Parametric information geometry with the package Geomstats

Alice Le Brigant (1) , Jules Deschamps (1, 2) , Antoine Collas (3, 4) , Nina Miolane (2)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
2 ECE-UCSB - Department of Electrical and Computer Engineering [Santa Barbara]
3 MIND - Modèles et inférence pour les données de Neuroimagerie
4 Université Paris-Saclay

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.

Domaines: Logiciel mathématique [cs.MS]; Apprentissage [cs.LG]; Géométrie différentielle [math.DG]; Statistiques [math.ST]

Alice Le Brigant, Jules Deschamps, Antoine Collas, Nina Miolane. Parametric information geometry with the package Geomstats. 2022. ⟨hal-03862556⟩