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Minimizing functionals in the space of probability distributions can be done with Wasserstein gradient flows.
A class of wasserstein metrics for probability distributions
Clark R Givens and Rae Michael Shortt · 1984
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An iterative procedure for obtaining i-projections onto the intersection of convex sets
Richard L Dykstra · 1985
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Polar factorization and monotone rearrangement of vector-valued functions
Yann Brenier · 1991
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Symmetric multivariate and related distributions
Kai-Tai Fang, Samuel Kotz, and Kai Wang Ng · 1992
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Time’s arrow: The origins of thermodynamic behavior
Michael C Mackey · 1992
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Fokker-planck equation
Hannes Risken · 1996
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Exponential convergence of langevin distributions and their discrete approximations
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The variational formulation of the fokker–planck equation
Richard Jordan, David Kinderlehrer, and Felix Otto · 1998
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Fisher discriminant analysis with kernels
Sebastian Mika, Gunnar Ratsch, Jason Weston, Bernhard Scholkopf, and Klaus-Robert Mullers · 1999
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A computational fluid mechanics solution to the monge-kantorovich mass transfer problem
Jean-David Benamou and Yann Brenier · 2000
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Topics in optimal transportation , volume 58
Cédric Villani · 2003
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Gradient flows: in metric spaces and in the space of probability measures
Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré · 2008
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Optimal transport: old and new , volume 338
Cédric Villani · 2008
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MNIST handwritten digit database
Yann LeCun and Corinna Cortes · 2010
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Convex analysis and monotone operator theory in Hilbert spaces , volume 408
Heinz H Bauschke, Patrick L Combettes, et al · 2011
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Scikit-learn: Machine learning in Python
F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay · 2011
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Wasserstein barycenter and its application to texture mixing
Julien Rabin, Gabriel Peyré, Julie Delon, and Marc Bernot · 2011
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Nonlocal interactions by repulsive–attractive potentials: radial ins/stability
Daniel Balagué, José A Carrillo, Thomas Laurent, and Gaël Raoul · 2013
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Unidimensional and evolution methods for optimal transportation
Nicolas Bonnotte · 2013
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Auto-encoding variational bayes
Diederik P Kingma and Max Welling · 2013
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A minimal model of predator–swarm interactions
Yuxin Chen and Theodore Kolokolnikov · 2014
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Fast computation of wasserstein barycenters
Marco Cuturi and Arnaud Doucet · 2014
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Generative adversarial nets
Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio · 2014
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Adam: A method for stochastic optimization
Diederik P Kingma and Jimmy Ba · 2014
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Proximal algorithms
Neal Parikh and Stephen Boyd · 2014
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A finite-volume method for nonlinear nonlocal equations with a gradient flow structure
José A Carrillo, Alina Chertock, and Yanghong Huang · 2015
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Deep learning face attributes in the wild
Ziwei Liu, Ping Luo, Xiaogang Wang, and Xiaoou Tang · 2015
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Entropic approximation of wasserstein gradient flows
Gabriel Peyré · 2015
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Optimal transport for applied mathematicians
Filippo Santambrogio · 2015
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Discretization of functionals involving the monge–ampère operator
Jean-David Benamou, Guillaume Carlier, Quentin Mérigot, and Edouard Oudet · 2016
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Fast projection onto the simplex and the l1 ball
Laurent Condat · 2016
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Density estimation using real nvp
Laurent Dinh, Jascha Sohl-Dickstein, and Samy Bengio · 2016
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Interacting particles systems, Wasserstein gradient flow approach
Maxime Laborde · 2016
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Brownian motion, martingales, and stochastic calculus
Jean-François Le Gall · 2016
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Stein variational gradient descent: A general purpose bayesian inference algorithm
Qiang Liu and Dilin Wang · 2016
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Input convex neural networks
Brandon Amos, Lei Xu, and J Zico Kolter · 2017
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Towards principled methods for training generative adversarial networks
Martín Arjovsky and Léon Bottou · 2017
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Wasserstein generative adversarial networks
Martin Arjovsky, Soumith Chintala, and Léon Bottou · 2017
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Convergence of entropic schemes for optimal transport and gradient flows
Guillaume Carlier, Vincent Duval, Gabriel Peyré, and Bernhard Schmitzer · 2017
Alternative way to derive the distribution of the multivariate ornstein–uhlenbeck process
P Vatiwutipong and N Phewchean · 2019
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A variational finite volume scheme for wasserstein gradient flows
Clément Cancès, Thomas O Gallouët, and Gabriele Todeschi · 2020
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Wasserstein and sliced-wasserstein distances
Jules Candau-Tilh · 2020
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Relaxing bijectivity constraints with continuously indexed normalising flows
Rob Cornish, Anthony Caterini, George Deligiannidis, and Arnaud Doucet · 2020
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Approximate inference with wasserstein gradient flows
Charlie Frogner and Tomaso Poggio · 2020
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Interacting langevin diffusions: Gradient structure and ensemble kalman sampler
Alfredo Garbuno-Inigo, Franca Hoffmann, Wuchen Li, and Andrew M Stuart · 2020
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A jko splitting scheme for kantorovich–fisher–rao gradient flows
Thomas O Gallouët and Leonard Monsaingeon · 2017
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Gans trained by a two time-scale update rule converge to a local nash equilibrium
Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter · 2017
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Stein variational gradient descent as gradient flow
Qiang Liu · 2017
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Masked autoregressive flow for density estimation
George Papamakarios, Theo Pavlakou, and Iain Murray · 2017
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{ \{ Euclidean, metric, and Wasserstein } \} gradient flows: an overview
Filippo Santambrogio · 2017
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Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms
Han Xiao, Kashif Rasul, and Roland Vollgraf · 2017
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Chin-Wei Huang, Ricky TQ Chen, Christos Tsirigotis, and Aaron Courville · 2020
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Normalizing flows: An introduction and review of current methods
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Statistical and topological properties of sliced probability divergences
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The wasserstein proximal gradient algorithm
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SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python
Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, Stéfan J. van der Walt, Matthew Brett, Joshua Wilson, K. Jarrod Millman, Nikolay Mayorov, Andrew R. J. Nelson, Eric Jones, Robert Kern, Eric Larson, C J Carey, İlhan Polat, Yu Feng, Eric W. Moore, Jake VanderPlas, Denis Laxalde, Josef Perktold, Robert Cimrman, Ian Henriksen, E. A. Quintero, Charles R. Harris, Anne M. Archibald, Antônio H. Ribeiro, Fabian Pedregosa, Paul van Mulbregt, and SciPy 1.0 Contributors · 2020
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Dpvi: A dynamic-weight particle-based variational inference framework
Chao Zhang, Zhijian Li, Hui Qian, and Xin Du · 2020
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Optimizing functionals on the space of probabilities with input convex neural networks
David Alvarez-Melis, Yair Schiff, and Youssef Mroueh · 2021
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Strong equivalence between metrics of wasserstein type
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Primal dual methods for wasserstein gradient flows
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Sliced iterative normalizing flows
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Variational wasserstein gradient flow
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Kernel stein discrepancy descent
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