Nonlinear Phenomena in Complex Systems, 2020, Vol.23, No.2, pp.221

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2020, Vol.23, No.2, pp.221 - 242

Information Geometry of the Probability Simplex: A Short Course
Giovanni Pistone

This set of notes is intended for a short course aiming to provide an (almost) selfcontained 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.

Key words: information geometry, probability simplex

DOI: https://doi.org/10.33581/1561-4085-2020-23-2-221-242

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