume 1
S. T. Rachev and L. Rüschendorf · 1998
Earlier work this paper cites.
Central limit theorems for the Wasserstein distance between the empirical and the true distributions
E. del Barrio, E. Giné, and C. Matrán · 1999
Earlier work this paper cites.
Concentration of measure and logarithmic sobolev inequalities
M. Ledoux · 1999
Earlier work this paper cites.
Infinite Dimensional Analysis: A Hitchhiker’s Guide
C. D. Aliprantis and K. C. Border · 2006
Earlier work this paper cites.
On minimum kantorovich distance estimators
F. Bassetti, A. Bodini, and E. Regazzini · 2006
Earlier work this paper cites.
Optimal Transport: Old and New , volume 338
C. Villani · 2008
Earlier work this paper cites.
Optimization Algorithms on Matrix Manifolds
P-A. Absil, R. Mahony, and R. Sepulchre · 2009
Earlier work this paper cites.
An empirical central limit theorem in L1 for stationary sequences
S. Dede · 2009
Earlier work this paper cites.
Variational Analysis , volume 317
R. T. Rockafellar and R. J-B. Wets · 2009
Earlier work this paper cites.
Statistical Inference: The Minimum Distance Approach
A. Basu, H. Shioya, and C. Park · 2011
Earlier work this paper cites.
Wasserstein barycenter and its application to texture mixing
J. Rabin, G. Peyré, J. Delon, and M. Bernot · 2011
Earlier work this paper cites.
Convergence of Probability Measures
P. Billingsley · 2013
Earlier work this paper cites.
Unidimensional and Evolution Methods for Optimal Transportation
N. Bonnotte · 2013
Earlier work this paper cites.
Sinkhorn distances: Lightspeed computation of optimal transport
Marco Cuturi · 2013
Earlier work this paper cites.
Multivariate elliptically contoured stable distributions: theory and estimation
J. P. Nolan · 2013
Earlier work this paper cites.
Fast computation of Wasserstein barycenters
M. Cuturi and A. Doucet · 2014
Earlier work this paper cites.
Sliced and radon Wasserstein barycenters of measures
N. Bonneel, J. Rabin, G. Peyré, and H. Pfister · 2015
Earlier work this paper cites.
On the rate of convergence in Wasserstein distance of the empirical measure
N. Fournier and A. Guillin · 2015
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ADAM: A method for stochastic optimization
D. P. Kingma and J. Ba · 2015
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Wasserstein barycentric coordinates: histogram regression using optimal transport
N. Bonneel, G. Peyré, and M. Cuturi · 2016
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Learning population-level diffusions with generative RNNs
T. Hashimoto, D. Gifford, and T. Jaakkola · 2016
Cited alongside, same era.
Sliced Wasserstein kernels for probability distributions
S. Kolouri, Y. Zou, and G. K. Rohde · 2016
Cited alongside, same era.
Wasserstein training of restricted Boltzmann machines
G. Montavon, K-R. Müller, and M. Cuturi · 2016
Cited alongside, same era.
Max-sliced Wasserstein distance and its use for GANs
I. Deshpande, Y-T. Hu, R. Sun, A. Pyrros, N. Siddiqui, S. Koyejo, Z. Zhao, D. Forsyth, and A. G. Schwing · 2019
Later among the works it cites.
Nonsmooth optimization over Stiefel manifold: Riemannian subgradient methods
X. Li, S. Chen, Z. Deng, Q. Qu, Z. Zhu, and A. M-C. So · 2019
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Quadratic optimization with orthogonality constraint: explicit łojasiewicz exponent and linear convergence of retraction-based line-search and stochastic variance-reduced gradient methods
H. Liu, A. M-C. So, and W. Wu · 2019
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Sliced-Wasserstein flows: Nonparametric generative modeling via optimal transport and diffusions
A. Liutkus, U. Simsekli, S. Majewski, A. Durmus, and F-R. Stöter · 2019
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Minimax confidence intervals for the sliced wasserstein distance
T. Manole, S. Balakrishnan, and Larry Wasserman · 2019
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Wasserstein generative adversarial networks
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Sliced Wasserstein kernel for persistence diagrams
M. Carriere, M. Cuturi, and S. Oudot · 2017
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Pot python optimal transport library, 2017
R. Flamary and N. Courty · 2017
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Improved training of Wasserstein GANs
I. Gulrajani, F. Ahmed, M. Arjovsky, V. Dumoulin, and A. C. Courville · 2017
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Multilevel clustering via Wasserstein means
N. Ho, X. Nguyen, M. Yurochkin, H. H. Bui, V. Huynh, and D. Phung · 2017
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On Wasserstein two-sample testing and related families of nonparametric tests
A. Ramdas, N. G. Trillos, and M. Cuturi · 2017
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Asymptotic guarantees for learning generative models with the sliced-Wasserstein distance
K. Nadjahi, A. Durmus, U. Simsekli, and R. Badeau · 2019
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Estimation of Wasserstein distances in the spiked transport model
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Statistical aspects of Wasserstein distances
V. M. Panaretos and Y. Zemel · 2019
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Subspace robust Wasserstein distances
F-P. Paty and M. Cuturi · 2019
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Computational optimal transport
G. Peyré and M. Cuturi · 2019
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High-dimensional Statistics: A Non-asymptotic Viewpoint , volume 48
M. J. Wainwright · 2019
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Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance
J. Weed and F. Bach · 2019
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Sliced Wasserstein generative models
J. Wu, Z. Huang, D. Acharya, W. Li, J. Thoma, D. P. Paudel, and L. V. Gool · 2019
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Multi-subject MEG/EEG source imaging with sparse multi-task regression
H. Janati, T. Bazeille, B. Thirion, M. Cuturi, and A. Gramfort · 2020
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Convergence and concentration of empirical measures under Wasserstein distance in unbounded functional spaces
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Projection robust Wasserstein distance and Riemannian optimization
T. Lin, C. Fan, N. Ho, M. Cuturi, and M. I. Jordan · 2020
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Statistical and topological properties of sliced probability divergences
K. Nadjahi, A. Durmus, L. Chizat, S. Kolouri, S. Shahrampour, and U. Şimşekli · 2020
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Statistical optimal transport posed as learning kernel embedding
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Distributional sliced-Wasserstein and applications to generative modeling
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Trajectorynet: A dynamic optimal transport network for modeling cellular dynamics
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Predicting cell lineages using autoencoders and optimal transport
K. D. Yang, K. Damodaran, S. Venkatachalapathy, A. C. Soylemezoglu, G. V. Shivashankar, and C. Uhler · 2020
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