Timeline for Wasserstein compactness of sublevel sets of relative entropy
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| May 9, 2023 at 21:59 | history | edited | leo monsaingeon | CC BY-SA 4.0 |
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| Jan 17, 2023 at 3:50 | comment | added | pseudocydonia | I think it is fine to assume that $\pi$ itself has finite second moment, but $\lambda$-log-concavity would be overly restrictive. | |
| Jan 16, 2023 at 21:35 | comment | added | leo monsaingeon | Neither. What can you tell us about the refernce measure $\pi$? By any chance, is it $\lambda$ log-concave for some $\lambda>0$? | |
| Jan 16, 2023 at 19:33 | comment | added | pseudocydonia | Agreed. Do you have a proof that this is a non-issue, or know of a counter-example? | |
| Jan 15, 2023 at 20:39 | comment | added | leo monsaingeon | Well, this means that the only issue is a posisble escape of mass at infinity. | |
| Jan 15, 2023 at 17:20 | comment | added | pseudocydonia | Sorry, fixed typo regarding $\pi$. As for your second comment, I agree this is surely relevant, but do you have an idea of how to use this to resolve the issue? | |
| Jan 15, 2023 at 17:18 | history | edited | pseudocydonia | CC BY-SA 4.0 |
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| Jan 15, 2023 at 7:21 | comment | added | leo monsaingeon | Perhaps a relevant comment is that the $W_2$ distance is well-known to metrize "weak convergence + convergence of the 2nd moments"? | |
| Jan 15, 2023 at 7:21 | comment | added | leo monsaingeon | What do you mean, $\pi\in \mathbb R^d$? Is $\pi$ a probability measure, or just a (posisbly unbounded, e.g. Lebesgue) nonnegative measure? | |
| Jan 15, 2023 at 2:49 | history | asked | pseudocydonia | CC BY-SA 4.0 |