Sharp comparisons between sliced and standard $1$-Wasserstein distances
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908601415630848 |
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| author | Carlier, Guillaume Figalli, Alessio Mérigot, Quentin Wang, Yi |
| author_facet | Carlier, Guillaume Figalli, Alessio Mérigot, Quentin Wang, Yi |
| contents | Sliced Wasserstein distances are widely used in practice as a computationally efficient alternative to Wasserstein distances in high dimensions. In this paper, motivated by theoretical foundations of this alternative, we prove quantitative estimates between the sliced $1$-Wasserstein distance and the $1$-Wasserstein distance. We construct a concrete example to demonstrate the exponents in the estimate is sharp. We also provide a general analysis for the case where slicing involves projections onto $k$-planes and not just lines. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_16465 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp comparisons between sliced and standard $1$-Wasserstein distances Carlier, Guillaume Figalli, Alessio Mérigot, Quentin Wang, Yi Statistics Theory Metric Geometry Optimization and Control 49Q22, 39B62 Sliced Wasserstein distances are widely used in practice as a computationally efficient alternative to Wasserstein distances in high dimensions. In this paper, motivated by theoretical foundations of this alternative, we prove quantitative estimates between the sliced $1$-Wasserstein distance and the $1$-Wasserstein distance. We construct a concrete example to demonstrate the exponents in the estimate is sharp. We also provide a general analysis for the case where slicing involves projections onto $k$-planes and not just lines. |
| title | Sharp comparisons between sliced and standard $1$-Wasserstein distances |
| topic | Statistics Theory Metric Geometry Optimization and Control 49Q22, 39B62 |
| url | https://arxiv.org/abs/2510.16465 |