针对时间依赖的面板数据，提出在线校准的置信预测方法。
Online Conformal Prediction for Non-Exchangeable Panel Data
- 利用相关单位的实时观测数据作为校准集，动态调整权重和置信水平。
- 在真实与合成数据上，显著提升最差目标单位的覆盖率。
- 适合存在时间依赖和个体异质性的在线预测场景。
面板数据在科学与工程中广泛存在，其预测不确定性量化面临挑战：传统校准预测虽无需分布假设且模型无关，但依赖交换性假设，在时间相关性和单位异质性下失效。本文提出一种适用于非交换性面板数据的在线校准框架。核心思路是：当需对某单位进行预测时，可利用同期其他相关单位的已观测结果作为校准集。每轮预测中，基于历史相似性权重（突出与目标相似的校准单位）和自适应误覆盖水平（根据目标反馈动态更新），构建预测集。该双状态设计实现逐步覆盖保证与长期覆盖保障。实验表明，在合成与真实面板数据上，通过自适应区间宽度分配而非均匀扩大，显著提升了最差目标单位的覆盖率。两者互补：相似性权重在反馈稀疏时保障覆盖，自适应水平随反馈积累进一步优化覆盖效果。
原文摘要 · Abstract (English)
Panel data, in which multiple units are repeatedly observed over time, arise throughout science and engineering. Quantifying predictive uncertainty in such settings is challenging because conformal prediction, while distribution-free and model-agnostic, classically relies on exchangeability assumptions that fail under temporal dependence and unit heterogeneity. We propose a simple online conformal framework for non-exchangeable panel data. The method exploits a key feature of online panel prediction: when a forecast is required for one unit, contemporaneous outcomes from related units may already be observed and can serve as a calibration panel. At each round, prediction sets are formed using currently observed calibration units together with two adaptive quantities: history-based similarity weights that emphasize calibration units resembling the target, and an adaptive miscoverage level that is updated whenever target feedback is revealed. This two-state design yields a stepwise coverage bound and a long-run coverage guarantee. Empirically, across synthetic and real panel data sets, the method improves coverage on the worst-covered target units through adaptive interval-width allocation rather than uniform inflation. The two states are complementary: similarity weights protect coverage when target feedback is sparse, while the adaptive level further improves coverage as feedback accumulates.
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