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.

我们介绍Python包Geomstats的信息几何模块。该模块首先实现了广泛使用的概率分布参数族的费舍尔-饶黎曼流形，例如正态分布、伽马分布、贝塔分布、狄利克雷分布等。给定参数化概率密度函数作为输入，该模块进一步给出任何感兴趣的分布参数族的 Fisher–Rao Riemannian 几何。实现的黎曼几何工具允许用户在给定族内的分布之间进行比较、平均和插值。重要的是，这些功能为概率分布的统计和机器学习打开了大门。我们展示了该模块的面向对象实现以及说明性示例，并展示了如何使用它来对参数概率分布流形进行学习。