GRAPHLCP: Structure-Aware Localized Conformal Prediction on Graphs

2026-05-08

AI Summary

This work addresses the limitations of traditional conformal prediction in graph neural networks, which often ignores graph structure, leading to inefficient prediction sets and insufficiently discriminative embeddings. The paper proposes the first localized conformal prediction framework that explicitly integrates graph topology: it employs feature-aware graph densification to mitigate local bias induced by sparsity and introduces a personalized PageRank–based, structure-aware kernel to model both local and long-range dependencies among nodes, enabling more precise neighborhood calibration. The approach supports structure-aware anchor sampling and weighting, achieving marginal coverage guarantees under finite-sample settings while significantly improving conditional coverage efficiency across diverse graph regression and classification tasks, particularly in complex conditional scenarios.

Abstract

Conformal prediction (CP) provides a distribution-free approach to uncertainty quantification with finite-sample guarantees. However, applying CP to graph neural networks (GNNs) remains challenging as the combinatorial nature of graphs often leads to insufficiently certain predictions and indiscriminative embeddings. Existing methods primarily rely on embedding-space proximity for localization, which can be unreliable for graphs and yield inefficient prediction sets. We propose GRAPHLCP, a proximity-based localized CP framework that explicitly incorporates graph topology and inter-node dependencies into localization and weighting. Our approach introduces a feature-aware densification step to mitigate locality bias in sparse graphs, followed by a Personalized PageRank-based kernel computation to model structural proximity. This enables topology-dependent anchor sampling and calibration weighting that captures both local and long-range dependencies. Extensive experiments on several regression and classification datasets demonstrate that GRAPHLCP guarantees marginal coverage with finite samples while efficiently attaining favorable test conditional coverage across various conditioning scenarios.

Problem

• Conformal Prediction
• Graph Neural Networks
• Uncertainty Quantification
• Localized Prediction
• Graph Topology

Innovation

• Graph Neural Networks
• Conformal Prediction
• Localized Conformal Prediction
• Personalized PageRank
• Graph Topology