conDENSE: Conditional Density Estimation for Time Series Anomaly Detection

Abstract

In recent years deep learning methods, based on reconstruction errors, have facilitated huge improvements in unsupervised anomaly detection. These methods make the limiting assumption that the greater the distance between an observation and a prediction the lower the likelihood of that observation. In this paper we propose conDENSE, a novel anomaly detection algorithm, which does not use reconstruction errors but rather uses conditional density estimation in masked autoregressive flows. By directly estimating the likelihood of data, our model moves beyond approximating expected behaviour with a single point estimate, as is the case in reconstruction error models. We show how conditioning on a dense representation of the current trajectory, extracted from a variational autoencoder with a gated recurrent unit (GRU VAE), produces a model that is suitable for periodic datasets, while also improving performance on non-periodic datasets. Experiments on 31 time-series, including real-world anomaly detection benchmark datasets and synthetically generated data, show that the model can outperform state-of-the-art deep learning methods.