Parametric information geometry with the package Geomstats

• URL: http://arxiv.org/abs/2211.11643v1
• Date: Mon, 21 Nov 2022 16:56:45 GMT
• Title: Parametric information geometry with the package Geomstats
• Authors: Alice Le Brigant, Jules Deschamps, Antoine Collas, Nina Miolane
• Abstract summary: We introduce the information geometry module of the Python package Geomstats. The module gives the Fisher-Rao Riemannian geometry of any parametric family of distributions of interest. Importantly, such capabilities open the door to statistics and machine learning on probability distributions.
• Score: 4.205692673448206
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce the information geometry module of the Python package Geomstats. The module first implements Fisher-Rao Riemannian manifolds of widely used parametric families of probability distributions, such as normal, gamma, beta, Dirichlet distributions, and more. The module further gives the Fisher-Rao Riemannian geometry of any parametric family of distributions of interest, given a parameterized probability density function as input. The implemented Riemannian geometry tools allow users to compare, average, interpolate between distributions inside a given family. Importantly, such capabilities open the door to statistics and machine learning on probability distributions. We present the object-oriented implementation of the module along with illustrative examples and show how it can be used to perform learning on manifolds of parametric probability distributions.

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