Anomaly Detection in Multivariate Time Series Using Uncertainty Estimation

Abstract Today’s industrial machines are equipped with several sensors that detect environmental changes and generate time series. One challenging task is the detection of anomalies in multivariate time series to proactively schedule machine maintenance and prevent failures during cost intense processes. Recent deep learning-based anomaly detectors demonstrate remarkable results as they can process large datasets of raw data. A common unsupervised method is to measure the discrepancy or anomaly score between observation and the expected behaviour approximated by a neural network. No approach incorporates multivariate uncertainties quantified by a Bayesian neural network and expert knowledge in the form of probabilistic relations into the anomaly score to enhance anomaly detection. We propose a Bayesian neural network that estimates uncertainty and multivariate time series forecasts. In this chapter, we introduce an anomaly score function based on Hotelling’s $${T^2}$$ T 2 statistic and the quantile function to estimate appropriate thresholds for the anomaly scores. Our experimental results show that anomaly scores are specifically separable into normal and anomalous regions when the discrepancies exploit probabilistic relations between multivariate features. Moreover, we compare the anomaly score separability and the anomaly detection accuracy against recent state-of-the-art methods. The evaluation shows that uncertainty-driven anomaly scores are competitive in both terms.