Title: A Causal Perspective on Jump-Diffusion for Time-Series Anomaly Detection
Primary area: learning on time series and dynamical systems
Keywords: Time series, Anomaly detection, Jump diffusion, Causal modeling

Abstract: Time series anomaly detection is essential for maintaining robustness in dynamic real-world systems. However, most existing methods rely on static distribution assumptions, while overlooking the latent causal structures and structural shifts that underlie real-world temporal dynamics. This often leads to poor explanation of anomalies and misclassification of environment-induced variations. To address these shortcomings, we propose Causal Soft Jump Diffusion Anomaly Detection (CSJD-AD), a novel framework that models both latent dynamics and soft-gated expected jumps through a structural jump diffusion process. We adopt a causal perspective grounded in environment-conditioned invariance by inferring discrete environment states and conditioning the jump-augmented process on them, yielding a practical detector for unlabeled sensor streams without aiming to identify true interventions. By generating paired counterfactual and factual trajectories, the model explicitly contrasts causally consistent behavior with unexplained deviations. Our method achieves state-of-the-art performance across benchmark datasets, demonstrating the importance of incorporating causal reasoning and jump-aware dynamics into time series anomaly detection.

TL;DR: We incorporated environment-aware variables into a jump–diffusion SDE and leveraged the contrast between counterfactual and factual generative trajectories to achieve precise anomaly detection.