单变量分布的 Kullback-Leibler Divergence 精确表达式。

IF 2.1 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY
Entropy Pub Date : 2024-11-07 DOI:10.3390/e26110959
Victor Nawa, Saralees Nadarajah
{"title":"单变量分布的 Kullback-Leibler Divergence 精确表达式。","authors":"Victor Nawa, Saralees Nadarajah","doi":"10.3390/e26110959","DOIUrl":null,"url":null,"abstract":"<p><p>The Kullback-Leibler divergence (KL divergence) is a statistical measure that quantifies the difference between two probability distributions. Specifically, it assesses the amount of information that is lost when one distribution is used to approximate another. This concept is crucial in various fields, including information theory, statistics, and machine learning, as it helps in understanding how well a model represents the underlying data. In a recent study by Nawa and Nadarajah, a comprehensive collection of exact expressions for the Kullback-Leibler divergence was derived for both multivariate and matrix-variate distributions. This work is significant as it expands on our existing knowledge of KL divergence by providing precise formulations for over sixty univariate distributions. The authors also ensured the accuracy of these expressions through numerical checks, which adds a layer of validation to their findings. The derived expressions incorporate various special functions, highlighting the mathematical complexity and richness of the topic. This research contributes to a deeper understanding of KL divergence and its applications in statistical analysis and modeling.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"26 11","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11592849/pdf/","citationCount":"0","resultStr":"{\"title\":\"Exact Expressions for Kullback-Leibler Divergence for Univariate Distributions.\",\"authors\":\"Victor Nawa, Saralees Nadarajah\",\"doi\":\"10.3390/e26110959\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>The Kullback-Leibler divergence (KL divergence) is a statistical measure that quantifies the difference between two probability distributions. Specifically, it assesses the amount of information that is lost when one distribution is used to approximate another. This concept is crucial in various fields, including information theory, statistics, and machine learning, as it helps in understanding how well a model represents the underlying data. In a recent study by Nawa and Nadarajah, a comprehensive collection of exact expressions for the Kullback-Leibler divergence was derived for both multivariate and matrix-variate distributions. This work is significant as it expands on our existing knowledge of KL divergence by providing precise formulations for over sixty univariate distributions. The authors also ensured the accuracy of these expressions through numerical checks, which adds a layer of validation to their findings. The derived expressions incorporate various special functions, highlighting the mathematical complexity and richness of the topic. This research contributes to a deeper understanding of KL divergence and its applications in statistical analysis and modeling.</p>\",\"PeriodicalId\":11694,\"journal\":{\"name\":\"Entropy\",\"volume\":\"26 11\",\"pages\":\"\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-11-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11592849/pdf/\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Entropy\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.3390/e26110959\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Entropy","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.3390/e26110959","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0

摘要

库尔巴克-莱伯勒发散(KL 发散)是一种统计量度,用于量化两个概率分布之间的差异。具体来说,它评估了用一种分布来近似另一种分布时所损失的信息量。这一概念在信息论、统计学和机器学习等多个领域都至关重要,因为它有助于了解模型对基础数据的代表程度。在 Nawa 和 Nadarajah 的最新研究中,推导出了多变量分布和矩阵变量分布的 Kullback-Leibler 分歧精确表达的综合集合。这项工作意义重大,它扩展了我们对 KL 发散的现有认识,为 60 多种单变量分布提供了精确的表达式。作者还通过数值检验确保了这些表达式的准确性,这为他们的研究结果增加了一层验证。推导出的表达式包含各种特殊函数,凸显了该课题的数学复杂性和丰富性。这项研究有助于加深对 KL 发散及其在统计分析和建模中的应用的理解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Exact Expressions for Kullback-Leibler Divergence for Univariate Distributions.

The Kullback-Leibler divergence (KL divergence) is a statistical measure that quantifies the difference between two probability distributions. Specifically, it assesses the amount of information that is lost when one distribution is used to approximate another. This concept is crucial in various fields, including information theory, statistics, and machine learning, as it helps in understanding how well a model represents the underlying data. In a recent study by Nawa and Nadarajah, a comprehensive collection of exact expressions for the Kullback-Leibler divergence was derived for both multivariate and matrix-variate distributions. This work is significant as it expands on our existing knowledge of KL divergence by providing precise formulations for over sixty univariate distributions. The authors also ensured the accuracy of these expressions through numerical checks, which adds a layer of validation to their findings. The derived expressions incorporate various special functions, highlighting the mathematical complexity and richness of the topic. This research contributes to a deeper understanding of KL divergence and its applications in statistical analysis and modeling.

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
Entropy
Entropy PHYSICS, MULTIDISCIPLINARY-
CiteScore
4.90
自引率
11.10%
发文量
1580
审稿时长
21.05 days
期刊介绍: Entropy (ISSN 1099-4300), an international and interdisciplinary journal of entropy and information studies, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish as much as possible their theoretical and experimental details. There is no restriction on the length of the papers. If there are computation and the experiment, the details must be provided so that the results can be reproduced.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信