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

Abstract

In this paper, we aim to improve anomaly detection (AD) by incorporating the time-varying non-linear spatio-temporal correlations of the multi-variate time series data in the modeling process. In multivariate AD, the simultaneous deviation of multiple nodes from their expected behavior can indicate an anomaly, even if no individual node shows a clearly abnormal pattern. 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 using a copula-based framework, which decouples the modeling of marginal distributions, temporal dynamics, and inter-variable dependencies. We use a transformer encoder to capture temporal patterns, and to model spatial (inter-variable) dependencies, we integrate a copula. Both 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.