Residual Reweighted Conformal Prediction for Graph Neural Networks

2025-06-09

AI Summary

Graph Neural Networks (GNNs) face deployment limitations in high-stakes applications due to the absence of calibrated, quantifiable uncertainty estimates. Existing conformal prediction (CP) methods for graphs provide statistical validity but yield overly conservative prediction sets; they neglect graph-specific characteristics—including heteroscedasticity, structural bias, and community heterogeneity—while residual reweighting variants fail to address topology-awareness and training-data leakage. Method: We propose RR-GNN, a novel conformal GNN framework featuring: (i) Mondrian hierarchical clustering for principled graph community partitioning; (ii) a residual-adaptive nonconformity score enabling cluster-conditional coverage; and (iii) a cross-training protocol eliminating information leakage. Contribution/Results: Evaluated on 15 real-world graph datasets, RR-GNN achieves significantly tighter prediction sets while strictly maintaining marginal coverage guarantees. It consistently outperforms state-of-the-art conformal graph learning approaches across all benchmarks.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Graph Neural Networks (GNNs) excel at modeling relational data but face significant challenges in high-stakes domains due to unquantified uncertainty. Conformal prediction (CP) offers statistical coverage guarantees, but existing methods often produce overly conservative prediction intervals that fail to account for graph heteroscedasticity and structural biases. While residual reweighting CP variants address some of these limitations, they neglect graph topology, cluster-specific uncertainties, and risk data leakage by reusing training sets. To address these issues, we propose Residual Reweighted GNN (RR-GNN), a framework designed to generate minimal prediction sets with provable marginal coverage guarantees. RR-GNN introduces three major innovations to enhance prediction performance. First, it employs Graph-Structured Mondrian CP to partition nodes or edges into communities based on topological features, ensuring cluster-conditional coverage that reflects heterogeneity. Second, it uses Residual-Adaptive Nonconformity Scores by training a secondary GNN on a held-out calibration set to estimate task-specific residuals, dynamically adjusting prediction intervals according to node or edge uncertainty. Third, it adopts a Cross-Training Protocol, which alternates the optimization of the primary GNN and the residual predictor to prevent information leakage while maintaining graph dependencies. We validate RR-GNN on 15 real-world graphs across diverse tasks, including node classification, regression, and edge weight prediction. Compared to CP baselines, RR-GNN achieves improved efficiency over state-of-the-art methods, with no loss of coverage.

Problem

• GNNs lack uncertainty quantification in high-stakes domains
• Existing CP methods produce overly conservative prediction intervals
• Current approaches neglect graph topology and cluster-specific uncertainties

Innovation

• Graph-Structured Mondrian CP for community-based coverage
• Residual-Adaptive Nonconformity Scores for dynamic intervals
• Cross-Training Protocol to prevent information leakage