🤖 AI Summary
This work addresses the challenge of calibrated probabilistic forecasting for spatial point processes, such as tropical cyclone genesis and earthquake occurrences. The authors propose a novel conformal prediction framework that models spatial point clouds as empirical measures and employs (sliced) Wasserstein distance for scoring. A key innovation is the introduction of manifold constraints, which enforce predicted sets to adhere closely to the support manifold of the training data—a feature not previously explored in this context. The method provides theoretical lower bounds on coverage probability and incorporates a data-adaptive criterion to facilitate practical manifold selection. Experiments on synthetic, tropical cyclone, and earthquake datasets demonstrate that the approach achieves near-nominal coverage while significantly outperforming highest density region (HDR) methods and state-of-the-art generative baselines in terms of energy distance and manifold-aware metrics.
📝 Abstract
We introduce a new conformal prediction method that constructs calibrated prediction sets over collections of spatial events, such as tropical cyclone genesis and earthquake locations. Forecasting natural hazards has become increasingly important, due to their significant economic impact, and quantifying the uncertainty of predictions is critical for accurate risk assessment. Our approach works by representing spatial point clouds as empirical measures so that we can score them using (sliced) Wasserstein distance, then constraining the resulting distribution-valued prediction set to be supported only near the training data manifold. We derive a coverage lower bound for the intersected sets and show that, in practice, this gap can be made small through a simple data-adaptive selection criterion. Because the resulting set is not analytically tractable, we introduce a modified flow-based sampling procedure, which allows us to represent and apply these prediction sets in practice as ensembles. Numerical experiments on synthetic data, tropical cyclone genesis, and earthquake occurrences show that our method achieves near-nominal coverage, with significantly lower energy distance and manifold distance than highest predictive density region (HDR) baselines along with generative model baselines.