A categorical characterization of relative entropy on standard Borel spaces
arXiv:1703.08853 · doi:10.46298/lmcs-19(4:10)2023
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.