CIF: Small: Shared Information: Theory and Applications

这项研究开发了共享信息的概念，作为一个基本的，可量化的，紧凑的措施，捕捉多个相关信号之间的相互依赖性。它将试图模仿和加强克劳德香农的著名的和巨大的影响互信息的概念，构成了两个随机信号之间的相关性的措施的精神。共享信息的作用将在网络信息理论的操作意义与相关的通信应用程序的影响，并作为一个独立的，紧凑的，可计算的数字的优点，可以优化的学习应用程序中的统计相关性是中央利益的调查。目标是建立中心的理论和实践作用，共享信息在网络数据压缩，分布式函数计算，可靠和安全的网络信息传输，信号簇检测，以及一类新的统计估计和学习算法。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。技术方法涉及（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，包括组合树包装和网络函数计算的算法，特别是信号获取或全知;（iii）查询公共随机性;（iv）用于簇和社区检测的假设检验;（v）多用户数据压缩和信道传输;以及（vi）当信号的潜在概率分布未知时共享信息的估计。植根于信息论，该研究与组合图论算法（理论计算机科学）和相关的多臂强盗（学习）有着丰富的联系。它旨在通过新的模式和方法，突出终端之间的互动通信，以共享信息的概念为关键，在网络信息理论方面取得进展。链接到组合算法中的重要问题，通过共享信息的方式，突出了承诺新的理解和解决方案的解释。此外，使用相关的多臂强盗来估计共享信息将在机器学习的一个重要但新兴的领域引入模型、概念和算法。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。预期的研究成果包括多用户数据压缩和信道传输的交互式技术、组合树包装算法、相关信号簇检测方法以及相关信号参数估计的bandit算法。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.