Parametric information geometry with the package Geomstats

IF 2.7 1区 数学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING
Alice Le Brigant, Jules Deschamps, Antoine Collas, Nina Miolane
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引用次数: 1

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.
参数信息几何与包Geomstats
我们介绍了Python包Geomstats中的信息几何模块。该模块首先实现了广泛使用的概率分布参数族的Fisher-Rao黎曼流形,如正态分布,伽玛分布,β分布,狄利克雷分布等。该模块进一步给出任何感兴趣的参数分布族的Fisher-Rao黎曼几何,给出一个参数化的概率密度函数作为输入。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,这种能力为概率分布的统计学和机器学习打开了大门。我们介绍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对参数概率分布的流形进行学习。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
ACM Transactions on Mathematical Software
ACM Transactions on Mathematical Software 工程技术-计算机:软件工程
CiteScore
5.00
自引率
3.70%
发文量
50
审稿时长
>12 weeks
期刊介绍: As a scientific journal, ACM Transactions on Mathematical Software (TOMS) documents the theoretical underpinnings of numeric, symbolic, algebraic, and geometric computing applications. It focuses on analysis and construction of algorithms and programs, and the interaction of programs and architecture. Algorithms documented in TOMS are available as the Collected Algorithms of the ACM at calgo.acm.org.
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