Next Article in Journal
Navigating the Chemical Space of HCN Polymerization and Hydrolysis: Guiding Graph Grammars by Mass Spectrometry Data
Next Article in Special Issue
The Phase Space Elementary Cell in Classical and Generalized Statistics
Previous Article in Journal
Evaluating the Spectrum of Unlocked Injection Frequency Dividers in Pulling Mode
Previous Article in Special Issue
Theoretical Foundations and Mathematical Formalism of the Power-Law Tailed Statistical Distributions
Article Menu

Export Article

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

Examples of the Application of Nonparametric Information Geometry to Statistical Physics

De Castro Statistics Initiative, Collegio Carlo Alberto, Via Real Collegio 30, Moncalieri 10024, Italy
Received: 15 August 2013 / Revised: 13 September 2013 / Accepted: 16 September 2013 / Published: 25 September 2013
(This article belongs to the Collection Advances in Applied Statistical Mechanics)
View Full-Text   |   Download PDF [278 KB, uploaded 24 February 2015]

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. View Full-Text
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 (CC BY 3.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

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

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top