Sharp bounds for max-sliced Wasserstein distances
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916495501557760 |
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| author | Boedihardjo, March T. |
| author_facet | Boedihardjo, March T. |
| contents | We obtain essentially matching upper and lower bounds for the expected max-sliced 1-Wasserstein distance between a probability measure on a separable Hilbert space and its empirical distribution from $n$ samples. By proving a Banach space version of this result, we also obtain an upper bound, that is sharp up to a log factor, for the expected max-sliced 2-Wasserstein distance between a symmetric probability measure $μ$ on a Euclidean space and its symmetrized empirical distribution in terms of the operator norm of the covariance matrix of $μ$ and the diameter of the support of $μ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00666 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp bounds for max-sliced Wasserstein distances Boedihardjo, March T. Probability Machine Learning We obtain essentially matching upper and lower bounds for the expected max-sliced 1-Wasserstein distance between a probability measure on a separable Hilbert space and its empirical distribution from $n$ samples. By proving a Banach space version of this result, we also obtain an upper bound, that is sharp up to a log factor, for the expected max-sliced 2-Wasserstein distance between a symmetric probability measure $μ$ on a Euclidean space and its symmetrized empirical distribution in terms of the operator norm of the covariance matrix of $μ$ and the diameter of the support of $μ$. |
| title | Sharp bounds for max-sliced Wasserstein distances |
| topic | Probability Machine Learning |
| url | https://arxiv.org/abs/2403.00666 |