CRII: III: Advance mathematical theorems for Extreme Value and Risk Measure in Robust Intelligence

该奖项的全部或部分资金来自《2021年美国救援计划法案》(公法117-2)。风险在信息系统中普遍存在。它发生在从硬件/软件故障、网络攻击、人为错误到欺诈的各个领域。风险通常与发生概率较低的极端情景(也称为长尾事件)有关，但一旦发生，就会带来巨大损失。因此，风险管理对于确保信息系统的健壮性和智能性至关重要。该项目将开发具有长尾的高维(HD)数据的风险度量。该项目克服了缺乏尾部数据、风险衡量和参数估计的维度以及高清风险衡量的数学性质不发达等方面的挑战。研究人员寻求推进数学风险度量，并为研究和教育做出贡献，使计算驱动的决策中的弹性风险管理成为可能。为了实现这一目标，该项目将通过提出数据密集型系统中高维风险度量的数学定理和科学方法来填补知识空白。研究活动包括：(I)通过集成Copula、极值理论和统计推理，开发新的针对重尾大数据的高维风险度量、风险分担和风险聚合方法；(Ii)深入了解风险度量的数学性质，探索高维风险度量具有理论保证(如渐近性、收敛)的统计推断新方法；(Iii)扩大重尾损失之间的相关性调查，特别是在极端条件下，并提出给定特定风险度量的最优决策策略。如果成功，该项目将为智能系统的风险量化和风险管理提供新的科学见解和数学定理/工具。它可以提高系统的安全性、稳定性和弹性，并增加美国在风险管理和最优决策方面的竞争力。将通过开发新的教学模块，推进面向计算的数学教育，以及提高科学、技术、工程和数学(STEM)劳动力发展的多样性和包容性来促进更广泛的影响。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影响审查标准进行评估，被认为值得支持。

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2).Risk is ubiquitous in information systems. It occurs in areas from hardware/software failure, cyber-attack, human error to fraud. Risk is usually associated with extreme scenarios (also called long tail events) that are of a low probability of happening, but, if once they happen, are tied to huge losses. Therefore, risk management is very critical to ensure robust information system and intelligence. This project will develop risk measurement for high-dimensional (HD) data with long tails. The project overcomes challenges caused by the lack of data on the tail, the dimensionality in risk measurement and parameter estimation, and the underdeveloped mathematical properties of HD risk measures. The investigator seeks to advance mathematical risk measures and contribute to research and education that enable resilient risk management in computing-driven decision-making.To achieve the goal, this project will fill the knowledge gaps by advancing mathematical theorems and scientific methods for high-dimensional risk measures in data-intensive systems. The research activities include: (i) developing new high-dimensional risk measures, risk sharing, and risk aggregation methods for big data with heavy tails by integrating Copula, extreme value theory, and statistical inferences; (ii) understanding in-depth mathematical properties of risk measures and exploring new methods of statistical inference with theoretical guarantees (e.g., asymptotic property, convergence) for high-dimensional risk measures; (iii) expanding the dependence investigation between heavy-tailed losses, especially under extreme conditions, and proposing the optimal decision-making strategy given specific risk measures. If successful, this project will provide new scientific insights and mathematical theorems/tools for intelligent systems' risk quantification and risk management. It can improve the system safety, stability, and resilience, and increase U.S. competitiveness in risk management and optimal decision making. Broader impacts will be promoted by developing new teaching modules, advancing computing-oriented math education, and improving diversity and inclusion in Science, Technology, Engineering, and Mathematics (STEM) workforce development.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.