Spatial Conformal Inference through Localized Quantile Regression
Hanyang Jiang, Yao Xie
TL;DR
The paper tackles uncertainty quantification for spatial data where exchangeability is violated due to heterogeneity. It introduces Localized Spatial Conformal Prediction (LSCP), which uses localized quantile regression on residuals from neighboring calibration points to build prediction intervals with valid coverage under spatial mixing and stationarity assumptions. The authors establish finite-sample bounds on the conditional coverage gap and prove asymptotic conditional coverage, offering rigorous guarantees beyond traditional i.i.d. frameworks. Empirically, LSCP yields tighter, more spatially consistent prediction intervals than existing conformal methods on synthetic and real spatial datasets, demonstrating practical impact for large-scale, heterogeneous spatial analyses.
Abstract
Reliable uncertainty quantification at unobserved spatial locations, especially in the presence of complex and heterogeneous datasets, remains a core challenge in spatial statistics. Traditional approaches like Kriging rely heavily on assumptions such as normality, which often break down in large-scale, diverse datasets, leading to unreliable prediction intervals. While machine learning methods have emerged as powerful alternatives, they primarily focus on point predictions and provide limited mechanisms for uncertainty quantification. Conformal prediction, a distribution-free framework, offers valid prediction intervals without relying on parametric assumptions. However, existing conformal prediction methods are either not tailored for spatial settings, or existing ones for spatial data have relied on rather restrictive i.i.d. assumptions. In this paper, we propose Localized Spatial Conformal Prediction (LSCP), a conformal prediction method designed specifically for spatial data. LSCP leverages localized quantile regression to construct prediction intervals. Instead of i.i.d. assumptions, our theoretical analysis builds on weaker conditions of stationarity and spatial mixing, which is natural for spatial data, providing finite-sample bounds on the conditional coverage gap and establishing asymptotic guarantees for conditional coverage. We present experiments on both synthetic and real-world datasets to demonstrate that LSCP achieves accurate coverage with significantly tighter and more consistent prediction intervals across the spatial domain compared to existing methods.