发表机构
Department of Statistics University of Connecticut; Sandia National Laboratories（统计学系 美国康乃狄克大学; 桑地亚国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对空间事件预测，提出基于将空间点云表示为经验测度，用（切片）瓦瑟斯坦距离评分，并约束预测集在训练数据流形附近的新共形预测方法，经实验其在覆盖及距离指标上优于基线。
AI 中文摘要
我们引入了一种新的共形预测方法，用于在空间事件集合（如热带气旋生成和地震位置）上构建校准预测集。由于自然灾害的重大经济影响，预测自然灾害变得越来越重要，而量化预测的不确定性对于准确的风险评估至关重要。我们的方法通过将空间点云表示为经验测度，以便使用（切片）瓦瑟斯坦距离对其进行评分，然后将所得的分布值预测集约束为仅在训练数据流形附近得到支持。我们推导了相交集的覆盖下限，并表明在实践中，通过简单的数据自适应选择标准可以减小这个差距。由于所得集合在分析上不易处理，我们引入了一种改进的基于流的采样程序，使我们能够在实践中将这些预测集表示为集成并应用。在合成数据、热带气旋生成和地震发生方面的数值实验表明，我们的方法实现了接近名义覆盖，与最高预测密度区域（HDR）基线以及生成模型基线相比，能量距离和流形距离显著更低。
英文摘要
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.
Comments21 pages, 10 figures, 4 tables
