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arXiv · 2304.14885

On Closed-Form Expressions for the Fisher-Rao Distance

Henrique K. Miyamoto·Fábio C. C. Meneghetti·Julianna Pinele·Sueli I. R. Costa
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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.

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Henrique K. Miyamoto, Fábio C. C. Meneghetti, Julianna Pinele, Sueli I. R. Costa. 2023-04-28. On Closed-Form Expressions for the Fisher-Rao Distance. https://doi.org/10.1007/s41884-024-00143-2

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