通过分布匹配自适应分箱，提升时间序列预测的不确定性量化鲁棒性。
DistMatch: Adaptive Binning via Distribution Matching for Robust Sequential Conformal Prediction
- 用KS统计量递归划分残差，构建近似可交换的叶子节点
- 在真实数据上显著优于现有方法，覆盖多种分布漂移场景
- 适合需要稳定置信区间的时间序列应用，如金融、气象
序列化置信预测（Sequential Conformal Prediction, CP）在残差可交换性假设下提供有效的不确定性量化。然而，真实时间序列常因时序依赖和分布漂移导致该假设不成立。尽管近期方法尝试通过重加权逼近可交换性，但最优权重的确定仍是开放问题。为此，本文提出DistMatch，一种基于分箱的方法：利用柯尔莫戈洛夫-斯米尔诺夫（KS）统计量，在二叉树中递归划分残差，理论上保证各叶子节点近似可交换，从而无需重加权。在每个叶子节点内使用在线更新的分位数回归，实现局部自适应推断，增强对分布漂移的鲁棒性。大量实验表明，DistMatch在多个真实数据集上均显著优于现有序列化CP方法。
原文摘要 · Abstract (English)
Sequential conformal prediction (CP) provides valid uncertainty quantification under the assumption of residual exchangeability. However, this assumption is often violated in real-world time series due to temporal dependencies and distributional shifts. While recent methods attempt to approximate exchangeability through reweighting, identifying optimal weights remains an open challenge. To address this limitation, we propose DistMatch, a binning-based method that recursively partitions residuals within a binary tree using the Kolmogorov-Smirnov (KS) statistic. We theoretically show that this partitioning induces approximately exchangeable leaves, thereby avoiding the need for reweighting. By applying quantile regression with online updates within each leaf, DistMatch enables locally adaptive inference and improves robustness to distributional shifts. Extensive experiments demonstrate that DistMatch outperforms existing sequential CP methods.
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