Positional Encoder Graph Quantile Neural Networks for Geographic Data

TL;DR

This paper introduces PE-GQNN, a novel neural network framework that enhances spatial data modeling by improving predictive accuracy and uncertainty quantification through combining positional encoding, quantile estimation, and calibration techniques.

Contribution

The paper presents PE-GQNN, a new framework that integrates PE-GNNs with quantile neural networks and calibration methods for better density estimation and uncertainty quantification.

Findings

PE-GQNN outperforms existing models in accuracy and calibration on benchmark datasets.

The method extends naturally to non-spatial tasks.

It achieves these improvements with minimal additional computational cost.

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.