Finite sample bounds for barycenter estimation in geodesic spaces
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909505291288576 |
|---|---|
| author | Brunel, Victor-Emmanuel Serres, Jordan |
| author_facet | Brunel, Victor-Emmanuel Serres, Jordan |
| contents | We study the problem of estimating the barycenter of a distribution given i.i.d. data in a geodesic space. Assuming an upper curvature bound in Alexandrov's sense and a support condition ensuring the strong geodesic convexity of the barycenter problem, we establish finite-sample error bounds in expectation and with high probability. Our results generalize Hoeffding- and Bernstein-type concentration inequalities from Euclidean to geodesic spaces. Building on these concentration inequalities, we derive statistical guarantees for two efficient algorithms for the computation of barycenters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14069 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite sample bounds for barycenter estimation in geodesic spaces Brunel, Victor-Emmanuel Serres, Jordan Statistics Theory Probability Machine Learning We study the problem of estimating the barycenter of a distribution given i.i.d. data in a geodesic space. Assuming an upper curvature bound in Alexandrov's sense and a support condition ensuring the strong geodesic convexity of the barycenter problem, we establish finite-sample error bounds in expectation and with high probability. Our results generalize Hoeffding- and Bernstein-type concentration inequalities from Euclidean to geodesic spaces. Building on these concentration inequalities, we derive statistical guarantees for two efficient algorithms for the computation of barycenters. |
| title | Finite sample bounds for barycenter estimation in geodesic spaces |
| topic | Statistics Theory Probability Machine Learning |
| url | https://arxiv.org/abs/2502.14069 |