24: Uncertainty Quantification for Rare Events Leveraging Optimal Transport

Thomas M. Menino Convention & Exhibition Center 

Accurate event prediction lies at the center of critical decision making in domains such as wildfire, earthquake and tropical cyclone prediction, where events are commonly modeled as point processes on a sphere. Recent advances in machine learning
have moved from point predictions to more complex structures including sets, distributions, and clouds of possible events, however, uncertainty quantification for these distributional structures remains a challenge.

We introduce a conformal prediction framework for spherical point processes based on optimal transport, utilizing spherical sliced Wasserstein as a conformity score along with a gradient based velocity field that generates ensembles of point clouds lying at
the boundary of our conformal region. By comparing predicted and observed event patterns in a geometrically faithful way, our method yields distribution-free prediction regions with finite sample validity. We demonstrate our approach on synthetic and real datasets with differing underlying manifolds, providing visual and quantitative uncertainty summaries over the space of point-process realizations.

Conformal Prediction

Optimal Transport

Spherical Sliced Wasserstein

Uncertainty Quantification

Point Processes

Natural Disaster Forecasting 

Section on Nonparametric Statistics