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The conventional sliced Wasserstein is defined between two probability measures that have realizations as vectors.
Neocognitron: A self-organizing neural network model for a mechanism of visual pattern recognition
K. Fukushima and S. Miyake · 1982
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Gradient-based learning applied to document recognition
Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner · 1998
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1.1 über die bestimmung von funktionen durch ihre integralwerte längs gewisser mannigfaltigkeiten
J. Radon · 2005
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Optimal transport: Old and New
C. Villani · 2008
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Learning multiple layers of features from tiny images
A. Krizhevsky, G. Hinton, et al · 2009
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Fast and robust earth mover’s distances
O. Pele and M. Werman · 2009
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An analysis of single-layer networks in unsupervised feature learning
A. Coates, A. Ng, and H. Lee · 2011
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Imagenet classification with deep convolutional neural networks
A. Krizhevsky, I. Sutskever, and G. E. Hinton · 2012
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Sinkhorn distances: Lightspeed computation of optimal transport
M. Cuturi · 2013
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Adam: A method for stochastic optimization
D. P. Kingma and J. Ba · 2014
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Sliced and Radon Wasserstein barycenters of measures
N. Bonneel, J. Rabin, G. Peyré, and H. Pfister · 2015
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On the rate of convergence in Wasserstein distance of the empirical measure
N. Fournier and A. Guillin · 2015
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Deep learning face attributes in the wild
Z. Liu, P. Luo, X. Wang, and X. Tang · 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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Deep learning
I. Goodfellow, Y. Bengio, and A. Courville · 2016
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Deep residual learning for image recognition
K. He, X. Zhang, S. Ren, and J. Sun · 2016
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Improved techniques for training GANs
T. Salimans, I. Goodfellow, W. Zaremba, V. Cheung, A. Radford, and X. Chen · 2016
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Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration
J. Altschuler, J. Niles-Weed, and P. Rigollet · 2017
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Wasserstein generative adversarial networks
M. Arjovsky, S. Chintala, and L. Bottou · 2017
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Joint distribution optimal transportation for domain adaptation
N. Courty, R. Flamary, A. Habrard, and A. Rakotomamonjy · 2017
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GANs trained by a two time-scale update rule converge to a local Nash equilibrium
M. Heusel, H. Ramsauer, T. Unterthiner, B. Nessler, and S. Hochreiter · 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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Deepjdot: Deep joint distribution optimal transport for unsupervised domain adaptation
B. Bhushan Damodaran, B. Kellenberger, R. Flamary, D. Tuia, and N. Courty · 2018
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Generative modeling using the sliced Wasserstein distance
I. Deshpande, Z. Zhang, and A. G. Schwing · 2018
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Sliced Wasserstein auto-encoders
S. Kolouri, P. E. Pope, C. E. Martin, and G. K. Rohde · 2018
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Sliced Wasserstein distance for learning Gaussian mixture models
S. Kolouri, G. K. Rohde, and H. Hoffmann · 2018
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Wasserstein auto-encoders
I. Tolstikhin, O. Bousquet, S. Gelly, and B. Schoelkopf · 2018
Cited alongside, same era.
‘One-dimensional empirical measures, order statistics, and Kantorovich transport distances
S. Bobkov and M. Ledoux · 2019
Cited alongside, same era.
Projection robust Wasserstein distance and Riemannian optimization
T. Lin, C. Fan, N. Ho, M. Cuturi, and M. Jordan · 2020
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Fixed-support Wasserstein barycenters: Computational hardness and fast algorithm
T. Lin, N. Ho, X. Chen, M. Cuturi, and M. I. Jordan · 2020
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Approximate Bayesian computation with the sliced-Wasserstein distance
K. Nadjahi, V. De Bortoli, A. Durmus, R. Badeau, and U. Şimşekli · 2020
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Computational optimal transport, 2020
G. Peyré and M. Cuturi · 2020
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Predicting cell lineages using autoencoders and optimal transport
K. D. Yang, K. Damodaran, S. Venkatachalapathy, A. C. Soylemezoglu, G. Shivashankar, and C. Uhler · 2020
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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
Cited alongside, same era.
Generalized sliced Wasserstein distances
S. Kolouri, K. Nadjahi, U. Simsekli, R. Badeau, and G. Rohde · 2019
Cited alongside, same era.
Sliced Wasserstein discrepancy for unsupervised domain adaptation
C.-Y. Lee, T. Batra, M. H. Baig, and D. Ulbricht · 2019
Cited alongside, same era.
On efficient optimal transport: An analysis of greedy and accelerated mirror descent algorithms
T. Lin, N. Ho, and M. Jordan · 2019
Cited alongside, same era.
On the efficiency of the Sinkhorn and Greenkhorn algorithms and their acceleration for optimal transport
T. Lin, N. Ho, and M. I. Jordan · 2019
Cited alongside, same era.
Sliced-Wasserstein flows: Nonparametric generative modeling via optimal transport and diffusions
A. Liutkus, U. Simsekli, S. Majewski, A. Durmus, and F.-R. Stöter · 2019
Cited alongside, same era.
C. Bonet, N. Courty, F. Septier, and L. Drumetz · 2021
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Sliced iterative normalizing flows
B. Dai and U. Seljak · 2021
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Sliced mutual information: A scalable measure of statistical dependence
Z. Goldfeld and K. Greenewald · 2021
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A Riemannian block coordinate descent method for computing the projection robust Wasserstein distance
M. Huang, S. Ma, and L. Lai · 2021
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Lamda: Label matching deep domain adaptation
T. Le, T. Nguyen, N. Ho, H. Bui, and D. Phung · 2021
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Run-sort-rerun: Escaping batch size limitations in sliced Wasserstein generative models
J. Lezama, W. Chen, and Q. Qiu · 2021
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Pooling by sliced-Wasserstein embedding
N. Naderializadeh, J. Comer, R. Andrews, H. Hoffmann, and S. Kolouri · 2021
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Fast approximation of the sliced-Wasserstein distance using concentration of random projections
K. Nadjahi, A. Durmus, P. E. Jacob, R. Badeau, and U. Simsekli · 2021
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Distributional sliced-Wasserstein and applications to generative modeling
K. Nguyen, N. Ho, T. Pham, and H. Bui · 2021
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Improving relational regularized autoencoders with spherical sliced fused Gromov-Wasserstein
K. Nguyen, S. Nguyen, N. Ho, T. Pham, and H. Bui · 2021
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Differentially private sliced Wasserstein distance
A. Rakotomamonjy and R. Liva · 2021
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Vocabulary learning via optimal transport for neural machine translation
J. Xu, H. Zhou, C. Gan, Z. Zheng, and L. Li · 2021
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Sliced Wasserstein variational inference
M. Yi and S. Liu · 2021
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Augmented sliced Wasserstein distances
X. Chen, Y. Yang, and Y. Li · 2022
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On transportation of mini-batches: A hierarchical approach
K. Nguyen, D. Nguyen, Q. Nguyen, T. Pham, H. Bui, D. Phung, T. Le, and N. Ho · 2022
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Improving mini-batch optimal transport via partial transportation
K. Nguyen, D. Nguyen, T. Pham, and N. Ho · 2022
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