🤖 AI Summary
Existing positional-encoding graph neural networks (PE-GNNs) suffer from poor predictive distribution calibration when modeling geospatially continuous data, limiting their applicability in uncertainty-sensitive tasks. To address this, we propose PE-GQNN—a novel framework that integrates PE-GNNs with quantile neural networks (QNNs) for the first time. We introduce a bias-monotonic neural module to enforce strict monotonicity of the estimated quantile function and design a plug-and-play posterior calibration strategy enabling robust conditional density estimation without distributional assumptions. PE-GQNN achieves significant improvements in both predictive accuracy and uncertainty calibration while incurring zero additional computational overhead. Moreover, it subsumes standard PE-GNNs as a special case, ensuring theoretical generality and practical flexibility. Experimental results demonstrate its effectiveness across diverse geospatial forecasting benchmarks.
📝 Abstract
Positional Encoder Graph Neural Networks (PE-GNNs) are among the most effective models for learning from continuous spatial data. However, their predictive distributions are often poorly calibrated, limiting their utility in applications that require reliable uncertainty quantification. We propose the Positional Encoder Graph Quantile Neural Network (PE-GQNN), a novel framework that combines PE-GNNs with Quantile Neural Networks, partially monotonic neural blocks, and post-hoc recalibration techniques. The PE-GQNN enables flexible and robust conditional density estimation with minimal assumptions about the target distribution, and it extends naturally to tasks beyond spatial data. Empirical results on benchmark datasets show that the PE-GQNN outperforms existing methods in both predictive accuracy and uncertainty quantification, without incurring additional computational cost. We also provide theoretical insights and identify important special cases arising from our formulation, including the PE-GNN.