arXiv：cs.LG（机器学习，全量分类）· Fred Xu, Thomas Markovich, Florence Regol, Yizhou Sun·· 5 小时前AI 评分42
EB-GAD：免训练的经验贝叶斯图异常检测，将评分建模为有限时域控制
Graph Anomaly Detection as Finite-Horizon Control: Training-Free Scoring via Empirical Bayes
AI 导读
研究者提出免训练框架 EB-GAD，将图异常检测建模为图感知的广义 Ornstein-Uhlenbeck 松弛，并用经验贝叶斯从残差场似然拟合图精度，把异常评分转化为闭式有限时域控制能量。
正文
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.
| Comments: | Paper already accepted at Neurips |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2609.38424 [cs.LG] |
| (or arXiv:2609.38424v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2609.38424 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Fred Xu [view email]
[v1]
Tue, 29 Sep 2026 19:15:12 UTC (912 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org