Smoothed estimation of Wasserstein barycenters
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866918482765938688 |
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| author | Li, Pengtao Zhu, Changbo Chen, Xiaohui |
| author_facet | Li, Pengtao Zhu, Changbo Chen, Xiaohui |
| contents | This paper studies the statistical estimation of exact Wasserstein barycenters. Existing non-asymptotic results for empirical barycenters exhibit a severe curse of dimensionality. Motivated by the semi-dual formulation of the barycenter problem and its associated Sobolev optimization geometry, we develop a smoothness-aware approach that combines density estimation with Sobolev geometric structure to estimate the population barycenter. We establish nonparametric convergence rates for estimating both the barycenter functional and its minimizer, demonstrating how smoothness can substantially improve statistical performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03300 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Smoothed estimation of Wasserstein barycenters Li, Pengtao Zhu, Changbo Chen, Xiaohui Statistics Theory This paper studies the statistical estimation of exact Wasserstein barycenters. Existing non-asymptotic results for empirical barycenters exhibit a severe curse of dimensionality. Motivated by the semi-dual formulation of the barycenter problem and its associated Sobolev optimization geometry, we develop a smoothness-aware approach that combines density estimation with Sobolev geometric structure to estimate the population barycenter. We establish nonparametric convergence rates for estimating both the barycenter functional and its minimizer, demonstrating how smoothness can substantially improve statistical performance. |
| title | Smoothed estimation of Wasserstein barycenters |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2605.03300 |