Unsupervised Symbolic Anomaly Detection

2026-03-18

AI Summary

This work addresses the lack of interpretability in unsupervised anomaly detection by proposing a novel approach based on symbolic regression. The method learns human-readable equations that approximate invariants characterizing normal data, thereby generating interpretable anomaly scores in an endogenous manner. By integrating symbolic regression, ensemble learning, and invariant modeling, the framework achieves transparent detection logic without requiring post-hoc explanations. Experimental results demonstrate that the proposed method attains detection performance comparable to state-of-the-art techniques, while the discovered equations align with established scientific or medical priors, significantly enhancing model trustworthiness and practical utility.

Technology Category

• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Interpretability, Explainability, and Transparency

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

We propose SYRAN, an unsupervised anomaly detection method based on symbolic regression. Instead of encoding normal patterns in an opaque, high-dimensional model, our method learns an ensemble of human-readable equations that describe symbolic invariants: functions that are approximately constant on normal data. Deviations from these invariants yield anomaly scores, so that the detection logic is interpretable by construction, rather than via post-hoc explanation. Experimental results demonstrate that SYRAN is highly interpretable, providing equations that correspond to known scientific or medical relationships, and maintains strong anomaly detection performance comparable to that of state-of-the-art methods.

Problem

• unsupervised anomaly detection
• symbolic regression
• interpretability
• symbolic invariants

Innovation

• symbolic regression
• unsupervised anomaly detection
• interpretable AI
• symbolic invariants
• human-readable models