Conformal Prediction for Spatially Dependent Data via Sequential Whitening
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.
Related
- COINS: Any-Stage-Valid and Utility-Oriented Sequential Conformal Prediction
- conformalForecast: An R package for sequential conformal prediction in time series
- Rolling Conformal Prediction in Sequential Model Training
- Conditional validity of prediction-powered inference for spatially dependent finite populations
- Conformal prediction regions for dependent censored lifetimes
BibTeX
@misc{sen2026conformal,
title = {{Conformal Prediction for Spatially Dependent Data via Sequential Whitening}},
author = {Ayush Baran Sen and Arkajyoti Saha},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10168},
eprint = {2610.10168},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10168},
}
RIS
TY - UNPB
TI - Conformal Prediction for Spatially Dependent Data via Sequential Whitening
AU - Ayush Baran Sen
AU - Arkajyoti Saha
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10168
UR - https://arxiv.org/abs/2610.10168
AB - 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.
ER -