Barycenters and a law of large numbers in Gromov hyperbolic spaces
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917695530729472 |
|---|---|
| author | Ohta, Shin-ichi |
| author_facet | Ohta, Shin-ichi |
| contents | We investigate barycenters of probability measures on Gromov hyperbolic spaces, toward development of convex optimization in this class of metric spaces. We establish a contraction property (the Wasserstein distance between probability measures provides an upper bound of the distance between their barycenters), a deterministic approximation of barycenters of uniform distributions on finite points, and a kind of law of large numbers. These generalize the corresponding results on CAT(0)-spaces, up to additional terms depending on the hyperbolicity constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_00193 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Barycenters and a law of large numbers in Gromov hyperbolic spaces Ohta, Shin-ichi Metric Geometry Optimization and Control Probability We investigate barycenters of probability measures on Gromov hyperbolic spaces, toward development of convex optimization in this class of metric spaces. We establish a contraction property (the Wasserstein distance between probability measures provides an upper bound of the distance between their barycenters), a deterministic approximation of barycenters of uniform distributions on finite points, and a kind of law of large numbers. These generalize the corresponding results on CAT(0)-spaces, up to additional terms depending on the hyperbolicity constant. |
| title | Barycenters and a law of large numbers in Gromov hyperbolic spaces |
| topic | Metric Geometry Optimization and Control Probability |
| url | https://arxiv.org/abs/2211.00193 |