Examples of the Application of Nonparametric Information Geometry to Statistical Physics

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 black-box optimization, Kullback-Leibler divergence, Boltzmann-Gibbs entropy and the Boltzmann equation.

Keywords

• information geometry
• exponential manifold
• statistical connections
• Boltzmann-Gibbs entropy
• Boltzmann operator