Learning Continuous and Discrete Dynamics for Multivariate Time Series Anomaly Detection

Anomaly detection for multivariate time series plays an important role in many applications, enabling, e.g., risk monitoring in cyber-physical systems. While existing methods achieve good results on continuous variates, they struggle when having to learn both continuous and discrete dynamics across continuous time. Further, existing methods simply sum up reconstruction or contrastive errors from each variate to obtain final anomaly scores. They suffer from variates with different measurement units. Thus, we propose TAD-UP that learns both continuous and discrete dynamics for Time series Anomaly Detection via Unified Probabilistic modeling. First, we propose two co-dependent branches of efficient neural ordinary differential equations with the compound Poisson process to learn continuous and discrete dynamics for different variates. We also propose a gate mechanism to learn correlations among different dynamics. Second, we propose to model a joint probability distribution for anomaly detection. The resulting model is optimized using Maximum Likelihood Estimation on joint variates, instead of using reconstruction or contrastive losses on each variate, which tackles the problem of different measurement units. Experiments on nine real-world datasets from different domains offer evidence that TAD-UP is capable of state-of-the-art performance and better efficiency tradeoff even compared to foundation models.