Examples of Application of Nonparametric Information Geometry to Statistical Physics

TL;DR

This paper explores a nonparametric information geometry framework applied to statistical physics and machine learning, utilizing Orlicz spaces to analyze divergence, entropy, and equations in these fields.

Contribution

It introduces a nonparametric geometric approach to statistical physics and machine learning problems using Orlicz Banach spaces, extending Amari's information geometry.

Findings

Framework for nonparametric information geometry on probability densities

Application to optimization, divergence, and entropy in physics and machine learning

Insights into Boltzmann entropy and equations using geometric methods

Abstract

We review a nonparametric version of Amari's Information Geometry in which the set of positive probability densities on a given sample space is endowed with an atlas of charts to form a differentiable manifold modeled on Orlicz Banach spaces. This nonparametric setting is used to discuss the setting of typical problems in Machine Learning and Statistical Physics, such as relaxed optimization, Kullback-Leibler divergence, Boltzmann entropy, Boltzmann equation