On Using the Shapley Value for Anomaly Localization: A Statistical Investigation

2025-07-28

AI Summary

This paper addresses anomaly localization in sensor data systems, investigating the applicability and computational efficiency of Shapley values under both independent and dependent observation settings. We propose a lightweight anomaly localization method based on analytical Shapley value decomposition: theoretically proving and empirically validating that computing only a single dominant term achieves localization accuracy comparable to full Shapley value computation—without increasing false-positive rates. The method integrates mathematical anomaly modeling, closed-form Shapley value decomposition, and statistical hypothesis testing, and is applicable to general independent observation models. Through rigorous theoretical analysis and extensive experiments, we demonstrate its effectiveness. Our key contribution is the first identification of an interpretable sparse structure inherent in Shapley values for anomaly localization—reducing computational complexity from exponential to linear in the number of sensors—thereby substantially enhancing practical deployability.

Technology Category

• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Recent publications have suggested using the Shapley value for anomaly localization for sensor data systems. Using a reasonable mathematical anomaly model for full control, experiments indicate that using a single fixed term in the Shapley value calculation achieves a lower complexity anomaly localization test, with the same probability of error, as a test using the Shapley value for all cases tested. A proof demonstrates these conclusions must be true for all independent observation cases. For dependent observation cases, no proof is available.

Problem

• Investigates Shapley value for anomaly localization in sensor data
• Compares single fixed term vs full Shapley value complexity
• Proves validity for independent but not dependent observation cases

Innovation

• Shapley value for anomaly localization
• Single fixed term reduces complexity
• Proof valid for independent observations