Timeline for Are 1-Wasserstein and 2-Wasserstein distances between multivariate normal distributions equivalent?
Current License: CC BY-SA 4.0
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| Mar 27 at 3:55 | comment | added | Vladimir Zolotov | @leomonsaingeon Hi Leo! I asked this question mostly out of curiosity there no specific app. Also my current project is the first one dealing with duality for Wassersteins. So do not expect much wisdom in details of my question. (1) The reasons to put a constant independent of dimensions are (a) I wanted to avoid arguments by compactness (if there are any) and (b) In AI apps which I'm exposed to, dimensions are large, so if the constant grows fast with dimension that's no good. (2)For $W_1$ we have Theorem 1.14 in Villani's "Topics in optimal transportation", may be useful I guess. | |
| Mar 25 at 23:17 | comment | added | leo monsaingeon | two quick questions: 1) do you really want the constant $C$ to be uniform in the dimension (you wrote it pretty explicitly, just checking) 2) the $W_p$ distances also enjoy a Kantorovich duality, so what's so special here about $p=1$? | |
| Feb 26 at 13:50 | history | edited | Vladimir Zolotov | CC BY-SA 4.0 |
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| Feb 26 at 11:46 | history | edited | Vladimir Zolotov | CC BY-SA 4.0 |
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| Feb 26 at 11:11 | history | asked | Vladimir Zolotov | CC BY-SA 4.0 |