arXiv：cs.LG· Ayush Baran Sen, Arkajyoti Saha·· 4 小时前AI 评分37
基于顺序白化的空间依赖数据共形预测方法
Conformal Prediction for Spatially Dependent Data via Sequential Whitening
AI 导读
研究人员提出一种针对空间依赖数据的共形预测方法，通过对校准残差进行顺序条件化，并利用最近邻近似扩展到大规模网络，使预测区间在任意空间设计下具有精确的有限样本覆盖率。在模拟数据和全国 PM2.5 应用中，该方法生成的区间比全局和局部 SOTA 替代方案更窄、更稳定，并能识别存在覆盖失败风险的区域。
正文
Abstract:Split conformal prediction uses prediction errors on held-out (calibration) data to determine how wide the prediction intervals should be. It guarantees distribution-free finite-sample coverage when these errors and the error at the target site are exchangeable. This assumption may fail under spatial dependence and nonrandom sampling geometry. Existing spatial methods use fitting residuals to remove the predictable part of spatial variation from calibration and target errors. However, the spatial variation that only the calibration residuals can predict remains in both the target and calibration errors, reducing the efficiency and stability of the interval. We address this by additionally conditioning on the calibration residuals sequentially, which scales to large networks through nearest-neighbour approximations. Under a correct working covariance and an elliptical residual law, the resulting interval has exact finite-sample coverage under any spatial design, and under further conditions it is asymptotically oracle efficient. We also bound coverage loss under covariance misspecification and develop a diagnostic that identifies regions at risk of undercoverage. In simulated data, our method produces narrower and more stable intervals than global and localized state-of-the-art alternatives. In a national PM2.5 application, it produces narrower intervals within the network and identifies regions at risk of coverage failure.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG); Applications (stat.AP); Methodology (stat.ME) |
| Cite as: | arXiv:2610.10168 [stat.ML] |
| (or arXiv:2610.10168v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.10168 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Arkajyoti Saha [view email]
[v1]
Wed, 7 Oct 2026 14:44:21 UTC (864 KB)
来源：arXiv：cs.LG · arxiv.org