Conference: Statistics Beyond Euclid: Functional Data, Random Objects and AI

The conference "Statistics Beyond Euclid: Functional Data, Random Objects and AI" will be held on November 13–14, 2026, at the University of California, Davis. Modern scientific data is increasingly captured in complex, non-traditional formats—such as the evolving shape of a virus, the connectivity patterns of a social network, or the continuous movement recorded by a wearable health monitor. Unlike simple numbers or coordinates, these "non-Euclidean" objects do not follow standard geometric rules, rendering traditional statistical tools ineffective for making accurate predictions or quantifying uncertainty. This project supports a landmark conference that brings together world-leading statisticians and artificial intelligence (AI) researchers to develop a new mathematical language for these data types. By integrating rigorous statistical reasoning with modern AI, the conference aims to create reliable methods for analyzing complex structures, ensuring that breakthroughs in technology are grounded in mathematical rigor. These advancements are vital for progress in diverse fields, from biomedical imaging to climate modeling. Furthermore, the project serves a critical national interest by providing travel support and mentorship to graduate students and early-career scientists, ensuring that the next generation of the American workforce is prepared to lead in the rapidly advancing landscape of data science and AI.

The conference "Statistics Beyond Euclid: Functional Data, Random Objects and AI" addresses the urgent need for foundational statistical methodology for data residing in general metric and geometric spaces, such as probability distributions, covariance matrices, manifolds, and functional trajectories. While modern deep learning architectures and large language models (LLMs) offer unprecedented computational power, they often lack the rigorous framework necessary to handle structured, non-Euclidean data or to provide valid uncertainty quantification. This project facilitates an interdisciplinary exchange among researchers in functional data analysis (FDA), metric-space statistics, and machine learning to address these challenges. Key focal points include extending FDA beyond Hilbert-space formulations, developing Fréchet regression and inference for object-valued outcomes, and creating geometry-aware AI architectures that respect the intrinsic properties of the response space. By exploring emerging frontiers such as causal inference for random objects and conformal inference in metric spaces, this conference aims to establish a robust theoretical and methodological bridge between classical statistical theory and modern AI applications for complex data structures. The conference website is: https://anson.ucdavis.edu/statisticsbeyondeuclid/.

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.

Award Number: 2623506
Principal Investigator: Jiming Jiang
Funds Obligated: $20,000
State: CA