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Wasserstein gradient flow has emerged as a promising approach to solve optimization problems over the space of probability distributions.
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Polar factorization and monotone rearrangement of vector-valued functions
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The variational formulation of the Fokker–Planck equation
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Gradient-based learning applied to document recognition
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Real analysis: modern techniques and their applications , volume 40
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Fisher discriminant analysis with kernels
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The geometry of dissipative evolution equations: the porous medium equation
Otto, F · 2001
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Information theory, inference and learning algorithms
MacKay, D. J. and Mac Kay, D. J · 2003
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Topics in optimal transportation
Villani, C · 2003
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Empirical processes: Theory and applications
Wellner, J. A · 2005
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The porous medium equation: mathematical theory
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Gradient flows: in metric spaces and in the space of probability measures
Ambrosio, L., Gigli, N., and Savaré, G · 2008
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Learning multiple layers of features from tiny images
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Estimating divergence functionals and the likelihood ratio by convex risk minimization
Nguyen, X., Wainwright, M. J., and Jordan, M. I · 2010
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From a large-deviations principle to the Wasserstein gradient flow: a new micro-macro passage
Adams, S., Dirr, N., Peletier, M. A., and Zimmer, J · 2011
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Nonparametric variational inference
Gershman, S., Hoffman, M., and Blei, D · 2012
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On the empirical estimation of integral probability metrics
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Generative adversarial nets
Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., and Bengio, Y · 2014
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Entropic approximation of Wasserstein gradient flows
Peyré, G · 2015
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U-net: Convolutional networks for biomedical image segmentation
Ronneberger, O., Fischer, P., and Brox, T · 2015
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Discretization of functionals involving the monge–ampère operator
Benamou, J.-D., Carlier, G., Mérigot, Q., and Oudet, E · 2016
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Deep residual learning for image recognition
He, K., Zhang, X., Ren, S., and Sun, J · 2016
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Stein variational gradient descent: A general purpose bayesian inference algorithm
Liu, Q. and Wang, D · 2016
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A kernelized stein discrepancy for goodness-of-fit tests
Liu, Q., Lee, J., and Jordan, M · 2016
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f-gan: Training generative neural samplers using variational divergence minimization
Nowozin, S., Cseke, B., and Tomioka, R · 2016
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Zagoruyko, S. and Komodakis, N · 2016
Ae-ot-gan: Training gans from data specific latent distribution
An, D., Guo, Y., Zhang, M., Qi, X., Lei, N., and Gu, X · 2020
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Experiment tracking with weights and biases, 2020
Biewald, L · 2020
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A framework for contrastive self-supervised learning and designing a new approach
Falcon, W. and Cho, K · 2020
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Scalable computations of Wasserstein barycenter via input convex neural networks
Fan, J., Taghvaei, A., and Chen, Y · 2020
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Approximate inference with Wasserstein gradient flows
Frogner, C. and Poggio, T · 2020
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Input convex neural networks
Amos, B., Xu, L., and Kolter, J. Z · 2017
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Generalization and equilibrium in generative adversarial nets (gans)
Arora, S., Ge, R., Liang, Y., Ma, T., and Zhang, Y · 2017
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Convergence of entropic schemes for optimal transport and gradient flows
Carlier, G., Duval, V., Peyré, G., and Schmitzer, B · 2017
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Gans trained by a two time-scale update rule converge to a local nash equilibrium
Heusel, M., Ramsauer, H., Unterthiner, T., Nessler, B., and Hochreiter, S · 2017
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Salimans, T., Karpathy, A., Chen, X., and Kingma, D. P · 2017
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Euclidean, metric, and wasserstein gradient flows: an overview
Santambrogio, F · 2017
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Huang, C.-W., Chen, R. T., Tsirigotis, C., and Courville, A · 2020
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Universal approximation with deep narrow networks
Kidger, P. and Lyons, T · 2020
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Fisher information regularization schemes for Wasserstein gradient flows
Li, W., Lu, J., and Wang, L · 2020
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Optimal transport mapping via input convex neural networks
Makkuva, A., Taghvaei, A., Oh, S., and Lee, J · 2020
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The Wasserstein proximal gradient algorithm
Salim, A., Korba, A., and Luise, G · 2020
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f-divergence variational inference
Wan, N., Li, D., and Hovakimyan, N · 2020
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Variational transport: A convergent particle-based algorithm for distributional optimization
Yang, Z., Zhang, Y., Chen, Y., and Wang, Z · 2020
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Optimizing functionals on the space of probabilities with input convex neural networks
Alvarez-Melis, D., Schiff, Y., and Mroueh, Y · 2021
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Sliced-wasserstein gradient flows
Bonet, C., Courty, N., Septier, F., and Drumetz, L · 2021
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Jkonet: Proximal optimal transport modeling of population dynamics
Bunne, C., Meng-Papaxanthos, L., Krause, A., and Cuturi, M · 2021
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Primal dual methods for Wasserstein gradient flows
Carrillo, J. A., Craig, K., Wang, L., and Wei, C · 2021
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Scalable computation of monge maps with general costs
Fan, J., Liu, S., Ma, S., Chen, Y., and Zhou, H · 2021
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The deep minimizing movement scheme
Hwang, H. J., Kim, C., Park, M. S., and Son, H · 2021
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Wasserstein proximal of gans
Lin, A. T., Li, W., Osher, S., and Montúfar, G · 2021
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Large-scale wasserstein gradient flows
Mokrov, P., Korotin, A., Li, L., Genevay, A., Solomon, J., and Burnaev, E · 2021
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Generative modeling with optimal transport maps
Rout, L., Korotin, A., and Burnaev, E · 2021
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seaborn: statistical data visualization
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Korotin, A., Selikhanovych, D., and Burnaev, E · 2022
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