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Energy-based Epistemic Uncertainty for Graph Neural Networks

NeurIPS 2024 · Graph learning › Graph self-supervised learning · approach: Graph domain adaptation · 3 citations (OpenAlex)

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Proposes GEBM, a post hoc energy-based epistemic uncertainty method for GNNs that aggregates energies at independent, local, and group scales via graph diffusion, with a Gaussian regularizer that makes the induced density integrable and an evidential reading for robust prediction.

Problem

Quantifying epistemic uncertainty of GNNs under distribution shifts that arise at different structural scales; logit-based energy models are overconfident far from training data and existing graph methods only partially address structure.

Approach

Interleave graph diffusion with energy marginalization to get independent, local, and group energies, regularize the logit-based joint energy with a class-conditional Gaussian prior so the density is integrable, and aggregate the three via log-sum-exp into one measure; the same model can be read as an evidential classifier.

Key results

• GCN-GEBM achieves the best average o.o.d.-detection rank over all datasets among epistemic and all uncertainty measures (e.g., rank 2.6 vs 3.1 for the second-best epistemic estimator on one dataset summary table).
• On average GEBM improves AUC-ROC by 5.8 to 10.9 percentage points (16%-32% relative) over a vanilla logit-based EBM across datasets.
• GEBM is best or second-best in o.o.d. separation on 6 of 7 anomaly types according to the abstract, and it is the only estimator effective across distribution shifts simultaneously.

Measured effects reported in the paper

Surprising findings

• Logit-based EBM energies diverge toward overconfidence far from training data, with probability bounded by (1/2)^(C*L') for piecewise affine classifiers.
• Many graph baselines perform well on the PageRank centrality shift mainly due to symmetric diffusion biasing toward high-degree nodes, and GEBM is less sensitive to this shift.

Limitations

• As a post hoc epistemic estimator, GEBM does not improve aleatoric uncertainty or its calibration.
• GEBM is less sensitive to the PageRank centrality shift and may need extra energy terms for such shifts.
• Restricted to homophilic node classification; the diffusion operator assumes smoothing is appropriate.

Experimental setup

Datasets: CoraML CoraML-LLM Citeseer PubMed Coauthor-Physics Coauthor-Computers Amazon Photos Amazon Computers

Benchmarks: CoraML CoraML-LLM Citeseer PubMed Coauthor-CS Coauthor-Physics Amazon Photo Amazon Computers

Metrics: AUC-ROC AUC-PR average rank accuracy ECE Brier score

Baselines: GCN-Ensemble GCN-MCD GCN-DropEdge BGCN GCN-Energy GNNSafe HEAT GPN SGCN G-DUQ

Builds on: GNNSafe Graph Posterior Network HEAT Posterior Network APPNP

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