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Entropy 2013, 15(10), 4042-4065; doi:10.3390/e15104042
Article

Examples of the Application of Nonparametric Information Geometry to Statistical Physics

Received: 15 August 2013; in revised form: 13 September 2013 / Accepted: 16 September 2013 / Published: 25 September 2013
(This article belongs to the collection Advances in Applied Statistical Mechanics)
Download PDF [278 KB, uploaded 25 September 2013]
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 information geometry; exponential manifold; statistical connections; Boltzmann-Gibbs entropy; Boltzmann operator
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Pistone, G. Examples of the Application of Nonparametric Information Geometry to Statistical Physics. Entropy 2013, 15, 4042-4065.

AMA Style

Pistone G. Examples of the Application of Nonparametric Information Geometry to Statistical Physics. Entropy. 2013; 15(10):4042-4065.

Chicago/Turabian Style

Pistone, Giovanni. 2013. "Examples of the Application of Nonparametric Information Geometry to Statistical Physics." Entropy 15, no. 10: 4042-4065.


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