Timeline for Cutting a Gaussian in two pieces that are maximally separated in the Wasserstein metric
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 12, 2018 at 10:56 | answer | added | user44143 | timeline score: 2 | |
| Dec 18, 2017 at 20:03 | comment | added | Benoît Kloeckner | For the spherical cap (which you interpreted as I intended), the optimal map should be spherical so it reduces to a 1D problem. I realize now that the half space case seems non-trivial. | |
| Dec 15, 2017 at 20:42 | comment | added | VSJ | I'm not sure how to compute those! (I assume by spherically symmetric cap you mean a ball around the origin that contains half the probability?) My guess is that there should be a constant upper bound on the largest possible Wasserstein distance, independent of $n$. The intuition is that most of the probability lies very close $\partial A$ on either side of it. So the optimal transport map would be to jump over the boundary to the other side, giving a small $W_2$ distance. But I'm not certain about any of this! | |
| Dec 15, 2017 at 19:46 | comment | added | Benoît Kloeckner | Have you compared a half-space to a spherically symmetric cap? Both Wasserstein distances should be computable. | |
| Dec 15, 2017 at 19:11 | history | asked | VSJ | CC BY-SA 3.0 |