Examples of the Application of Nonparametric Information Geometry to Statistical Physics
Open Access
- 25 September 2013
- Vol. 15 (10) , 4042-4065
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
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