Shapley Values of Reconstruction Errors of PCA for Explaining Anomaly Detection

TL;DR

This paper introduces a method to compute Shapley values for PCA reconstruction errors, enhancing the interpretability of PCA-based anomaly detection by accounting for feature correlations.

Contribution

It presents an exact computation of Shapley values for PCA reconstruction errors using a probabilistic approach, improving explanation of anomalies.

Findings

Shapley values better explain anomalies than raw errors.

The method accounts for feature correlations in PCA.

Numerical examples demonstrate the effectiveness of the approach.

Abstract

We present a method to compute the Shapley values of reconstruction errors of principal component analysis (PCA), which is particularly useful in explaining the results of anomaly detection based on PCA. Because features are usually correlated when PCA-based anomaly detection is applied, care must be taken in computing a value function for the Shapley values. We utilize the probabilistic view of PCA, particularly its conditional distribution, to exactly compute a value function for the Shapely values. We also present numerical examples, which imply that the Shapley values are advantageous for explaining detected anomalies than raw reconstruction errors of each feature.