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We develop a theory of finite-dimensional polyhedral subsets over the Wasserstein space and optimization of functionals over them via first-order methods.
Accelerating Langevin sampling with birth-death
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Fundamentals of convex analysis
Hiriart-Urruty, J.-B. and Lemaréchal, C. (2004) · 2004
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Transport-based single frame super resolution of very low resolution face images
Kolouri, S. and Rohde, G. K. (2015) · 2015
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Optimal transport for applied mathematicians
Santambrogio, F. (2015) · 2015
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Wasserstein barycentric coordinates: histogram regression using optimal transport
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A continuous linear optimal transport approach for pattern analysis in image datasets
Kolouri, S., Tosun, A. B., Ozolek, J. A., and Rohde, G. K. (2016) · 2016
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Optimal transport in competition with reaction: the Hellinger–Kantorovich distance and geodesic curves
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Amplitude and phase variation of point processes
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Variational inference: a review for statisticians
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Geodesic PCA versus log-PCA of histograms in the Wasserstein space
Cazelles, E., Seguy, V., Bigot, J., Cuturi, M., and Papadakis, N. (2018) · 2018
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Neural ordinary differential equations
Chen, R. T. Q., Rubanova, Y., Bettencourt, J., and Duvenaud, D. K. (2018) · 2018
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Minimax estimation of smooth optimal transport maps
Hütter, J.-C. and Rigollet, P. (2021) · 2021
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Frank–Wolfe methods in probability space
Kent, C., Blanchet, J., and Glynn, P. (2021) · 2021
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Plugin estimation of smooth optimal transport maps
Manole, T., Balakrishnan, S., Niles-Weed, J., and Wasserman, L. (2021) · 2021
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Entropic estimation of optimal transport maps
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Topics in optimal transportation
Villani, C. (2021) · 2021
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Variational inference via Wasserstein gradient flows
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On linear optimization over Wasserstein balls
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On the convergence of coordinate ascent variational inference
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An entropic generalization of Caffarelli’s contraction theorem via covariance inequalities
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Provable convergence guarantees for black-box variational inference
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Supervised learning of sheared distributions using linearized optimal transport
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On the convergence of black-box variational inference
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