Modeling uncertainty and dependency improves multivariate time series anomaly detection
GT-PSSM: Unified Probabilistic Framework for Stochastic Dynamics Modeling and Dependency Learning in Multivariate Time Series Anomaly Detection
Machine Learning
Summary
Finding unusual events in data that changes over time and across many parts is important for safety. The authors point out that usual methods often treat these data as predictable and may mistake normal random changes for problems. They created a new approach that combines a way to handle randomness with a method to understand both how things change over time and relate to each other. This combined approach helps detect true problems more reliably.
What this means in practice
- •For industrial control teams: Monitor complex system sensors to distinguish real faults from normal random fluctuations for safer operations.
- •For network operations teams: Detect anomalies in multi-metric network traffic data while accounting for natural variability and interactions among metrics.
Authors
Wonmo Koo, Jaeyeong Lee, Taeseong Yoon, Heeyoung Kim
Abstract
Multivariate time series anomaly detection (MTAD) is crucial for ensuring the safe and reliable operation of complex systems. Many existing methods learn normal patterns by training reconstruction or forecasting models on predominantly normal data. However, a large portion of these approaches rely on deterministic models and their associated point-wise output errors for anomaly scoring. Since real-world multivariate time series are inherently stochastic due to measurement noise and intrinsic system randomness, purely error-based scores can be unreliable, as large errors may arise from benign fluctuations rather than true anomalies. Probabilistic approaches address this limitation by quantifying uncertainty in model outputs. In particular, probabilistic state-space models (PSSMs) provide a principled framework by modeling stochastic system dynamics through latent state transitions and measurement noise via emission models. Despite this advantage, existing PSSM-based MTAD methods often struggle to capture long-range temporal dependencies and inter-variable dependencies, as they typically rely on noise-sensitive recurrent architectures and lack explicit cross-variable structure modeling. To address these limitations, we propose Graph-Transformer-Enhanced Probabilistic State-Space Model (GT-PSSM), a novel PSSM-based MTAD method that tightly integrates PSSM-based probabilistic modeling of stochastic dynamics with Graph Transformer-based learning of temporal and inter-variable dependencies. By jointly modeling stochasticity, long-range temporal dependence, and variable interactions within a unified probabilistic framework, GT-PSSM enables more robust anomaly detection.