Learning Continuous and Discrete Dynamics for Time Series Anomaly Detection via Probabilistic Modeling

Kai Zhao, Yuying Qiu, Yunyao Cheng, Christian S. Jensen, Xiaokui Xiao, Bin Yang, Chenjuan Guo

Keywords: Time Series Anomaly Detection, Continuous and Discrete Dynamics

Abstract: 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 without recognizing differences in importance of variates with different measurement units. To overcome these limitations, 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 both 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. We detect anomalies using joint probabilities, which take the marginal probabilities of different variates into account. Experiments on nine real-world datasets from different domains offer evidence that TAD-UP is capable of state-of-the-art accuracy and better efficiency tradeoff.

Primary Area: learning on time series and dynamical systems

Submission Number: 1761