Quantile-Free Uncertainty Quantification in Graph Neural Networks

TL;DR

QpiGNN is a novel graph neural network framework that provides reliable, efficient, and robust uncertainty quantification without relying on quantile inputs or resampling, outperforming existing methods.

Contribution

It introduces a quantile-free approach to uncertainty quantification in GNNs with a dual-head architecture and theoretical guarantees, improving coverage and interval width.

Findings

Achieves 22% higher coverage on average compared to baselines.

Produces 50% narrower prediction intervals.

Demonstrates robustness to noise and structural shifts.

Abstract

Uncertainty quantification (UQ) in graph neural networks (GNNs) is crucial in high-stakes domains but remains a significant challenge. In graph settings, message passing often relies on strong assumptions such as exchangeability, which are rarely satisfied in practice. Moreover, achieving reliable UQ typically requires costly resampling or post-hoc calibration. To address these issues, we introduce Quantile-free Prediction Interval GNN (QpiGNN), a framework that builds on quantile regression (QR) to enable GNN-based UQ by directly optimizing coverage and interval width without requiring quantile inputs or post-processing. QpiGNN employs a dual-head architecture that decouples prediction and uncertainty, and is trained with label-only supervision through a quantile-free joint loss. This design allows efficient training and yields robust prediction intervals, with theoretical guarantees of asymptotic coverage and near-optimal width under mild assumptions. Experiments on 19 synthetic and real-world benchmarks show QpiGNN achieves average 22\% higher coverage and 50\% narrower intervals than baselines, while ensuring efficiency and robustness to noise and structural shifts.