A categorical characterization of relative entropy on standard Borel spaces
Information Theory
2024-02-14 v6 math.IT
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.
Keywords
Cite
@article{arxiv.1703.08853,
title = {A categorical characterization of relative entropy on standard Borel spaces},
author = {Nicolas Gagne and Prakash Panangaden},
journal= {arXiv preprint arXiv:1703.08853},
year = {2024}
}