Timeline for Practical bounds for the Wasserstein distance in 2 dimensions
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Aug 29, 2015 at 18:55 | vote | accept | Tom Solberg | ||
| Aug 29, 2015 at 18:55 | vote | accept | Tom Solberg | ||
| Aug 29, 2015 at 18:55 | |||||
| Aug 29, 2015 at 12:55 | comment | added | Qzyx | I was referring to the same one (i.e. the one on Wikipedia). As you say, this is a maximization problem: you get $W_{1}(\mu,\hat{\mu}) = \sup_{f \in \mathcal{F}} | \mu(f) - \hat{\mu}(f) |$. At first this looks hard, but a covering argument allows you to take the max over a (large) finite set $\mathcal{F}_{\epsilon}$ rather than the sup over the uncountable set $\mathcal{F}$. (Unrelated: one can use many things in place of the DKW inequality; I just thought it was probably sharp-ish in your situation and I didn't compare to others.) | |
| Aug 27, 2015 at 19:21 | comment | added | Tom Solberg | Thanks a lot for this! Could you elaborate on "Wasserstein duality"? The duality that I am familiar with would use the fact that $W_1$ is a minimum over all transport maps, so its dual would be a maximization problem, which is probably not the same thing you are referring to. | |
| Aug 27, 2015 at 12:29 | history | edited | Qzyx | CC BY-SA 3.0 |
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| Aug 27, 2015 at 12:21 | review | First posts | |||
| Aug 27, 2015 at 13:03 | |||||
| Aug 27, 2015 at 12:20 | history | answered | Qzyx | CC BY-SA 3.0 |