为函数型模型提供自适应的不确定性预测，提升高风险场景下的可靠性。
Locally Adaptive Conformal Inference for Operator Models
- 基于局部切片的校准方法，实现函数值预测集的自适应生成。
- 在真实数据上覆盖误差更小，且对偏差和分布外噪声更鲁棒。
- 适合需要精准不确定性评估的物理模拟与时空预测任务。
算子模型是函数空间之间的回归算法，在时空预测与物理模拟中日益重要，尤其在需要稳健、校准的不确定性量化高风险场景中。本文提出局部切片共形推断（LSCI），一种无需分布假设的框架，用于为算子模型生成函数值、局部自适应的预测集。我们证明了有限样本下的有效性，并在局部可交换性假设下推导出覆盖误差的依赖数据上界。在合成高斯过程任务及真实应用（空气质量监测、能源需求预测、天气预报）中，LSCI生成的预测集更紧凑且自适应性更强，优于传统共形基准。同时，实验还验证了其对偏差预测和特定分布外噪声的鲁棒性。
原文摘要 · Abstract (English)
Operator models are regression algorithms between Banach spaces of functions. They have become an increasingly critical tool for spatiotemporal forecasting and physics emulation, especially in high-stakes scenarios where robust, calibrated uncertainty quantification is required. We introduce Local Sliced Conformal Inference (LSCI), a distribution-free framework for generating function-valued, locally adaptive prediction sets for operator models. We prove finite-sample validity and derive a data-dependent upper bound on the coverage gap under local exchangeability. On synthetic Gaussian-process tasks and real applications (air quality monitoring, energy demand forecasting, and weather prediction), LSCI yields tighter sets with stronger adaptivity compared to conformal baselines. We also empirically demonstrate robustness against biased predictions and certain out-of-distribution noise regimes.
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