Examples of Application of Nonparametric Information Geometry to Statistical Physics
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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 equationKeywords
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- Version 1, 2013-08-24, ArXiv
- Published version: Entropy, 15 (10), 4042.
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