Learning Robust Deep State Space for Unsupervised Anomaly Detection in Contaminated Time-Series

Anomalies are ubiquitous in real-world time-series data which call for effective and timely detection, especially in an unsupervised setting for labeling cost saving. In this paper, we develop an unsupervised density reconstruction model for multi-dimensional time-series anomaly detection. In particular, it directly handles an important realistic setting that the detection is achieved towards raw time-series contaminated with noise for training, in contrast to most existing anomaly detection works that assume the training data is in general clean i.e., not contaminated with anomaly. It extends recent advancements in deep generative models and state space models to achieve robust anomaly detection. Our approach comprises of a novel state space based generative model, a filtering based inference model, together with a carefully-designated emission model based on robust statistics theory. Extensive experimental results are conducted to show that our approach can adapt to complex patterns even given severely contaminated training data. We also develop visualization techniques to help better understand the behavior of the anomaly detection models. Empirical results show that our method outperforms state-of-the-arts on both synthetic and real-world datasets.