Spatial prediction intervals improve accuracy and stability with sequential whitening
Conformal Prediction for Spatially Dependent Data via Sequential Whitening
Machine Learning
Summary
When predicting numbers for places on a map, it's hard to know how confident to be because nearby places often influence each other. The authors created a new way to adjust predictions that carefully accounts for these connections between locations. Their method makes the range of possible values more dependable and often narrower than before, even when the map is oddly shaped. They tested it on simulated and real pollution data showing it gives better confidence intervals and spots areas where predictions might still be tricky.
What this means in practice
- •For environmental data analysts: Provide more accurate confidence intervals for pollution level predictions across geographic regions, improving risk assessment and policy decisions.
- •For geospatial data engineers: Build scalable prediction tools that adjust for spatial relationships to produce reliable interval estimates over large spatial networks.
Authors
Ayush Baran Sen, Arkajyoti Saha
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.