NSF-DMS 2610696 (Starting 07/15/2026, three years, single-PI)
This project tackles a foundational challenge in modern data analysis: providing reliable measures of confidence for the unobserved structures in large, complex datasets that are often organized as matrices and/or networks. Recovering these structures from massive, noisy data, typically done by factorizing complex matrix/network measurements into compact, interpretable, and accessible summaries that reveal meaningful signal and support downstream decision-making, has emerged as a powerful strategy. As data scales and complexity grow, accurate recovery of these structures requires principled, rigorous, and easy-to-implement uncertainty quantification methods, enabling researchers and decision-makers to assess the reliability of the inferred structures with confidence. This project will address these challenges by developing new theory, methodology, and practical tools for uncertainty quantification in complex, high-dimensional data. In addition, it will also lead to broad impacts through the development of publicly available interfaces, the creation of a new relevant graduate-level course, and the training of graduate students across statistics, informatics, biostatistics, and mathematics, fostering interdisciplinary collaboration.
