CIF: Small: Bridging the Inequality Gap

CIF：小：缩小不平等差距

基本信息

批准号：
1907786
负责人：
Robert Nowak
金额：
$ 15万
依托单位：
University of Wisconsin-Madison
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-08-01 至 2021-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1907786&HistoricalAwards=false
关键词：
CIF Small Bridging Inequality Gap

项目摘要

Inequalities are a vital component of information theory and comprise one of the most versatile mathematical tools in an information theorist's toolbox. Breakthroughs in obtaining strong information inequalities have invariably led to significant progress on longstanding open problems in information theory, and in turn contribute to the advancement of computer science, probability theory, and combinatorics. This project aims to advance the state-of-the-art knowledge of information inequalities by identifying and addressing key gaps in the existing literature. Being able to provide a better characterization of information inequalities and narrowing existing gaps can greatly increase our understanding of what is feasible in many computationally intractable problems in computer science and mathematics. The project will also support the educational goals of the investigator by training multiple graduate students working at the interface of engineering and mathematics.The project consists of a specific set of research questions that will uncover novel theoretical aspects of information inequalities and will lead to new mathematical strategies to establish novel inequalities. The work will be divided into the following sub-projects, each with a distinct set of research objectives: (1) Perform stability analyses of fundamental information inequalities; (2) Develop a principled approach for establishing new information inequalities by leveraging sub-additivity properties in information theory; and (3) Explore applications of stability results and proof strategies to areas beyond information theory, such as probability, queuing theory, and combinatorics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

不平等是信息理论的重要组成部分，它是信息理论工具箱中用途最广泛的数学工具之一。获得强大信息不平等的突破总是导致信息理论中长期开放问题的重大进展，进而有助于计算机科学，概率理论和组合学的发展。该项目旨在通过识别和解决现有文献中的关键差距来提高信息不平等的最新知识。能够更好地表征信息不平等和缩小现有差距可以极大地增加我们对计算机科学和数学中许多计算棘手问题的可行问题的理解。该项目还将通过培训在工程和数学界面上工作的多个研究生来支持研究人员的教育目标。该项目包括一组特定的研究问题，这些问题将揭示信息不平等的新理论方面，并将导致新的数学策略建立新的不平等。这项工作将分为以下次项目，每个项目都有一组不同的研究目标：（1）对基本信息不平等的稳定分析；（2）开发一种原则性的方法来通过利用信息理论中的次级性能来建立新信息不平等；（3）探索稳定结果和证明策略在信息理论之外的领域的应用，例如概率，排队理论和组合学。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的智力优点和更广泛的影响来通过评估来支持的。