Cluster-Aware Conformal Calibration for Spatio-Temporal Distributional Prediction

2026-06-04

AI Summary

This work addresses the challenge of calibrating prediction intervals in highly irregularly sampled spatiotemporal data, where conventional fixed-grid spatial basis functions fail to capture heterogeneity within clustered regions, leading to miscalibrated uncertainty estimates. The authors propose a deep Kriging extension that innovatively integrates spatial clustering information into both basis function design and conformal calibration. Specifically, basis centers and scales are adaptively initialized according to local sampling density, and prediction interval widths are dynamically adjusted within each spatial cluster, with a global fallback mechanism to handle sparsely observed areas. Experiments on synthetic data and PM$_{2.5}$ analysis demonstrate that the proposed method significantly outperforms global conformal baselines, achieving notably improved coverage accuracy and tail reliability—particularly when observations exhibit clustered spatial patterns.

Abstract

DeepKriging-style models, such as Spatio-Temporal DeepKriging, improve scalability through basis-function embeddings and stochastic gradient learning; however, fixed regular-grid spatial bases remain inefficient under highly non-uniform sampling patterns, often over-allocating capacity to sparse regions while under-resolving dense clusters. To address this limitation, we propose a practical extension of DeepKriging for reliable spatio-temporal distributional forecasting, incorporating cluster-adaptive spatial bases - whose centers and scales are initialized from {the spatial sampling density} - to better capture heterogeneous spatial sampling, together with cluster-aware conformal calibration that determines prediction-interval widths within spatial clusters (with a global fallback when calibration samples are insufficient). The resulting calibration pipeline explicitly targets spatial heterogeneity and local miscalibration, and experiments, including simulation studies and PM$_{2.5}$ data analysis, demonstrate substantially improved coverage accuracy and tail reliability under clustered observation patterns compared with a global conformal baseline.

Problem

• spatio-temporal prediction
• non-uniform sampling
• spatial heterogeneity
• distributional forecasting
• local miscalibration

Innovation

• cluster-adaptive spatial bases
• conformal calibration
• spatio-temporal distributional prediction
• spatial heterogeneity
• DeepKriging