Manifold Constrained Conformal Prediction For Spatial Distributions

We introduce a conformal prediction method for spatial distributions observed through finite samples of events, such as tropical cyclone genesis and earthquake locations. Our approach scores empirical measures using spherical sliced Wasserstein distance, then constrains the resulting prediction set to lie near the training data manifold. We derive a finite sample coverage lower bound for future empirical measures using a data adaptive manifold tolerance and then extend this to the underlying distribution by upper bounding the for sampling error. Because the resulting set is not analytically tractable, we introduce a modified flow based sampling procedure that represents candidate distributions by particle clouds and produces an ensemble over spatial distributions. Numerical experiments assess empirical measure coverage on synthetic data and compare energy distance and manifold distance on synthetic processes, tropical cyclone genesis, and earthquake occurrences.