Timeline for Upper bound of Wasserstein distance given by subvariables of codim 1
Current License: CC BY-SA 4.0
7 events
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| Jul 12, 2021 at 12:15 | comment | added | Iosif Pinelis | @YUANZhiri : All right. Now that your posted question has been fully answered and you "do not think there exists a general result for the upper bound", what about the closure? You can always ask another question with any additional conditions specified. | |
| Jul 12, 2021 at 10:08 | comment | added | YUAN Zhiri | Yeah, I understand your point. BTW, I did not mention "dependence structures (like the correlation/copulas)", because for lower bound such terms would naturally appear, so I wonder whether for the upper bound similar phenomenon/structure will also appear. Anyway, I do not think there exists a general result for the upper bound. Thanks. | |
| Jul 11, 2021 at 3:15 | comment | added | Iosif Pinelis | @YUANZhiri : In your post, you did not mention any "dependence structures (like the correlation/copulas)". So, your question, "can we formulate an inequality of the form $W_p(X,Y) \leq \sum \limits_{i=1}^na_i W_p(\tilde{X}_i,\tilde{Y}_i)$" has been fully answered. The answer shows that such upper bounds do not exist, even if you want/need them. Do you disagree with any of these statements? | |
| Jul 10, 2021 at 8:31 | comment | added | YUAN Zhiri | honestly speaking, no. My aim is to construct an upper bound of Wasserstein distance between two distributions, by using their sub-distributions and dependence structures (like the correlation/copulas). We have formulated similar results of LOWER bounds for lots of distances like Wasserstein and chi2, and now we are interested in the UPPER bounds of Wasserstein. Should you provide any reference about it, I would be rather grateful. | |
| Jul 7, 2021 at 0:31 | comment | added | Iosif Pinelis | @YUANZhiri : So, to have a closure, are you satisfied with this answer? | |
| Jul 2, 2021 at 15:24 | comment | added | YUAN Zhiri | Thanks for your answer, it is illustrative. | |
| Jul 2, 2021 at 13:26 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |