A plug-in module for detecting and explaining anomalies in inter-variable dependencies in multivariate time series

As modern industrial systems grow increasingly complex, the demand for effective techniques that can detect anomalies and provide explanatory insights from multivariate time series data has become critical. Although recent deep learning models have achieved high detection accuracy, their explainability remains limited, particularly regarding anomalies that arise from disruptions in inter-variable dependencies. We propose a simple plug-in module that enhances both the detection accuracy and explainability of existing anomaly detection models by quantifying structural deviations in inter-variable dependencies. The proposed module is implemented as an auxiliary autoencoder that reconstructs dependency matrices generated by any base anomaly detection model capable of explaining such dependencies. Trained solely on normal data, it learns the stable dependency patterns of normal states and quantifies deviations between the original and reconstructed matrices as dependency-based anomaly scores. These scores are combined with the base model’s anomaly scores to improve detection performance. Moreover, the deviation matrices provide intuitive, fine-grained explanations by identifying specific variable dependencies responsible for structural shifts. Experiments conducted on two industrial benchmark datasets, the Secure Water Treatment (SWaT) dataset and the Water Distribution (WADI) dataset, demonstrate that integrating the proposed module consistently improves detection performance across different base models, yielding an F1-score gain of up to 0.417 on the WADI dataset, while offering clearer explainability of inter-variable dependency shifts.