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The Sliced-Wasserstein distance (SW) is a computationally efficient and theoretically grounded alternative to the Wasserstein distance.
Generalized sliced wasserstein distances
Kolouri, S., Nadjahi, K., Simsekli, U., Badeau, R., and Rohde, G. K · 1902
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Computational optimal transport: With applications to data science
Peyré, G. and Cuturi, M · 1935
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Asymptotic evaluation of certain markov process expectations for large time, i
Donsker, M. D. and Varadhan, S. S · 1975
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On the method of bounded differences
McDiarmid, C · 1989
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Some PAC-Bayesian theorems
McAllester, D. A · 1999
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A PAC-Bayesian approach to adaptive classification
Catoni, O · 2003
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Statistical and topological properties of sliced probability divergences
Nadjahi, K., Durmus, A., Chizat, L., Kolouri, S., Shahrampour, S., and Şimşekli, U · 2003
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A pac-bayes approach to the set covering machine
Laviolette, F., Marchand, M., and Shah, M · 2006
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Tighter pac-bayes bounds
Ambroladze, A., Parrado-hernández, E., and Shawe-taylor, J · 2007
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Pac-Bayesian Supervised Classification: The Thermodynamics of Statistical Learning , volume 56
Catoni, O · 2007
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Pac-bayesian learning of linear classifiers
Germain, P., Lacasse, A., Laviolette, F., and Marchand, M · 2009
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Optimal transport: old and new , volume 338
Villani, C · 2009
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A pac-bayes bound for tailored density estimation
Higgs, M. and Shawe-Taylor, J · 2010
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Chromatic PAC-Bayes Bounds for Non-IID Data: Applications to Ranking and Stationary
Ralaivola, L., Szafranski, M., and Stempfel, G · 2010
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The mnist database of handwritten digit images for machine learning research
Deng, L · 2012
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Wasserstein Barycenter and Its Application to Texture Mixing
Rabin, J., Peyré, G., Delon, J., and Bernot, M · 2012
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Subgaussian random variables : An expository note
Rivasplata, O · 2012
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Unidimensional and Evolution Methods for Optimal Transportation
Bonnotte, N · 2013
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Sinkhorn distances: Lightspeed computation of optimal transport
Cuturi, M · 2013
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Modelling extremal events: for insurance and finance , volume 33
Embrechts, P., Klüppelberg, C., and Mikosch, T · 2013
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Concentration in unbounded metric spaces and algorithmic stability
Kontorovich, A · 2014
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Wasserstein propagation for semi-supervised learning
Solomon, J., Rustamov, R., Guibas, L., and Butscher, A · 2014
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Weight uncertainty in neural networks
Blundell, C., Cornebise, J., Kavukcuoglu, K., and Wierstra, D · 2015
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Sliced and radon wasserstein barycenters of measures
Bonneel, N., Rabin, J., Peyré, G., and Pfister, H · 2015
Cited alongside, same era.
On the rate of convergence in wasserstein distance of the empirical measure
Fournier, N. and Guillin, A · 2015
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Learning with a wasserstein loss
Frogner, C., Zhang, C., Mobahi, H., Araya-Polo, M., and Poggio, T · 2015
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Adam: A Method for Stochastic Optimization
Kingma, D. P. and Ba, J · 2015
Cited alongside, same era.
An efficient linear programming method for optimal transportation
Oberman, A. M. and Ruan, Y · 2015
Cited alongside, same era.
Optimal transport for domain adaptation
Wasserstein dictionary learning: Optimal transport-based unsupervised nonlinear dictionary learning
Schmitz, M. A., Heitz, M., Bonneel, N., Ngole, F., Coeurjolly, D., Cuturi, M., Peyré, G., and Starck, J.-L · 2018
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Max-sliced wasserstein distance and its use for gans
Deshpande, I., Hu, Y.-T., Sun, R., Pyrros, A., Siddiqui, N., Koyejo, S., Zhao, Z., Forsyth, D., and Schwing, A. G · 2019
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Sliced-wasserstein flows: Nonparametric generative modeling via optimal transport and diffusions
Liutkus, A., Simsekli, U., Majewski, S., Durmus, A., and Stöter, F.-R · 2019
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Asymptotic guarantees for learning generative models with the sliced-wasserstein distance
Nadjahi, K., Durmus, A., Şimşekli, U., and Badeau, R · 2019
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Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance
Weed, J. and Bach, F · 2019
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Courty, N., Flamary, R., Tuia, D., and Rakotomamonjy, A · 2016
Cited alongside, same era.
A smoothed dual approach for variational wasserstein problems
Cuturi, M. and Peyré, G · 2016
Cited alongside, same era.
Sliced wasserstein kernels for probability distributions
Kolouri, S., Zou, Y., and Rohde, G. K · 2016
Cited alongside, same era.
Wasserstein training of restricted boltzmann machines
Montavon, G., Müller, K.-R., and Cuturi, M · 2016
Cited alongside, same era.
A sparse multiscale algorithm for dense optimal transport
Schmitzer, B · 2016
Cited alongside, same era.
Wasserstein generative adversarial networks
Arjovsky, M., Chintala, S., and Bottou, L · 2017
Cited alongside, same era.
From optimal transport to generative modeling: the vegan cookbook
Bousquet, O., Gelly, S., Tolstikhin, I., Simon-Gabriel, C.-J., and Schoelkopf, B · 2017
Cited alongside, same era.
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Generalized sliced distances for probability distributions
Kolouri, S., Nadjahi, K., Simsekli, U., and Shahrampour, S · 2020
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Convergence and concentration of empirical measures under Wasserstein distance in unbounded functional spaces
Lei, J · 2020
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Approximate bayesian computation with the sliced-wasserstein distance
Nadjahi, K., De Bortoli, V., Durmus, A., Badeau, R., and Şimşekli, U · 2020
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User-friendly introduction to PAC-Bayes bounds, 2021
Alquier, P · 2021
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Strong equivalence between metrics of Wasserstein type
Bayraktar, E. and Guo, G · 2021
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Sliced-wasserstein gradient flows
Bonet, C., Courty, N., Septier, F., and Drumetz, L · 2021
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Reliable estimation of kl divergence using a discriminator in reproducing kernel hilbert space
Ghimire, S., Masoomi, A., and Dy, J · 2021
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Pac-bayes unleashed: Generalisation bounds with unbounded losses
Haddouche, M., Guedj, B., Rivasplata, O., and Shawe-Taylor, J · 2021
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On projection robust optimal transport: Sample complexity and model misspecification
Lin, T., Zheng, Z., Chen, E. Y., Cuturi, M., and Jordan, M. I · 2021
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Fast approximation of the sliced-wasserstein distance using concentration of random projections
Nadjahi, K., Durmus, A., Jacob, P., Badeau, R., and Simsekli, U · 2021
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Distributional sliced-wasserstein and applications to generative modeling
Nguyen, K., Ho, N., Pham, T., and Bui, H · 2021
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Differentially private sliced wasserstein distance
Rakotomamonjy, A. and Ralaivola, L · 2021
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von mises–fisher loss: An exploration of embedding geometries for supervised learning
Scott, T. R., Gallagher, A. C., and Mozer, M. C · 2021
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Learning Stochastic Majority Votes by Minimizing a PAC-Bayes Generalization Bound
Zantedeschi, V., Viallard, P., Morvant, E., Emonet, R., Habrard, A., Germain, P., and Guedj, B · 2021
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On pac-bayesian reconstruction guarantees for vaes
Chérief-Abdellatif, B.-E., Shi, Y., Doucet, A., and Guedj, B · 2022
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Minimax confidence intervals for the Sliced Wasserstein distance
Manole, T., Balakrishnan, S., and Wasserman, L · 2022
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Estimation of Wasserstein distances in the Spiked Transport Model
Niles-Weed, J. and Rigollet, P · 2022
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