Unsupervised Anomaly Detection & Diagnosis: A Stein Variational Gradient Descent Approach

Detecting and diagnosing anomalies in observational data plays a crucial role in various real-world applications, such as e-commerce applet maintenance. Unsupervised machine learning techniques are typically employed for anomaly detection and diagnosis due to their convenience and independence from labeled data. Density estimation (DE), as one of the most widely used unsupervised machine learning techniques for anomaly detection, can be categorized into kernel density estimation (KDE)-based methods and normalizing flow (NF)-based methods. While KDE-based methods offer fast computation speed, they often ignore the complex manifold structure present in observational data. On the other hand, NF-based methods address the manifold issue but suffer from longer computation times. In this study, we propose a novel DE-based anomaly detection & diagnosis method using Stein Variational Gradient Descent (SVGD), aiming to leverage the strengths of KDE and NF approaches. Firstly, we rigorously derive the DE capability of SVGD through mathematical analysis. Subsequently, we demonstrate the ability of the SVGD method to perform anomaly diagnosis based on input feature attribution. Finally, to validate the effectiveness of our approach, we conduct experiments using synthetic, benchmark, and industrial datasets. The results demonstrate the superior performance and practical applicability of our proposed method.