Examples of the Application of Nonparametric Information Geometry to Statistical Physics

Giovanni Pistone

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Examples of the Application of Nonparametric Information Geometry to Statistical Physics

机译：非参数信息几何在统计物理中的应用示例

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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.

机译：我们回顾了Amari信息几何的非参数版本，其中给定样本空间上的一组正概率密度具有图表集，从而形成了以Orlicz Banach空间为模型的可微流形。此非参数设置用于讨论机器学习和统计物理学中的典型问题的设置，例如黑盒优化，Kullback-Leibler发散，Boltzmann-Gibbs熵和Boltzmann方程。

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《Entropy》 |2013年第10期|共24页
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Giovanni Pistone;
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中图分类生理学;
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机译：非参数信息几何在统计物理中的应用实例
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Examples of the Application of Nonparametric Information Geometry to Statistical Physics

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