CIF: Small: Bridging the Inequality Gap

CIF：小：缩小不平等差距

• 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

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.

不等式是信息论的重要组成部分，也是信息理论家工具箱中最通用的数学工具之一。获得强信息不平等的突破总是会在信息论中长期存在的开放问题上带来重大进展，进而促进计算机科学、概率论和组合学的进步。该项目旨在通过识别和解决现有文献中的关键差距来推进信息不平等的最新知识。能够更好地描述信息不平等并缩小现有差距，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性的理解。该项目还将通过培训多名在工程和数学交叉领域工作的研究生来支持研究者的教育目标。该项目由一组特定的研究问题组成，这些问题将揭示信息不平等的新颖理论方面，并将导致新的数学研究建立新的不平等的策略。该工作将分为以下子项目，每个子项目都有不同的研究目标：（1）对基本信息不平等进行稳定性分析； (2) 通过利用信息论中的次可加性性质，制定建立新信息不平等的原则方法； (3) 探索稳定性结果和证明策略在信息论之外的领域的应用，例如概率、排队论和组合学。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优势和更广泛的评估进行评估，认为值得支持。影响审查标准。

项目成果

Extracting robust and accurate features via a robust information bottleneck

通过稳健的信息瓶颈提取稳健且准确的特征

• DOI: 10.1109/jsait.2020.2991005
• 发表时间: 2020-05
• 期刊: IEEE Journal on Selected Areas in Information Theory
• 作者: Pensia, Ankit;Jog, Varun;Loh, Po
• 通讯作者: Loh, Po

Reverse Euclidean and Gaussian Isoperimetric Inequalities for Parallel Sets With Applications

平行集的逆欧几里得和高斯等周不等式及其应用

• DOI: 10.1109/tit.2021.3102828
• 发表时间: 2021-10
• 期刊: IEEE Transactions on Information Theory
• 影响因子: 2.5
• 作者: Jog; Varun
• 通讯作者: Varun

Estimating location parameters in sample-heterogeneous distributions

估计样本异质分布中的位置参数

• DOI: 10.1093/imaiai/iaab013
• 发表时间: 2021-06
• 期刊: Information and Inference: A Journal of the IMA
• 作者: Pensia, Ankit;Jog, Varun;Loh, Po
• 通讯作者: Loh, Po

Adversarial risk via optimal transport and optimal couplings

通过最佳运输和最佳耦合来对抗风险

• 发表时间: 2020-07
• 期刊: Proceedings of Machine Learning Research
• 作者: Pydi, Muni Sreenivas;Jog, Varun
• 通讯作者: Jog, Varun

Adversarial Risk via Optimal Transport and Optimal Couplings

通过最优传输和最优耦合的对抗风险

• DOI: 10.1109/tit.2021.3100107
• 发表时间: 2019-12-05
• 期刊: IEEE Transactions on Information Theory
• 影响因子: 2.5
• 作者: Muni Sreenivas Pydi;Varun Jog
• 通讯作者: Varun Jog