Conformal Graph Prediction with Z-Gromov Wasserstein Distances

2026-03-04 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Life Sciences & Biology · Depth: Expert, extended

Summary

A new conformal prediction framework has been developed for supervised graph prediction, addressing the challenge of uncertainty quantification for graph-valued outputs. This framework provides distribution-free coverage guarantees in structured output spaces by defining nonconformity using the Z-Gromov-Wasserstein (Z-GW) distance, practically implemented via Fused Gromov-Wasserstein (FGW) for permutation-invariant graph comparison. To enhance adaptability, the authors introduce Score Conformalized Quantile Regression (SCQR), an extension of Conformalized Quantile Regression (CQR) tailored for complex graph-valued outputs. The approach was evaluated on a synthetic image-to-graph task (Coloring dataset) and a real-world molecule identification problem using mass spectrometry data (MassSpecGym benchmark), demonstrating empirical coverage close to the nominal 90% level. SCQR, particularly when conditioned on spectral embeddings, significantly reduced conformal set sizes in metabolite retrieval.

Key takeaway

For research scientists developing graph prediction models, this framework offers a robust method for quantifying uncertainty in graph-valued outputs. You should consider integrating Z-Gromov-Wasserstein distances for nonconformity scoring and implementing Score Conformalized Quantile Regression (SCQR) to achieve adaptive, efficient, and statistically valid prediction sets, especially in applications like molecular identification where experimental validation is costly.

Key insights

Conformal prediction for graph-valued outputs ensures coverage guarantees using Z-Gromov-Wasserstein distances and adaptive SCQR.

Principles

• Permutation invariance is crucial for graph comparison.
• Conformal prediction offers distribution-free coverage guarantees.
• Adaptive thresholds improve efficiency in heteroscedastic data.

Method

The method defines nonconformity via Z-Gromov-Wasserstein distance, then applies Score Conformalized Quantile Regression (SCQR) to calibrate conditional quantiles of this score, generating locally adaptive prediction sets for graphs.

In practice

• Use FGW for permutation-invariant graph comparisons.
• Condition SCQR on input-dependent attributes like embeddings.
• Apply to molecular identification from mass spectra.

Topics

• Conformal Prediction
• Graph Prediction
• Z-Gromov–Wasserstein Distance
• Score Conformalized Quantile Regression
• Uncertainty Quantification

Best for: Research Scientist, AI Researcher, AI Scientist, AI Student

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.