Positional Encoder Graph Quantile Neural Networks for Geographic Data

TMLR Paper5669 Authors

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 identify important special cases arising from our formulation, including the PE-GNN.

Submission Length: Regular submission (no more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=MicosERoex&noteId=MicosERoex

Changes Since Last Submission: The modifications in this version are limited to the LaTeX source to ensure compliance with TMLR’s style requirements. In particular, the set of imported packages and their order of importation were adjusted so that the font and formatting conform to the official style file. No changes were made to the paper’s content, results, or structure.

Assigned Action Editor: ~Fred_Roosta1

Submission Number: 5669