[Paper] GRAPHLCP: Structure-Aware Localized Conformal Prediction on Graphs

Source: arXiv - 2605.08074v1

Overview

Graph Neural Networks (GNNs) have become the go‑to tool for learning on relational data, but quantifying the uncertainty of their predictions remains an open problem. The paper GRAPHLCP: Structure‑Aware Localized Conformal Prediction on Graphs introduces a new conformal prediction (CP) framework that respects the underlying graph topology, delivering finite‑sample coverage guarantees while producing much tighter prediction sets than prior methods.

Key Contributions

• Topology‑aware localization: Combines node features with graph structure (via Personalized PageRank) to define a more meaningful notion of “neighbourhood” for CP.
• Feature‑aware densification: A preprocessing step that enriches sparse regions of the graph, reducing the bias that arises when local data are scarce.
• Adaptive calibration weighting: Uses the structural proximity scores to weight calibration examples, allowing the method to capture both short‑range and long‑range dependencies.
• Theoretical guarantees: Proves marginal coverage under finite samples and provides empirical evidence of improved conditional coverage across multiple conditioning regimes.
• Extensive empirical validation: Benchmarks on several regression and classification graph datasets show that GRAPHLCP consistently yields smaller, more informative prediction sets while preserving the required coverage level.

Methodology

1. Embedding & Densification

   • Each node is first embedded using a standard GNN (e.g., GCN, GraphSAGE).
   • In sparse parts of the graph, the method injects synthetic “anchor” points derived from nearby feature distributions, mitigating the risk that a node has too few calibration neighbours.

2. Structural Proximity via Personalized PageRank (PPR)

   • For any test node, a PPR vector is computed, giving a weighted reachability score to every other node.
   • These scores serve as a kernel that quantifies how “close” each calibration node is to the test node, not just in embedding space but also in graph topology.

3. Localized Calibration

   • Calibration residuals (e.g., absolute errors for regression) are collected from the training set.
   • Each residual is assigned a weight proportional to its PPR‑based proximity to the test node.

4. Prediction Set Construction

   • The weighted empirical quantile of the calibration residuals is taken as the conformal threshold.
   • For classification, the same weighting scheme is applied to class‑wise scores to produce a set of plausible labels.

Because the weighting respects both feature similarity and graph connectivity, the resulting prediction sets are “localized” in a way that mirrors the true dependency structure of the data.

Results & Findings

• Coverage: All experiments meet or exceed the prescribed marginal coverage, confirming the theoretical guarantee.
• Conditional coverage: When conditioning on node degree, community membership, or feature density, GRAPHLCP’s coverage remains close to the target, whereas naïve CP (embedding‑only) often under‑covers high‑degree nodes.
• Efficiency: Prediction sets are 30‑45 % smaller on average, translating to more decisive downstream actions (e.g., fewer candidate labels to inspect).

Practical Implications

• Safer deployment of GNN‑based services: Whether you’re recommending friends, flagging fraudulent transactions, or predicting molecular properties, GRAPHLCP gives you a calibrated confidence interval or label set that respects the relational structure of your data.
• Active learning & data acquisition: Smaller, reliable prediction sets can be used to prioritize which nodes to label next, focusing effort on the most uncertain or high‑impact regions of the graph.
• Model‑agnostic plug‑in: The framework works with any off‑the‑shelf GNN encoder; you only need to run a PPR computation (efficiently approximated with power‑iteration) and the densification step.
• Regulatory compliance: In domains like finance or healthcare where explainability and risk bounds are mandatory, GRAPHLCP provides finite‑sample guarantees without assuming any distributional form.

Limitations & Future Work

• Scalability of exact PPR: Computing full‑graph PPR vectors can be costly for massive graphs; the authors rely on approximate methods, which may affect the tightness of the weighting.
• Densification heuristics: The synthetic anchor generation is heuristic; its effectiveness may vary across domains with highly heterogeneous feature spaces.
• Extension to dynamic graphs: The current formulation assumes a static graph; handling evolving edge structures would require incremental updates to the proximity kernel.
• Broader uncertainty metrics: Future research could explore integrating other uncertainty quantifiers (e.g., Bayesian GNNs) with the topology‑aware CP framework to further improve conditional coverage.

GRAPHLCP bridges a critical gap between rigorous uncertainty quantification and the relational nature of graph data, offering developers a practical tool to make GNN predictions both trustworthy and actionable.

Authors

• Peyman Baghershahi
• Fangxin Wang
• Debmalya Mandal
• Sourav Medya

Paper Information

• arXiv ID: 2605.08074v1
• Categories: cs.LG
• Published: May 8, 2026
• PDF: Download PDF