SPATIAL CONFORMAL INFERENCE THROUGH LOCALIZED QUANTILE REGRESSION

ICLR 2026 Conference Submission15153 Authors

Keywords: Conformal prediction, uncertainty quantification, spatial statistics, machine learning

Abstract: Reliable uncertainty quantification at unobserved spatial locations, particularly for complex and heterogeneous datasets, is a key challenge in spatial statistics. Traditional methods like Kriging rely on strong distributional assumptions such as normality, which often fail in large-scale datasets, leading to unreliable intervals. Conformal prediction offers distribution-free coverage, yet most implementations rely on i.i.d. data and ignore spatial dependence. We propose Localized Spatial Conformal Prediction (LSCP), a model-agnostic framework that couples local quantile regression with conformal calibration to produce spatially adaptive prediction intervals. LSCP conditions on neighborhoods in space to capture local heterogeneity and relaxes i.i.d. requirements: it retains finite-sample marginal coverage under exchangeability and, under stationarity and spatial mixing, attains asymptotic conditional coverage. Across synthetic and real datasets, LSCP consistently achieves near-nominal coverage with tighter and more stable intervals than other existing CP methods.

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

Submission Number: 15153