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arXiv · 1308.5312

Examples of Application of Nonparametric Information Geometry to Statistical Physics

Giovanni Pistone
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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 equation

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Giovanni Pistone. 2013-08-24. Examples of Application of Nonparametric Information Geometry to Statistical Physics. https://doi.org/10.3390/e15104042

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