Examples of 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 relaxed optimization, Kullback-Leibler divergence, Boltzmann entropy, Boltzmann equation

24 pages

References in corpus (1)

• On applications of Orlicz Spaces to Statistical Physics

Cited by in corpus (5)

• New results on mixture and exponential models by Orlicz spaces
• Information Geometry Formalism for the Spatially Homogeneous Boltzmann Equation
• An eikonal equation approach to thermodynamics and the gradient flows in information geometry
• Lagrangian and Hamiltonian Mechanics for Probabilities on the Statistical Manifold
• Parameter-free description of the manifold of non-degenerate density matrices