标准Borel空间上相对熵的分类表征

IF 0.6 4区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Logical Methods in Computer Science Pub Date : 2023-11-09 DOI:10.46298/lmcs-19(4:10)2023

Nicolas Gagne, Prakash Panangaden

{"title":"标准Borel空间上相对熵的分类表征","authors":"Nicolas Gagne, Prakash Panangaden","doi":"10.46298/lmcs-19(4:10)2023","DOIUrl":null,"url":null,"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.","PeriodicalId":49904,"journal":{"name":"Logical Methods in Computer Science","volume":" 96","pages":"0"},"PeriodicalIF":0.6000,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A categorical characterization of relative entropy on standard Borel spaces\",\"authors\":\"Nicolas Gagne, Prakash Panangaden\",\"doi\":\"10.46298/lmcs-19(4:10)2023\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":49904,\"journal\":{\"name\":\"Logical Methods in Computer Science\",\"volume\":\" 96\",\"pages\":\"0\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-11-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Logical Methods in Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46298/lmcs-19(4:10)2023\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Logical Methods in Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/lmcs-19(4:10)2023","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}

引用次数: 0

摘要

在Baez和Fritz的精神下，我们给出了定义在标准Borel空间上的概率分布的相对熵的分类处理。我们定义了一个适合于在标准Borel空间上进行统计推理的范畴。我们将相对熵定义为Lawvere范畴的函子，并证明了它的凸性、下半连续性和唯一性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A categorical characterization of relative entropy on standard Borel spaces

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Logical Methods in Computer Science 工程技术-计算机：理论方法

CiteScore

1.80

自引率

0.00%

发文量

105

审稿时长

6-12 weeks

期刊介绍： Logical Methods in Computer Science is a fully refereed, open access, free, electronic journal. It welcomes papers on theoretical and practical areas in computer science involving logical methods, taken in a broad sense; some particular areas within its scope are listed below. Papers are refereed in the traditional way, with two or more referees per paper. Copyright is retained by the author. Topics of Logical Methods in Computer Science: Algebraic methods Automata and logic Automated deduction Categorical models and logic Coalgebraic methods Computability and Logic Computer-aided verification Concurrency theory Constraint programming Cyber-physical systems Database theory Defeasible reasoning Domain theory Emerging topics: Computational systems in biology Emerging topics: Quantum computation and logic Finite model theory Formalized mathematics Functional programming and lambda calculus Inductive logic and learning Interactive proof checking Logic and algorithms Logic and complexity Logic and games Logic and probability Logic for knowledge representation Logic programming Logics of programs Modal and temporal logics Program analysis and type checking Program development and specification Proof complexity Real time and hybrid systems Reasoning about actions and planning Satisfiability Security Semantics of programming languages Term rewriting and equational logic Type theory and constructive mathematics.