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Barycenters in the Wasserstein Space
Open accessAbstract
In this paper, we introduce a notion of barycenter in the Wasserstein space which generalizes McCann's interpolation to the case of more than two measures. We provide existence, uniqueness, characterizations, and regularity of the barycenter and relate it to the multimarginal optimal transport problem considered by Gangbo and Święch in [Comm. Pure Appl. Math., 51 (1998), pp. 23–45]. We also consider some examples and, in particular, rigorously solve the Gaussian case. We finally discuss convexity of functionals in the Wasserstein space.
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Cited by
Computational Optimal Transport
Peyré, G., & Cuturi, M. (2019) · now publishers, Inc. eBooks · doi:10.1561/9781680835519 · Cited by 847
Convolutional wasserstein distances: efficient optimal transportation on geometric domains
Solomon, J., de Goes, F., Peyré, G., Cuturi, M., Butscher, A., Nguyen, A., Du, T., & Guibas, L. (2015) · ACM Transactions on Graphics · doi:10.1145/2766963 · Cited by 481
Scaling algorithms for unbalanced optimal transport problems
Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F.-X. (2018) · Mathematics of Computation · doi:10.1090/mcom/3303 · Cited by 336
Exploration in Deep Reinforcement Learning: From Single-Agent to Multiagent Domain
Hao, J., Yang, T., Tang, H., Bai, C., Liu, J., Meng, Z., Liu, P., & Wang, Z. (2021) · arXiv · doi:10.48550/arxiv.2109.06668 · Cited by 192
Fair Regression with Wasserstein Barycenters
Chzhen, E., Denis, C., Hebiri, M., Oneto, L., & Pontil, M. (2020) · arXiv · doi:10.48550/arxiv.2006.07286 · Cited by 46
“The next result is standard and can be found for instance in [2, Section 6.1] or [38, Section 5.5.5].”
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Metadata
- Authors
- Agueh, M., & Carlier, G.
- Venue
- SIAM Journal on Mathematical Analysis
- Published
- 2011-01
- Volume
- 43
- Issue
- 2
- Pages
- 904-924
- ISSN
- 0036-1410 (ISSN-L)
- 1095-7154
- OpenAlex
- W1968333723
- Cited by
- 749
- References
- 0
- FWCI
- 17.49
- Type
- journal article
- Language
- en
- Open access
- green
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