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Graph Anomaly Detection as Dynamical Transport: Training-Free Scoring via Empirical Bayes

NeurIPS 2026 · Graph learning › Graph self-supervised learning · approach: Graph anomaly detection

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Proposes EB-GAD, a training-free node-level graph anomaly detector that fits a graph-aware generalized Ornstein-Uhlenbeck prior by empirical Bayes and scores nodes with a bank of finite-horizon control-energy and ratio scores chosen by a label-free selector.

Problem

Unsupervised node-level graph anomaly detection, where existing methods entangle graph trust, graph-spectral weighting, and anomaly-score choice in architectures and tuned objectives, yielding costly, opaque, and unstable scores across graph regimes.

Approach

Model normality as a graph-aware GOU process relaxing toward a graph-filtered template; fit graph precision by closed-form empirical Bayes on the residual field; score nodes by finite-horizon control energy (and scale-normalized ratio) that share one fitted prior, with equilibrium Mahalanobis as a limit.

Key results

• EB-GAD has best or tied-best AUROC on 9 of 11 benchmarks without labels, e.g., T-Finance 84.8 vs 63.1 best baseline (CoLA) and Elliptic 74.5 vs 65.3.
• Finite-horizon families add +3.6 (Facebook), +4.7 (T-Finance), and +4.7 (ACM) AUROC over the equilibrium score of the same configuration.
• Selector cutoffs perturbed by ±25% leave selection unchanged in 99.4% of evaluations.

Surprising findings

• Several baselines (DIF, DiffGAD) score below 50 AUROC on Elliptic and Elliptic++; an orientation audit attributes this to genuine native-score anti-correlation rather than missing data.
• The Weibo and Reddit results depend on a post-hoc anchor-bandwidth rule; with the likelihood-selected bandwidth they fall to 92.5 and 48.5.

Limitations

• Selector cutoffs are implementation defaults tuned on the benchmarks studied, not derived from a principle, and may not transfer.
• Gaussian residual model fails on binarized features (AUROC below 61) and is sensitive to multimodal normal populations (9 to 19 points).
• BlogCatalog and ACM trail TAM; heterophily is handled only via feature-affinity reweighting.

Experimental setup

Datasets: Weibo Reddit Amazon YelpChi BlogCatalog Facebook ACM T-Finance Elliptic Elliptic++ DGraph

Benchmarks: Weibo Reddit Amazon YelpChi BlogCatalog Facebook ACM Elliptic Elliptic++ DGraph T-Finance

Metrics: AUROC AUPRC

Baselines: LOF DIF ANOMALOUS DOMINANT AnomalyDAE CONAD CoLA DiffGAD TAM

Builds on: Ornstein-Uhlenbeck process Matern Gaussian processes on graphs empirical Bayes TAM PyGOD

Closest papers by meaning

• ARC: A Generalist Graph Anomaly Detector with In-Context Learning (NeurIPS 2024 · similarity 0.91)
• UniFORM: Towards Unified Framework for Anomaly Detection on Graphs (AAAI 2025 · similarity 0.90)
• DiffGAD: A Diffusion-based Unsupervised Graph Anomaly Detector (ICLR 2025 · similarity 0.90)
• Leveraging Diffusion Model as Pseudo-Anomalous Graph Generator for Graph-Level Anomaly Detection (ICML 2025 · similarity 0.90)
• UniGAD: Unifying Multi-level Graph Anomaly Detection (NeurIPS 2024 · similarity 0.90)
• ADA-GAD: Anomaly-Denoised Autoencoders for Graph Anomaly Detection (AAAI 2024 · similarity 0.89)