# Entropy Causal Graphs for Multivariate Time Series Anomaly Detection

arXiv: https://arxiv.org/abs/2312.09478 · HTML: https://mlsanity.com/paper/2312.09478/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 80 references that are in the map.
- First posted on arXiv 15 Dec 2023.

## Builds on (most cited first, 28 of 28)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding](https://mlsanity.com/paper/1802.04431/) (2018)
- [Graph Neural Network-Based Anomaly Detection in Multivariate Time Series](https://mlsanity.com/paper/2106.06947/) (2021)
- [TranAD: Deep Transformer Networks for Anomaly Detection in Multivariate Time Series Data](https://mlsanity.com/paper/2201.07284/) (2022)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [A review on outlier/anomaly detection in time series data](https://mlsanity.com/paper/2002.04236/) (2020)
- [MAD-GAN: Multivariate Anomaly Detection for Time Series Data with Generative Adversarial Networks](https://mlsanity.com/paper/1901.04997/) (2019)
- [Deep Learning for Spatio-Temporal Data Mining: A Survey](https://mlsanity.com/paper/1906.04928/) (2019)
- [Discrete Graph Structure Learning for Forecasting Multiple Time Series](https://mlsanity.com/paper/2101.06861/) (2021)
- [Multivariate Time-series Anomaly Detection via Graph Attention Network](https://mlsanity.com/paper/2009.02040/) (2020)
- [Graph Learning: A Survey](https://mlsanity.com/paper/2105.00696/) (2021)
- [Deep Learning for Time Series Anomaly Detection: A Survey](https://mlsanity.com/paper/2211.05244/) (2022)
- [Learning Graph Structures with Transformer for Multivariate Time Series Anomaly Detection in IoT](https://mlsanity.com/paper/2104.03466/) (2021)
- [Towards a Rigorous Evaluation of Time-series Anomaly Detection](https://mlsanity.com/paper/2109.05257/) (2021)
- [An Evaluation of Anomaly Detection and Diagnosis in Multivariate Time Series](https://mlsanity.com/paper/2109.11428/) (2021)
- [GSLB: The Graph Structure Learning Benchmark](https://mlsanity.com/paper/2310.05174/) (2023)
- [Graph Neural Networks: Taxonomy, Advances and Trends](https://mlsanity.com/paper/2012.08752/) (2020)
- [CUTS+: High-dimensional Causal Discovery from Irregular Time-series](https://mlsanity.com/paper/2305.05890/) (2023)
- [Graph Anomaly Detection in Time Series: A Survey](https://mlsanity.com/paper/2302.00058/) (2023)
- [Graph Learning for Anomaly Analytics: Algorithms, Applications, and Challenges](https://mlsanity.com/paper/2212.05532/) (2022)
- [Multivariate Time Series Forecasting with Transfer Entropy Graph](https://mlsanity.com/paper/2005.01185/) (2020)
- [Causal Mechanism Transfer Network for Time Series Domain Adaptation in Mechanical Systems](https://mlsanity.com/paper/1910.06761/) (2019)

## Built on by (most cited first, 6 of 6)

- [Causality-Aware Contrastive Learning for Robust Multivariate Time-Series Anomaly Detection](https://mlsanity.com/paper/2506.03964/) (2025)
- [Incremental Causal Graph Learning for Online Cyberattack Detection in Cyber-Physical Infrastructures](https://mlsanity.com/paper/2507.14387/) (2025)
- [Knowledge-Assisted Multi-Graph Dependency Learning for Multivariate Time Series Anomaly Detection in Multi-Stage Industrial Processes](https://mlsanity.com/paper/2607.15799/) (2026)
- [MotifDisco: Motif Causal Discovery For Time Series Motifs](https://mlsanity.com/paper/2409.15219/) (2024)
- [Causal Graph Profiling via Structural Divergence for Robust Anomaly Detection in Cyber-Physical Systems](https://mlsanity.com/paper/2508.09504/) (2025)
- [Explainable Graph Neural Networks: Understanding Brain Connectivity and Biomarkers in Dementia](https://mlsanity.com/paper/2509.18568/) (2025)

## Abstract (arXiv)

Many multivariate time series anomaly detection frameworks have been proposed and widely applied. However, most of these frameworks do not consider intrinsic relationships between variables in multivariate time series data, thus ignoring the causal relationship among variables and degrading anomaly detection performance. This work proposes a novel framework called CGAD, an entropy Causal Graph for multivariate time series Anomaly Detection. CGAD utilizes transfer entropy to construct graph structures that unveil the underlying causal relationships among time series data. Weighted graph convolutional networks combined with causal convolutions are employed to model both the causal graph structures and the temporal patterns within multivariate time series data. Furthermore, CGAD applies anomaly scoring, leveraging median absolute deviation-based normalization to improve the robustness of the anomaly identification process. Extensive experiments demonstrate that CGAD outperforms state-of-the-art methods on real-world datasets with a 9% average improvement in terms of three different multivariate time series anomaly detection metrics.