On Closed-Form Expressions for the Fisher-Rao Distance
Abstract
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.
Keywords
Cite
@article{arxiv.2304.14885,
title = {On Closed-Form Expressions for the Fisher-Rao Distance},
author = {Henrique K. Miyamoto and Fábio C. C. Meneghetti and Julianna Pinele and Sueli I. R. Costa},
journal= {arXiv preprint arXiv:2304.14885},
year = {2024}
}
Comments
44 pages, 3 figures, minor corrections. Accepted for publication in Information Geometry