Parametric information geometry with the package Geomstats

TL;DR

This paper introduces a Python module in Geomstats that implements Fisher-Rao Riemannian geometry for various parametric probability distributions, enabling advanced statistical and machine learning operations on these manifolds.

Contribution

The paper presents a new module in Geomstats that provides tools for Riemannian geometry of parametric distributions, facilitating analysis and learning on distribution manifolds.

Findings

Implementation of Fisher-Rao geometry for multiple distributions

Tools for comparing, averaging, and interpolating distributions

Applications demonstrated in statistical and machine learning contexts

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.