On Closed-Form Expressions for the Fisher-Rao Distance
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910617638535168 |
|---|---|
| author | Miyamoto, Henrique K. Meneghetti, Fábio C. C. Pinele, Julianna Costa, Sueli I. R. |
| author_facet | Miyamoto, Henrique K. Meneghetti, Fábio C. C. Pinele, Julianna Costa, Sueli I. R. |
| contents | The Fisher-Rao distance is the geodesic distance between probability distributions in a statistical manifold equipped with the Fisher metric, which is a natural choice of Riemannian metric on such manifolds. It has recently been applied to supervised and unsupervised problems in machine learning, in various contexts. Finding closed-form expressions for the Fisher-Rao distance is generally a non-trivial task, and those are only available for a few families of probability distributions. In this survey, we collect examples of closed-form expressions for the Fisher-Rao distance of both discrete and continuous distributions, aiming to present them in a unified and accessible language. In doing so, we also: illustrate the relation between negative multinomial distributions and the hyperbolic model, include a few new examples, and write a few more in the standard form of elliptical distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_14885 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Closed-Form Expressions for the Fisher-Rao Distance Miyamoto, Henrique K. Meneghetti, Fábio C. C. Pinele, Julianna Costa, Sueli I. R. Statistics Theory Information Theory Differential Geometry The Fisher-Rao distance is the geodesic distance between probability distributions in a statistical manifold equipped with the Fisher metric, which is a natural choice of Riemannian metric on such manifolds. It has recently been applied to supervised and unsupervised problems in machine learning, in various contexts. Finding closed-form expressions for the Fisher-Rao distance is generally a non-trivial task, and those are only available for a few families of probability distributions. In this survey, we collect examples of closed-form expressions for the Fisher-Rao distance of both discrete and continuous distributions, aiming to present them in a unified and accessible language. In doing so, we also: illustrate the relation between negative multinomial distributions and the hyperbolic model, include a few new examples, and write a few more in the standard form of elliptical distributions. |
| title | On Closed-Form Expressions for the Fisher-Rao Distance |
| topic | Statistics Theory Information Theory Differential Geometry |
| url | https://arxiv.org/abs/2304.14885 |