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Hierarchical Uncertainty-Aware Graph Neural Network

Yoonhyuk Choi, Jiho Choi, Taewook Ko, Chong-Kwon Kim

TL;DR

HU-GNN tackles semi-supervised node classification on graphs with varying homophily by integrating multi-scale representations (local, community, global) with principled uncertainty estimation in an end-to-end framework. It introduces uncertainty-guided local message passing, differentiable community pooling via Gumbel-Softmax, and a global integration node, with a loss that jointly optimizes accuracy and calibration. The paper provides PAC-Bayes generalization bounds, a contraction-based convergence proof, and robustness guarantees under heterophily, along with extensive experiments showing state-of-the-art resilience and interpretability. This approach yields practical benefits in noisy or adversarial environments while maintaining predictive performance across diverse graph structures.

Abstract

Recent research on graph neural networks (GNNs) has explored mechanisms for capturing local uncertainty and exploiting graph hierarchies to mitigate data sparsity and leverage structural properties. However, the synergistic integration of these two approaches remains underexplored. This work introduces a novel architecture, the Hierarchical Uncertainty-Aware Graph Neural Network (HU-GNN), which unifies multi-scale representation learning, principled uncertainty estimation, and self-supervised embedding diversity within a single end-to-end framework. Specifically, HU-GNN adaptively forms node clusters and estimates uncertainty at multiple structural scales from individual nodes to higher levels. These uncertainty estimates guide a robust message-passing mechanism and attention weighting, effectively mitigating noise and adversarial perturbations while preserving predictive accuracy on semi-supervised classification tasks. We also offer key theoretical contributions, including a probabilistic formulation, rigorous uncertainty-calibration guarantees, and formal robustness bounds. Extensive experiments on standard benchmarks demonstrate that our model achieves state-of-the-art robustness and interpretability.

Hierarchical Uncertainty-Aware Graph Neural Network

TL;DR

HU-GNN tackles semi-supervised node classification on graphs with varying homophily by integrating multi-scale representations (local, community, global) with principled uncertainty estimation in an end-to-end framework. It introduces uncertainty-guided local message passing, differentiable community pooling via Gumbel-Softmax, and a global integration node, with a loss that jointly optimizes accuracy and calibration. The paper provides PAC-Bayes generalization bounds, a contraction-based convergence proof, and robustness guarantees under heterophily, along with extensive experiments showing state-of-the-art resilience and interpretability. This approach yields practical benefits in noisy or adversarial environments while maintaining predictive performance across diverse graph structures.

Abstract

Recent research on graph neural networks (GNNs) has explored mechanisms for capturing local uncertainty and exploiting graph hierarchies to mitigate data sparsity and leverage structural properties. However, the synergistic integration of these two approaches remains underexplored. This work introduces a novel architecture, the Hierarchical Uncertainty-Aware Graph Neural Network (HU-GNN), which unifies multi-scale representation learning, principled uncertainty estimation, and self-supervised embedding diversity within a single end-to-end framework. Specifically, HU-GNN adaptively forms node clusters and estimates uncertainty at multiple structural scales from individual nodes to higher levels. These uncertainty estimates guide a robust message-passing mechanism and attention weighting, effectively mitigating noise and adversarial perturbations while preserving predictive accuracy on semi-supervised classification tasks. We also offer key theoretical contributions, including a probabilistic formulation, rigorous uncertainty-calibration guarantees, and formal robustness bounds. Extensive experiments on standard benchmarks demonstrate that our model achieves state-of-the-art robustness and interpretability.
Paper Structure (34 sections, 22 equations, 3 figures, 4 tables, 1 algorithm)

This paper contains 34 sections, 22 equations, 3 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Problem Formulation
  5. Graph Homophily
  6. Message-Passing Scheme
  7. Uncertainty Types
  8. Methodology
  9. Local Message-Passing
  10. Uncertainty‑aware attention.
  11. Low‑/high‑frequency decomposition.
  12. Aggregation.
  13. Community Assignment and Pooling
  14. Trainable assignment scores.
  15. Differentiable community selection.
  16. ...and 19 more sections

Figures (3)

  • Figure 1: The overall framework of HU-GNN, illustrating message‑passing and pooling for node $i$. Dashed lines indicate connections with low confidence, whereas solid lines represent connections with high confidence
  • Figure 2: (RQ2) Ablation study on HU-GNN under two perspectives: w/o community ($h_{C_m}$) and global information ($h_G$)
  • Figure 3: (RQ4) Hyperparameter analysis on the Cora and Chameleon dataset, varying $\beta_1$ (x-axis) and $\beta_2$ (y-axis) in Equation \ref{['overall_loss']}. Here, the z-axis represents validation accuracy