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arXiv · 1703.08853

A categorical characterization of relative entropy on standard Borel spaces

Nicolas Gagne·Prakash Panangaden
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Abstract

We give a categorical treatment, in the spirit of Baez and Fritz, of relative entropy for probability distributions defined on standard Borel spaces. We define a category suitable for reasoning about statistical inference on standard Borel spaces. We define relative entropy as a functor into Lawvere's category and we show convexity, lower semicontinuity and uniqueness.

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Nicolas Gagne, Prakash Panangaden. 2017-03-26. A categorical characterization of relative entropy on standard Borel spaces. https://doi.org/10.46298/lmcs-19(4%3A10)2023

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