Timeline for Wasserstein distance in R^d from one dimensional marginals
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Jun 18, 2022 at 10:14 | history | edited | Martin Sleziak |
added the tag (wasserstein-distance)
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| Jun 18, 2022 at 8:02 | history | edited | Glorfindel | CC BY-SA 4.0 |
broken link fixed, cf. https://math.meta.stackexchange.com/a/34713/228959
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| Aug 30, 2015 at 19:39 | answer | added | VictorZurkowski | timeline score: 4 | |
| Jun 4, 2013 at 12:51 | vote | accept | Roberto Imbuzeiro Oliveira | ||
| Oct 2, 2010 at 10:30 | answer | added | R W | timeline score: 6 | |
| Oct 1, 2010 at 14:04 | comment | added | Benoît Kloeckner | That a probability measure $\mu$ on $\mathbb{R}^d$ is entirely defined by its projections on lines is more or less Radon's theorem. What you want is a quantitative version of this, you could therefore try to use the inversion formula for Radon transform: it gives you, at least when $\mu$ has a density, an expression of $\mu$ in terms of the $\mu_v$. However it seems difficult to relate this formula with the Wasserstein distance. | |
| Oct 1, 2010 at 10:05 | history | edited | Roberto Imbuzeiro Oliveira | CC BY-SA 2.5 |
Corrected the formula for W.
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| Oct 1, 2010 at 10:04 | comment | added | Roberto Imbuzeiro Oliveira | Thanks! I guess I had the dual definition in mind when writing this. | |
| Oct 1, 2010 at 8:51 | comment | added | Florian | There is an error in your definition of the Wasserstein metric: you have to replace inf by sup. | |
| Sep 7, 2010 at 23:33 | history | edited | Roberto Imbuzeiro Oliveira | CC BY-SA 2.5 |
Corrected typo.
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| Sep 4, 2010 at 11:40 | comment | added | Mark Meckes | I don't have time to think about your question at the moment, but you may be interested in the results for typical $d$-dimensional projections here: arxiv.org/abs/0912.2044 | |
| Sep 4, 2010 at 3:28 | history | edited | Roberto Imbuzeiro Oliveira | CC BY-SA 2.5 |
Minor rephrasing of first sentence.
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| Sep 4, 2010 at 0:55 | history | edited | Roberto Imbuzeiro Oliveira | CC BY-SA 2.5 |
Corrected spelling
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| Sep 4, 2010 at 0:46 | history | asked | Roberto Imbuzeiro Oliveira | CC BY-SA 2.5 |