# GT-PSSM: Unified Probabilistic Framework for Stochastic Dynamics Modeling and Dependency Learning in Multivariate Time Series Anomaly Detection

arXiv: https://arxiv.org/abs/2609.34161 · HTML: https://mlsanity.com/paper/2609.34161/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 45 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding](https://mlsanity.com/paper/1802.04431/) (2018)
- [Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy](https://mlsanity.com/paper/2110.02642/) (2021)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Graph Neural Network-Based Anomaly Detection in Multivariate Time Series](https://mlsanity.com/paper/2106.06947/) (2021)
- [A Unified Model for Multi-class Anomaly Detection](https://mlsanity.com/paper/2206.03687/) (2022)
- [Unsupervised Anomaly Detection via Variational Auto-Encoder for Seasonal KPIs in Web Applications](https://mlsanity.com/paper/1802.03903/) (2018)
- [MAD-GAN: Multivariate Anomaly Detection for Time Series Data with Generative Adversarial Networks](https://mlsanity.com/paper/1901.04997/) (2019)
- [Multivariate Time-series Anomaly Detection via Graph Attention Network](https://mlsanity.com/paper/2009.02040/) (2020)
- [Deep Learning for Time Series Anomaly Detection: A Survey](https://mlsanity.com/paper/2211.05244/) (2022)
- [Sequential Neural Models with Stochastic Layers](https://mlsanity.com/paper/1605.07571/) (2016)
- [Learning Graph Structures with Transformer for Multivariate Time Series Anomaly Detection in IoT](https://mlsanity.com/paper/2104.03466/) (2021)
- [Time Series Anomaly Detection for Cyber-Physical Systems via Neural System Identification and Bayesian Filtering](https://mlsanity.com/paper/2106.07992/) (2021)
- [Nominality Score Conditioned Time Series Anomaly Detection by Point/Sequential Reconstruction](https://mlsanity.com/paper/2310.15416/) (2023)
- [Multivariate Time-Series Anomaly Detection based on Enhancing Graph Attention Networks with Topological Analysis](https://mlsanity.com/paper/2408.13082/) (2024)
- [Knowledge-Assisted Multi-Graph Dependency Learning for Multivariate Time Series Anomaly Detection in Multi-Stage Industrial Processes](https://mlsanity.com/paper/2607.15799/) (2026)

## Abstract (arXiv)

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.