Conformal Prediction for Spatially Dependent Data via Sequential Whitening

2026-10-07

AI Summary

This study addresses the failure of exchangeability assumptions in spatially dependent data, which leads to inadequate coverage and instability in conformal prediction intervals. To overcome this, we propose a sequential conditioning framework that calibrates residuals through sequential whitening to eliminate spatial heterogeneity. This approach is extended to large-scale networks via nearest-neighbor approximation, with theoretical bounds established for coverage loss under covariance misspecification. The method achieves distribution-free, finite-sample exact coverage and asymptotic oracle efficiency under arbitrary spatial designs. Empirical evaluations demonstrate that the proposed framework yields narrower and more stable prediction intervals. In a PM2.5 application, it effectively identifies regions at risk of undercoverage, significantly outperforming existing global and local methods.

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.

Problem

• conformal prediction
• spatial dependence
• prediction intervals
• exchangeability
• calibration residuals

Innovation

• Conformal Prediction
• Spatial Dependence
• Sequential Whitening
• Finite-Sample Coverage
• Oracle Efficiency