Explaining Anomalies with Tensor Networks
This work incrementally extends quantum-inspired tensor network methods to broader real-valued anomaly detection problems while preserving explainability.
The authors extended tensor network methods from discrete-valued to real-valued data for explainable anomaly detection, introducing tree tensor networks and demonstrating adequate predictive performance on three benchmark problems while maintaining explainability of anomalies.
Tensor networks, a class of variational quantum many-body wave functions have attracted considerable research interest across many disciplines, including classical machine learning. Recently, Aizpurua et al. demonstrated explainable anomaly detection with matrix product states on a discrete-valued cyber-security task, using quantum-inspired methods to gain insight into the learned model and detected anomalies. Here, we extend this framework to real-valued data domains. We furthermore introduce tree tensor networks for the task of explainable anomaly detection. We demonstrate these methods with three benchmark problems, show adequate predictive performance compared to several baseline models and both tensor network architectures' ability to explain anomalous samples. We thereby extend the application of tensor networks to a broader class of potential problems and open a pathway for future extensions to more complex tensor network architectures.