概率单纯形的信息几何:短期课程

IF 0.3 Q4 PHYSICS, MULTIDISCIPLINARY

Nonlinear Phenomena in Complex Systems Pub Date : 2019-11-05 DOI:10.33581/1561-4085-2020-23-2-221-242

Giovanni Pistone

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引用次数: 6

摘要

这套笔记是为一门短期课程准备的，旨在为概率单纯形的信息几何（IG）主题提供（几乎）独立和（几乎）基本的介绍。这样的课程可以被认为是对Amari和Nagaoka[1]的原始专著的介绍，以及Amari[2]和Ay、Jost、Lê和Schwachhöfer[3]最近的专著的介绍。重点是非参数方法，也就是说，我考虑全概率单纯形的几何，并将IG形式与统计物理学中的经典方法进行比较。

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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Information Geometry of the Probability Simplex: A Short Course

This set of notes is intended for a short course aiming to provide an (almost) self-contained and (almost) elementary introduction to the topic of Information Geometry (IG) of the probability simplex. Such a course can be considered an introduction to the original monograph by Amari and Nagaoka [1], and to the recent monographs by Amari [2] and by Ay, Jost, Lê, and Schwachhöfer [3]. The focus is on a non-parametric approach, that is, I consider the geometry of the full probability simplex and compare the IG formalism with what is classically done in Statistical Physics.

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来源期刊

Nonlinear Phenomena in Complex Systems PHYSICS, MULTIDISCIPLINARY-

CiteScore

0.90

自引率

25.00%

发文量