GT-PSSM: Unified Probabilistic Framework for Stochastic Dynamics Modeling and Dependency Learning in Multivariate Time Series Anomaly Detection
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.
Related
- Nonparametric framework for the definition, adaptive detection and probabilistic interpretation of outliers
- RDDMPI: Residual Denoising Diffusion Model for Probabilistic Multivariate Time Series Imputation
- Stochastic Inversion of Multivariate Uniform-Distribution-Preserving Transformations
- Tractable Relaxations of Multivariate Stochastic Dominance via Optimal Transport and CVaR
- Stochastic Mutation Semigroups: From Deterministic Collapse to Probabilistic Evolutionary Dynamics
BibTeX
@misc{koo2026gtpssm,
title = {{GT-PSSM: Unified Probabilistic Framework for Stochastic Dynamics Modeling and Dependency Learning in Multivariate Time Series Anomaly Detection}},
author = {Wonmo Koo and Jaeyeong Lee and Taeseong Yoon and Heeyoung Kim},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34161},
eprint = {2609.34161},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34161},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - GT-PSSM: Unified Probabilistic Framework for Stochastic Dynamics Modeling and Dependency Learning in Multivariate Time Series Anomaly Detection
AU - Wonmo Koo
AU - Jaeyeong Lee
AU - Taeseong Yoon
AU - Heeyoung Kim
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34161
UR - https://arxiv.org/abs/2609.34161
AB - 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.
ER -