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

TL;DR

This paper investigates the effectiveness of using the Shapley value for anomaly localization in sensor data, demonstrating that a simplified approach can achieve similar error probabilities with lower complexity.

Contribution

It provides a mathematical analysis showing that a fixed-term Shapley value approach is as effective as the full method for independent observations, with implications for complexity reduction.

Findings

A fixed-term Shapley value achieves lower complexity with same error probability in independent cases.

Proof confirms the result for all independent observation scenarios.

No proof available for dependent observation cases.

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.