Hypothesis Testing for Unknown Dynamical Systems and System Anomaly Detection via Autoencoders

We study the hypothesis testing problem for unknown dynamical systems. More specifically, we observe sequential input and output data from a dynamical system with unknown parameters, and we aim to determine whether the collected data is from a null distribution. Such a problem can have many applications. Here we formulate anomaly detection as hypothesis testing where the anomaly is defined through the alternative hypothesis. Consequently, hypothesis testing algorithms can detect faults in real-world systems such as robots, weather, energy systems, and stock markets. Although recent works achieved state-of-the-art performances in these tasks with deep learning models, we show that a careful analysis using hypothesis testing and graphical models can not only justify the effectiveness of autoencoder models, but also lead to a novel neural network design, termed DyAD (DYnamical system Anomaly Detection), with improved performances. We then show that DyAD achieves state-of-the-art performance on several existing datasets and a new dataset on battery anomaly detection in electric vehicles.