CIF: Small: Shared Information: Theory and Applications

CIF：小：共享信息：理论与应用

• 批准号: 2310203
• 负责人: Prakash Narayan
• 金额: $ 60万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-05-15 至 2026-04-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2310203&HistoricalAwards=false
• 关键词: CIF; Small; Shared; Information; Theory

This research develops the concept of shared information as a fundamental, quantifiable, and compact measure for capturing interdependence among multiple correlated signals. It will seek to emulate and enhance the spirit of Claude Shannon’s celebrated and enormously consequential notion of mutual information which constitutes a measure of correlation between two random signals. The role of shared information will be investigated for operational meanings in network information theory with implications for related communication applications and as a self-contained, compact, and calculable figure-of-merit that can be optimized in learning applications where statistical correlation is of central interest. The goal is to establish central theoretical and practical roles for shared information in network data compression, distributed function computation, reliable and secure information transmission in networks, signal cluster detection, and a new category of statistical estimation and learning algorithms. Engineering applications include communication and signal processing in a smart home, satellite image reconstruction, and messaging protocols in automated guided vehicles and drone swarms.The technical approach involves (i) establishing basic properties of shared information; (ii) examining its role in common randomness generation including algorithms for combinatorial tree packing and network function computation, especially signal acquisition or omniscience; (iii) querying common randomness; (iv) hypothesis testing for cluster and community detection; (v) multiuser data compression and channel transmission; and (vi) estimation of shared information when the underlying probability distribution of the signals is unknown. Rooted in information theory, the research has rich connections to algorithms in combinatorial graph theory (in Theoretical Computer Science) and correlated multiarmed bandits (in Learning). It aims to create advances in network information theory through new models and methods that highlight interactive communication among the terminals, with the concept of shared information serving as a linchpin. Links to important problems in combinatorial algorithms, by way of shared information, highlight interpretations that promise new understanding and solutions. Furthermore, the estimation of shared information using correlated multiarmed bandits will introduce models, concepts, and algorithms in an essential but fledgling realm of machine learning. The research will be accomplished using methods from information theory, Markov random fields, combinatorial graph theory, and statistical inference. Expected research outcomes include interactive techniques for multiuser data compression and channel transmission, algorithms for combinatorial tree packing, methods for detecting clusters of correlated signals, and bandit algorithms for parameter estimation in correlated signals.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.

这项研究将共享信息的概念发展为一种基本的、可量化的、紧凑的措施，用于捕获多个相关信号之间的相互依赖关系，它将寻求模仿和增强克劳德·香农著名的、具有重大影响的互信息概念的精神，该概念构成了一种衡量信息的方法。两个随机信号之间的相关性将研究网络信息理论中的操作意义，以及对相关通信应用的影响，并作为一个独立的、紧凑的、可计算的、可以优化的品质因数。目标是在网络数据压缩、分布式函数计算、网络中可靠和安全的信息传输、信号簇检测和新类别中建立共享信息的中心理论和实践角色。工程应用包括智能家居中的通信和信号处理、卫星图像重建以及自动引导车辆和无人机群中的消息传递协议。技术方法包括（i）建立共享信息的基本属性；（ii）检查其在常见随机性生成中的作用，包括算法组合树打包和网络函数计算，特别是信号采集或全知性；(iv) 集群和社区检测的假设检验；​​(v) 多用户数据压缩和信道传输；当信号的潜在概率分布未知时，该研究与组合图论（理论计算机科学）和相关多臂老虎机（学习）中的算法有丰富的联系。理论通过强调终端之间的交互通信的新模型和方法，以共享信息的概念为关键，通过共享信息链接到组合算法中的重要问题，强调新的理解和解决方案的解释。使用相关多臂老虎机估计共享信息将在机器学习的一个重要但新兴领域引入模型、概念和算法，该研究将使用信息论、马尔可夫随机场、组合图论和统计推断的方法来完成。研究成果包括多用户数据压缩和信道传输的交互技术、组合树打包算法、相关信号簇检测方法以及相关信号参数估计的强盗算法。该奖项反映了 NSF 的法定使命，并被认为值得支持通过使用基金会的智力优点和更广泛的影响审查标准进行评估。

项目成果

Shared Information for the Cliqueylon Graph

Cliqueylon 图的共享信息

• 发表时间: 2023-06
• 期刊: Proceedings of the 2023 IEEE International Symposium on Information Theory
• 作者: Bhattacharya, S;Narayan, P
• 通讯作者: Narayan, P

Shared Information for a Markov Chain on a Tree

树上马尔可夫链的共享信息

• 发表时间: 2024-01
• 期刊: IEEE transactions on information theory
• 影响因子: 2.5
• 作者: Bhattacharya, S;Narayan, P.
• 通讯作者: Narayan, P.

Shared Information for the Cliqueylon Graph

Cliqueylon 图的共享信息

• 发表时间: 2023-06
• 期刊: Proceedings of the 2023 IEEE International Symposium on Information Theory
• 作者: Bhattacharya, S;Narayan, P.
• 通讯作者: Narayan, P.