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

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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.