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Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way.
On the transfer of masses (in russian)
L. Kantorovich · 1942
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A relationship between arbitrary positive matrices and doubly stochastic matrices
R. Sinkhorn · 1964
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On the scaling of multidimensional matrices
J. Franklin and J. Lorenz · 1989
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Acceleration of stochastic approximation by averaging
B. T Polyak and A. B Juditsky · 1992
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Asymptotic analysis of the exponential penalty trajectory in linear programming
R. Cominetti and J. San Martin · 1994
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Minkowski-type theorems and least-squares clustering
F. Aurenhammer, F. Hoffmann, and B. Aronov · 1998
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The earth mover’s distance as a metric for image retrieval
Y. Rubner, C. Tomasi, and L. J. Guibas · 2000
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Topics in Optimal Transportation
C. Villani · 2003
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On minimum kantorovich distance estimators
F. Bassetti, A. Bodini, and E. Regazzini · 2006
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Incremental approximate matrix factorization for speeding up support vector machines
G. Wu, E. Chang, Y. K. Chen, and C. Hughes · 2006
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Random features for large-scale kernel machines
A. Rahimi and B. Recht · 2007
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Support vector machines
I. Steinwart and A. Christmann · 2008
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Assignment Problems
R. Burkard, M. Dell’Amico, and S. Martello · 2009
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A multiscale approach to optimal transport
Q. Mérigot · 2011
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Sinkhorn distances: Lightspeed computation of optimal transport
Non-parametric stochastic approximation with large step sizes
A. Dieuleveut and F. Bach · 2014
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Glove: Global vectors for word representation
J. Pennington, R. Socher, and C.D. Manning · 2014
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Convergence of entropic schemes for optimal transport and gradient flows
G. Carlier, V. Duval, G. Peyré, and B. Schmitzer · 2015
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Learning with a Wasserstein loss
C. Frogner, C. Zhang, H. Mobahi, M. Araya, and T. Poggio · 2015
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From word embeddings to document distances
M. J. Kusner, Y. Sun, N. I. Kolkin, and K. Q. Weinberger · 2015
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Wasserstein training of Boltzmann machines
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M. Cuturi · 2013
Cited alongside, same era.
Minimizing finite sums with the stochastic average gradient
M. Schmidt, N. Le Roux, and F. Bach · 2013
Cited alongside, same era.
G. Montavon, K.-R. Muller, and M. Cuturi · 2015
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Optimal transport for applied mathematicians
F. Santambrogio · 2015
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Convolutional Wasserstein distances: Efficient optimal transportation on geometric domains
J. Solomon, F. de Goes, G. Peyré, M. Cuturi, A. Butscher, A. Nguyen, T. Du, and L. Guibas · 2015
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