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We develop a notion of projections between sets of probability measures using the geometric properties of the 2-Wasserstein space.
A theorem on triangles in a metric space and some of its applications
Aleksandrov, A. D. (1951) · 1951
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The speed of mean glivenko-cantelli convergence
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Convex Analysis
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Ajtai, M., Komlós, J., and Tusnády, G. (1984) · 1984
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Asymptotics for semiparametric econometric models: Iii. testing and examples
Andrews, D. (1989) · 1989
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Caffarelli, L. A. (1990) · 1990
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Brenier, Y. (1991) · 1991
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Deformable Templates for Face Recognition
Yuille, A. L. (1991) · 1991
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The regularity of mappings with a convex potential
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Matching random samples in many dimensions
Talagrand, M. (1992) · 1992
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Asymptotics for semiparametric econometric models via stochastic equicontinuity
Andrews, D. W. (1994) · 1994
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Newey, W. K. and McFadden, D. (1994) · 1994
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The transportation cost from the uniform measure to the empirical measure in dimension ⩾ 3 \geqslant 3
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McCann, R. J. (1997) · 1997
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Optimal maps for the multidimensional monge-kantorovich problem
Gangbo, W. and Święch, A. (1998) · 1998
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Infinite dimensional analysis: a hitchhiker’s guide
Aliprantis, C. D. and Border, K. C. (1999) · 1999
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A computational fluid mechanics solution to the monge-kantorovich mass transfer problem
Benamou, J.-D. and Brenier, Y. (2000) · 2000
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Asymptotic statistics
van der Vaart, A. W. (2000) · 2000
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Distributional synthetic controls
Gunsilius, F. (2022) · 2001
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The geometry of dissipative evolution equations: The porous medium equation
Otto, F. (2001) · 2001
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The economic costs of conflict: A case study of the basque country
Abadie, A. and Gardeazabal, J. (2003) · 2003
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Topics in optimal transportation
Villani, C. (2003) · 2003
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Gradient flows in metric spaces and in the space of probability measures
Ambrosio, L., Gigli, N., and Savaré, G. (2008) · 2008
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Optimal transport: old and new
Villani, C. (2009) · 2009
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Synthetic control methods for comparative case studies: Estimating the effect of california’s tobacco control program
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Matching for teams
Carlier, G. and Ekeland, I. (2010) · 2010
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Matching with trade-offs: Revealed preferences over competing characteristics
Galichon, A. and Salanié, B. (2010) · 2010
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A geometric study of wasserstein spaces: Euclidean spaces
Kloeckner, B. (2010) · 2010
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Barycenters in the Wasserstein Space
Agueh, M. and Carlier, G. (2011) · 2011
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Sinkhorn distances: Lightspeed computation of optimal transport
Cuturi, M. (2013) · 2013
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The effects of medicaid expansion under the aca: a systematic review
Mazurenko, O., Balio, C. P., Agarwal, R., Carroll, A. E., and Menachemi, N. (2018) · 2018
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Large scale optimal transport and mapping estimation
Seguy, V., Damodaran, B. B., Flamary, R., Courty, N., Rolet, A., and Blondel, M. (2018) · 2018
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Statistical optimal transport via factored couplings
Forrow, A., Hütter, J.-C., Nitzan, M., Rigollet, P., Schiebinger, G., and Weed, J. (2019) · 2019
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Computational optimal transport
Peyré, G. and Cuturi, M. (2019) · 2019
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Ipums usa: Version 9.0 [dataset]
Ruggles, S., Flood, S., Goeken, R., Grover, J., Meyer, E., Pacas, J., and Sobek, M. (2019) · 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) · 2019
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W 2 , 1 W^{2,1} regularity for solutions of the monge–ampère equation
de Philippis, G. and Figalli, A. (2013) · 2013
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Weak convergence and empirical processes: with applications to statistics
van der Vaart, A. and Wellner, J. (2013) · 2013
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Geodesic PCA in the Wasserstein space
Bigot, J., Gouet, R., Klein, T., and López, A. (2014) · 2014
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Medicaid expansion did not result in significant employment changes or job reductions in 2014
Gooptu, A., Moriya, A. S., Simon, K. I., and Sommers, B. D. (2016) · 2014
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Overview of object oriented data analysis
Marron, J. S. and Alonso, A. M. (2014) · 2014
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Comparative politics and the synthetic control method
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Fréchet means and procrustes analysis in wasserstein space
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A fast approach to optimal transport: The back-and-forth method
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Optimal transport mapping via input convex neural networks
Makkuva, A., Taghvaei, A., Oh, S., and Lee, J. (2020) · 2020
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The effects of medicaid expansion on labor market outcomes: evidence from border counties
Peng, L., Guo, X., and Meyerhoefer, C. D. (2020) · 2020
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A machine learning framework for solving high-dimensional mean field game and mean field control problems
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Using synthetic controls: Feasibility, data requirements, and methodological aspects
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A novel notion of barycenter for probability distributions based on optimal weak mass transport
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Wasserstein regression
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Rates of estimation of optimal transport maps using plug-in estimators via barycentric projections
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Pot: Python optimal transport
Flamary, R., Courty, N., Gramfort, A., Alaya, M. Z., Boisbunon, A., Chambon, S., Chapel, L., Corenflos, A., Fatras, K., Fournier, N., Gautheron, L., Gayraud, N. T., Janati, H., Rakotomamonjy, A., Redko, I., Rolet, A., Schutz, A., Seguy, V., Sutherland, D. J., Tavenard, R., Tong, A., and Vayer, T. (2021) · 2021
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On the convergence rate of potentials of Brenier maps
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Minimax estimation of smooth optimal transport maps
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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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Fast pca in 1-d wasserstein spaces via b-splines representation and metric projection
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Entropic estimation of optimal transport maps
Pooladian, A.-A. and Niles-Weed, J. (2021) · 2021
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Distribution-on-distribution regression via optimal transport maps
Ghodrati, L. and Panaretos, V. M. (2022) · 2022
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Measure estimation in the barycentric coding model
Werenski, M. E., Jiang, R., Tasissa, A., Aeron, S., and Murphy, J. M. (2022) · 2022
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Riemannian center of mass and so called karcher mean
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