Beyond Marginals: Learning Joint Spatio-Temporal Patterns for Multivariate Anomaly Detection

In this paper, we aim to improve multivariate anomaly detection (AD) by modeling the $\mathit{\text{time-varying}}\mathit{\text{non-linear}}\mathit{\text{spatio-temporal}}\mathit{\text{correlations}}$ found in multivariate time series data . In multivariate time series data, an anomaly may be indicated by the simultaneous deviation of interrelated time series from their expected collective behavior, even when no individual time series exhibits a clearly abnormal pattern on its own. In many existing approaches, time series variables are assumed to be (conditionally) independent, which oversimplifies real-world interactions. Our approach addresses this by modeling joint dependencies in the latent space and decoupling the modeling of $\mathit{\text{marginal}}\mathit{\text{distributions,}}\mathit{\text{temporal}}\mathit{\text{dynamics,}}\mathit{\text{and}}\mathit{\text{inter-variable}}\mathit{\text{dependencies}}$. We use a transformer encoder to capture temporal patterns, and to model spatial (inter-variable) dependencies, we fit a multi-variate likelihood and a copula. The temporal and the spatial components are trained jointly in a latent space using a self-supervised contrastive learning objective to learn meaningful feature representations to separate normal and anomaly samples.