Examples of the Application of Nonparametric Information Geometry to Statistical Physics

Entropy

关键词: information geometry;    exponential manifold;    statistical connections;    Boltzmann-Gibbs entropy;    Boltzmann operator;   

DOI  :  10.3390/e15104042

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2013 by the authors; licensee MDPI, Basel, Switzerland.