Uncertainty-Aware Graph Structure Learning

TL;DR

This work tackles the sensitivity of graph neural networks to suboptimal graph structures by introducing UnGSL, an uncertainty-aware graph structure learning module. UnGSL leverages node-level information quality, quantified by entropy, to modulate directional edge weights and enable asymmetric, confidence-based refinement of the learned graph, while remaining a lightweight plug-in for existing GSL methods. The authors provide theoretical insights showing how neighbor uncertainty propagates through aggregation and demonstrate substantial empirical gains across seven datasets and six GSL baselines, with robust performance under structural noise and across diverse GNN backbones. The proposed approach offers a practical, scalable path to more robust GNNs by directly incorporating information quality into graph structure learning, with future work aimed at finer uncertainty metrics and broader unsupervised settings.

Abstract

Graph Neural Networks (GNNs) have become a prominent approach for learning from graph-structured data. However, their effectiveness can be significantly compromised when the graph structure is suboptimal. To address this issue, Graph Structure Learning (GSL) has emerged as a promising technique that refines node connections adaptively. Nevertheless, we identify two key limitations in existing GSL methods: 1) Most methods primarily focus on node similarity to construct relationships, while overlooking the quality of node information. Blindly connecting low-quality nodes and aggregating their ambiguous information can degrade the performance of other nodes. 2) The constructed graph structures are often constrained to be symmetric, which may limit the model's flexibility and effectiveness. To overcome these limitations, we propose an Uncertainty-aware Graph Structure Learning (UnGSL) strategy. UnGSL estimates the uncertainty of node information and utilizes it to adjust the strength of directional connections, where the influence of nodes with high uncertainty is adaptively reduced. Importantly, UnGSL serves as a plug-in module that can be seamlessly integrated into existing GSL methods with minimal additional computational cost. In our experiments, we implement UnGSL into six representative GSL methods, demonstrating consistent performance improvements.

Figures (6)

• Figure 1: Performance varies with the ratios of eliminated neighbors on Cora and Citeseer datasets. Here we first constructed a graph based on GRCN yu2021graph. We then eliminate a certain ratio of neighbors with the highest entropy for each node, and evaluate the performance of GCN on such a pruned graph. For comparison, we also report the performance under random elimination.
• Figure 2: Illustration of how our UnGSL differs from existing embedding-based GSL methods. Existing GSL learns symmetric relationships, leading to a dilemma when managing connections between high-quality and low-quality nodes. In contrast, UnGSL learns asymmetric relationships, allowing low-quality nodes to benefit from high-quality nodes while mitigating the negative influence of low-quality nodes.
• Figure 3: Visualization of node entropy after GNN aggregation (i.e., $u_{i}$) alongside the average entropy of its neighbors (i.e., $\sum_{v_j \in \mathcal{N}{(v_i)}}\mathbf{\hat{A}}_{ij} u_{j}^{\prime}$) on Cora dataset.
• Figure 4: Comparsion of different $\beta$ on Cora and Citeseer datasets.
• Figure 5: Visualization of node entropy after GNN aggregation (i.e., $u_{i}$) alongside the average entropy of its neighbors (i.e., $\sum_{v_j \in \mathcal{N}{(v_i)}}\mathbf{\hat{A}}_{ij}u_{j}^{\prime}$) on Citeseer and Flickr datasets.

Theorems & Definitions (2)

• Proposition 1
• Lemma 1: Log-sum Inequality