A Cubing Strategy for Identifying Stable Hyperparameter Regions for Uncertainty Quantification in Spatial Deep Learning

Abstract

Spatially referenced datasets have become increasingly prevalent across many fields, largely driven by advances in data collection methods such as satellite remote sensing. In many applications, predictions at unobserved locations are accompanied by reliable uncertainty estimates. While deep learning methods provide both scalable and accurate models for spatial predictions, there remains no clear consensus for addressing uncertainty quantification in spatial deep learning. Monte Carlo (MC) dropout has become a popular approach for uncertainty quantification, yet existing implementations typically focus on tuning the dropout rate while fixing other influential hyperparameters, such as weight decay and the predictive standard deviation multiplier, often through ad-hoc or manual tuning. We propose a cubing-based diagnostic framework that recursively partitions the hyperparameter space to identify stable regions where MC dropout yields well-calibrated predictive intervals. The approach evaluates hyperparameter regions using scoring rules relative to a statistical baseline model, which serves as a calibration anchor. Through a simulation study spanning multiple spatial dependence regimes as well as a large remotely-sensed land surface temperature dataset, we demonstrate that our approach produces competitive or superior predictive intervals compared to the baseline model. Our methodology provides practitioners with a systematic procedure for incorporating uncertainty quantification into spatial deep learning models.