Graph Anomaly Detection as Finite-Horizon Control: Training-Free Scoring via Empirical Bayes

2026-09-29

AI Summary

This study addresses the limitations of existing graph anomaly detection architectures, where tight coupling leads to high scoring costs, poor interpretability, and weak cross-scenario generalization. To this end, we propose the EB-GAD framework, which models normality as a graph-aware generalized Ornstein-Uhlenbeck relaxation process and employs empirical Bayes inference to estimate precision parameters. Notably, this work pioneers the reformulation of anomaly scoring as finite-horizon closed-loop control energy and introduces an unsupervised selector to automatically adapt the optimal scoring family. Extensive experiments on eleven benchmark datasets demonstrate that, without requiring any labels, EB-GAD achieves the best or tied-best AUROC on nine datasets, yielding improvements of up to 21.7 percentage points over existing methods.

Abstract

Node-level graph anomaly detection (GAD) identifies nodes whose attributes and interactions deviate from dominant graph regularities. Existing GAD models encode normality and anomaly scoring indirectly through architectures, message passing, reconstruction or contrastive objectives, and tuned score families. This entangles graph trust (how strongly graph structure should define normality), graph-spectral weighting, and anomaly-score choice, yielding scores that are costly, opaque, and unstable across graph regimes. We propose EB-GAD (Empirical-Bayes GAD), a training-free framework that models normality as graph-aware generalized Ornstein-Uhlenbeck (GOU) relaxation toward a graph-filtered template. Empirical Bayes fits the graph precision from the residual-field likelihood; the GOU then turns scoring into a closed-form finite-horizon control energy, the minimum effort to steer a feature-neutral node to its observed endpoint along graph-spectral relaxation. Sweeping relaxation horizon and endpoint tolerance yields a bank of scores that share one fitted prior: equilibrium Mahalanobis scoring is one limit, while finite-horizon control-energy and scale-normalized ratio scores reveal anomalies that static equilibrium scoring can mask. A label-free selector chooses the score family from feature homophily, edge density, and feature dimension, then ranks candidates by fitted-null deviation and rank stability. On 11 benchmarks and without labels at any step, EB-GAD has the best or tied-best AUROC on 9: the four financial fraud networks (up to 3.7M nodes), the YelpChi and Amazon review graphs, Weibo, Reddit and Facebook, with margins of up to 21.7 points. It is second on BlogCatalog and ACM.

Problem

• Graph Anomaly Detection
• Node-level Anomaly
• Anomaly Scoring
• Entangled Objectives

Innovation

• Graph Anomaly Detection
• Empirical Bayes
• Training-Free
• Ornstein-Uhlenbeck Process
• Finite-Horizon Control