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The Sinkhorn "distance", a variant of the Wasserstein distance with entropic regularization, is an increasingly popular tool in machine learning and statistical inference.
Diagonal equivalence to matrices with prescribed row and column sums
R. Sinkhorn · 1967
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On Stirling numbers of the second kind
B. C. Rennie and A. J. Dobson · 1969
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The use of entropy maximising models, in the theory of trip distribution, mode split and route split
A. G. Wilson · 1969
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A remark on Dobrushin’s uniqueness theorem
B. Simon · 1979
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On the scaling of multidimensional matrices
J. Franklin and J. Lorenz · 1989
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A multivariate Faa di Bruno formula with applications
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A deterministic strongly polynomial algorithm for matrix scaling and approximate permanents
N. Linial, A. Samorodnitsky, and A. Wigderson · 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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Sparse greedy matrix approximation for machine learning
A. J. Smola and B. Schölkopf · 2000
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Efficient SVM training using low-rank kernel representations
S. Fine and K. Scheinberg · 2001
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The elements of statistical learning , volume 1
J. Friedman, T. Hastie, and R. Tibshirani · 2001
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Fundamentals of convex analysis
J.-B. Hiriart-Urruty and C. Lemaréchal · 2001
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Using the Nyström method to speed up kernel machines
C. Williams and M. Seeger · 2001
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Sobolev spaces , volume 140
R. A. Adams and J. J. Fournier · 2003
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Kernel Methods for Pattern Analysis
J. Shawe-Taylor and N. Cristianini · 2004
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Scattered data approximation , volume 17
H. Wendland · 2004
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Learning bounds for kernel regression using effective data dimensionality
T. Zhang · 2005
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On the complexity of general matrix scaling and entropy minimization via the RAS algorithm
B. Kalantari, I. Lari, F. Ricca, and B. Simeone · 2008
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Optimal transport: old and new , volume 338
C. Villani · 2008
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CUR matrix decompositions for improved data analysis
M. W. Mahoney and P. Drineas · 2009
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Kernel approximation on manifolds I: bounding the Lebesgue constant
T. Hangelbroek, F. J. Narcowich, and J. D. Ward · 2010
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The interplay between entropy and variational distance
S.-W. Ho and R. W. Yeung · 2010
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NIST handbook of mathematical functions
F. W. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark · 2010
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Sampling inequalities for infinitely smooth functions, with applications to interpolation and machine learning
C. Rieger and B. Zwicknagl · 2010
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Explicit approximations of the gaussian kernel
A. Cotter, J. Keshet, and N. Srebro · 2011
M. Arjovsky, S. Chintala, and L. Bottou · 2017
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From optimal transport to generative modeling: the VEGAN cookbook
O. Bousquet, S. Gelly, I. Tolstikhin, C.-J. Simon-Gabriel, and B. Schoelkopf · 2017
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Matrix scaling and balancing via box constrained Newton’s method and interior point methods
M. B. Cohen, A. Madry, D. Tsipras, and A. Vladu · 2017
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Optimal transport for domain adaptation
N. Courty, R. Flamary, D. Tuia, and A. Rakotomamonjy · 2017
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Optimal mass transport: Signal processing and machine-learning applications
S. Kolouri, S. R. Park, M. Thorpe, D. Slepcev, and G. K. Rohde · 2017
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The spectral norm error of the naive Nyström extension
A. Gittens · 2011
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Scattered data interpolation on embedded submanifolds with restricted positive definite kernels: Sobolev error estimates
E. Fuselier and G. B. Wright · 2012
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Sharp analysis of low-rank kernel matrix approximations
F. Bach · 2013
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Sinkhorn distances: Lightspeed computation of optimal transport
M. Cuturi · 2013
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A novel earth mover’s distance methodology for image matching with Gaussian mixture models
P. Li, Q. Wang, and L. Zhang · 2013
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Domain adaptation with regularized optimal transport
N. Courty, R. Flamary, and D. Tuia · 2014
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Recursive sampling for the Nystrom method
C. Musco and C. Musco · 2017
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Computational optimal transport
G. Peyré and M. Cuturi · 2017
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Approximating the quadratic transportation metric in near-linear time
J. Altschuler, F. Bach, A. Rudi, and J. Weed · 2018
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Approximation beats concentration? An approximation view on inference with smooth radial kernels
M. Belkin · 2018
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Towards optimal running times for optimal transport
J. Blanchet, A. Jambulapati, C. Kent, and A. Sidford · 2018
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P. Dvurechensky, A. Gasnikov, and A. Kroshnin · 2018
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Statistical optimal transport via factored couplings
A. Forrow, J.-C. Hütter, M. Nitzan, P. Rigollet, G. Schiebinger, and J. Weed · 2018
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Learning generative models with Sinkhorn divergences
A. Genevay, G. Peyré, and M. Cuturi · 2018
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Entropic optimal transport is maximum-likelihood deconvolution
P. Rigollet and J. Weed · 2018
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On fast leverage score sampling and optimal learning
A. Rudi, D. Calandriello, L. Carratino, and L. Rosasco · 2018
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Fast Entropic Regularized Optimal Transport Using Semidiscrete Cost Approximation
E. Tenetov, G. Wolansky, and R. Kimmel · 2018
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Approximating optimal transport with linear programs
K. Quanrud · 2019
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Reconstruction of developmental landscapes by optimal-transport analysis of single-cell gene expression sheds light on cellular reprogramming
G. Schiebinger, J. Shu, M. Tabaka, B. Cleary, V. Subramanian, A. Solomon, S. Liu, S. Lin, P. Berube, L. Lee, et al · 2019
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Stabilized sparse scaling algorithms for entropy regularized transport problems
B. Schmitzer · 2019
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