Positional Encoder Graph Quantile Neural Networks for Geographic Data
Keywords: Graph Neural Networks (GNNs); Quantile regression; Geospatial data; Uncertainty quantification; Calibration; Model recalibration.
TL;DR: We propose PE-GQNN, which combines GNNs, quantile loss, and recalibration to improve uncertainty quantification and predictive accuracy in spatial data, outperforming current methods without increasing computational complexity.
Abstract: Positional Encoder Graph Neural Networks (PE-GNNs) are a leading approach for modeling continuous spatial data. However, they often fail to produce calibrated predictive distributions, limiting their effectiveness for uncertainty quantification. We introduce the Positional Encoder Graph Quantile Neural Network (PE-GQNN), a novel method that integrates PE-GNNs, Quantile Neural Networks, and recalibration techniques in a fully nonparametric framework, requiring minimal assumptions about the predictive distributions. We propose a new network architecture that, when combined with a quantile-based loss function, yields accurate and reliable probabilistic models without increasing computational complexity. Our approach provides a flexible, robust framework for conditional density estimation, applicable beyond spatial data contexts. We further introduce a structured method for incorporating a KNN predictor into the model while avoiding data leakage through the GNN layer operation. Experiments on benchmark datasets demonstrate that PE-GQNN significantly outperforms existing state-of-the-art methods in both predictive accuracy and uncertainty quantification.
Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
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Submission Number: 10833
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