Examples of Application of Nonparametric Information Geometry to Statistical Physics
Statistics Theory
2015-06-17 v1 Mathematical Physics
math.MP
Statistics Theory
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
Keywords
Cite
@article{arxiv.1308.5312,
title = {Examples of Application of Nonparametric Information Geometry to Statistical Physics},
author = {Giovanni Pistone},
journal= {arXiv preprint arXiv:1308.5312},
year = {2015}
}
Comments
24 pages