Parametric information geometry with the package Geomstats
This provides a tool for researchers and practitioners in statistics and machine learning to perform geometric operations on probability distributions, though it is incremental as it builds on existing information geometry concepts.
The authors introduced a Python module for information geometry, implementing Fisher-Rao Riemannian manifolds for parametric probability distributions like normal and gamma, enabling tasks such as comparison and interpolation within distribution families.
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.