Positional Encoder Graph Quantile Neural Networks for Geographic Data
This addresses the need for reliable uncertainty quantification in geographic data applications, representing an incremental improvement by extending existing methods with new components.
The paper tackles the problem of poorly calibrated predictive distributions in Positional Encoder Graph Neural Networks for spatial data, proposing a novel framework that combines these with Quantile Neural Networks and other techniques to improve uncertainty quantification, resulting in outperformance of existing methods in accuracy and uncertainty without extra computational cost.
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.