Information Geometry of the Probability Simplex: A Short Course

Abstract

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.