一句话：为标准 Borel 空间上的概率分布建立范畴论框架，将相对熵刻画为到 Lawvere 范畴的函子并证其凸性、下半连续与唯一性。
本文研究标准 Borel 空间上概率分布的相对熵的范畴论刻画。相对熵（KL 散度）是统计推断与信息论的核心量，但此前范畴论处理多集中于离散或一般测度空间。作者受 Baez 与 Fritz 工作启发，构建了一个适合在标准 Borel 空间上推理统计推断的范畴，并将相对熵定义为从该范畴到 Lawvere 范畴的函子。关键结果是证明该相对熵函子具有凸性、下半连续性和唯一性。这些性质以范畴论方式给出相对熵的特征，为概率分布与统计推断提供了统一的形式语义基础。
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.
@article{paperbot2184,
title = {A categorical characterization of relative entropy on standard Borel spaces},
author = {Nicolas Gagne and Prakash Panangaden},
journal = {Logical Methods in Computer Science},
volume = {Volume 19, Issue 4},
year = {2023},
doi = {10.46298/lmcs-19(4:10)2023}
}