# Graph-Augmented Normalizing Flows for Anomaly Detection of Multiple Time Series

arXiv: https://arxiv.org/abs/2202.07857 · HTML: https://mlsanity.com/paper/2202.07857/

## Key facts

- Cited by 42 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 45 references that are in the map.
- First posted on arXiv 16 Feb 2022.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Using Self-Supervised Learning Can Improve Model Robustness and Uncertainty](https://mlsanity.com/paper/1906.12340/) (2019)
- [T-GCN: A Temporal Graph ConvolutionalNetwork for Traffic Prediction](https://mlsanity.com/paper/1811.05320/) (2018)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Graph Neural Network-Based Anomaly Detection in Multivariate Time Series](https://mlsanity.com/paper/2106.06947/) (2021)
- [Deep Semi-Supervised Anomaly Detection](https://mlsanity.com/paper/1906.02694/) (2019)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Deep Anomaly Detection Using Geometric Transformations](https://mlsanity.com/paper/1805.10917/) (2018)
- [LSTM-based Encoder-Decoder for Multi-sensor Anomaly Detection](https://mlsanity.com/paper/1607.00148/) (2016)
- [Adversarially Learned One-Class Classifier for Novelty Detection](https://mlsanity.com/paper/1802.09088/) (2018)
- [On the (Statistical) Detection of Adversarial Examples](https://mlsanity.com/paper/1702.06280/) (2017)
- [Discrete Graph Structure Learning for Forecasting Multiple Time Series](https://mlsanity.com/paper/2101.06861/) (2021)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [DROCC: Deep Robust One-Class Classification](https://mlsanity.com/paper/2002.12718/) (2020)
- [Object-centric Auto-encoders and Dummy Anomalies for Abnormal Event Detection in Video](https://mlsanity.com/paper/1812.04960/) (2018)
- [Graph Normalizing Flows](https://mlsanity.com/paper/1905.13177/) (2019)
- [Anomaly Detection with Generative Adversarial Networks for Multivariate Time Series](https://mlsanity.com/paper/1809.04758/) (2018)
- [An overview of deep learning based methods for unsupervised and semi-supervised anomaly detection in videos](https://mlsanity.com/paper/1801.03149/) (2018)
- [Emerging Convolutions for Generative Normalizing Flows](https://mlsanity.com/paper/1901.11137/) (2019)

## Built on by (most cited first, 30 of 42)

- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Deep Learning for Time Series Anomaly Detection: A Survey](https://mlsanity.com/paper/2211.05244/) (2022)
- [Self-Supervised Learning for Time Series Analysis: Taxonomy, Progress, and Prospects](https://mlsanity.com/paper/2306.10125/) (2023)
- [Large Language Model Guided Knowledge Distillation for Time Series Anomaly Detection](https://mlsanity.com/paper/2401.15123/) (2024)
- [Navigating the Metric Maze: A Taxonomy of Evaluation Metrics for Anomaly Detection in Time Series](https://mlsanity.com/paper/2303.01272/) (2023)
- [Detecting Multivariate Time Series Anomalies with Zero Known Label](https://mlsanity.com/paper/2208.02108/) (2022)
- [Graph Anomaly Detection in Time Series: A Survey](https://mlsanity.com/paper/2302.00058/) (2023)
- [Nominality Score Conditioned Time Series Anomaly Detection by Point/Sequential Reconstruction](https://mlsanity.com/paper/2310.15416/) (2023)
- [Deep Learning Advancements in Anomaly Detection: A Comprehensive Survey](https://mlsanity.com/paper/2503.13195/) (2025)
- [Interpretation of Time-Series Deep Models: A Survey](https://mlsanity.com/paper/2305.14582/) (2023)
- [Explainable Time Series Anomaly Detection using Masked Latent Generative Modeling](https://mlsanity.com/paper/2311.12550/) (2023)
- [Graph Neural Flows for Unveiling Systemic Interactions Among Irregularly Sampled Time Series](https://mlsanity.com/paper/2410.14030/) (2024)
- [Label-Free Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2312.11549/) (2023)
- [Deep Causal Learning: Representation, Discovery and Inference](https://mlsanity.com/paper/2211.03374/) (2022)
- [Graph Spatiotemporal Process for Multivariate Time Series Anomaly Detection with Missing Values](https://mlsanity.com/paper/2401.05800/) (2024)
- [Is it worth it? Comparing six deep and classical methods for unsupervised anomaly detection in time series](https://mlsanity.com/paper/2212.11080/) (2022)
- [A Causal Approach to Detecting Multivariate Time-series Anomalies and Root Causes](https://mlsanity.com/paper/2206.15033/) (2022)
- [The voraus-AD Dataset for Anomaly Detection in Robot Applications](https://mlsanity.com/paper/2311.04765/) (2023)
- [PeFAD: A Parameter-Efficient Federated Framework for Time Series Anomaly Detection](https://mlsanity.com/paper/2406.02318/) (2024)
- [GC-Flow: A Graph-Based Flow Network for Effective Clustering](https://mlsanity.com/paper/2305.17284/) (2023)
- [DoFlow: Flow-based Generative Models for Interventional and Counterfactual Forecasting on Time Series](https://mlsanity.com/paper/2511.02137/) (2025)
- [Contaminated Multivariate Time-Series Anomaly Detection with Spatio-Temporal Graph Conditional Diffusion Models](https://mlsanity.com/paper/2308.12563/) (2023)
- [GDFlow: Anomaly Detection with NCDE-based Normalizing Flow for Advanced Driver Assistance System](https://mlsanity.com/paper/2409.05346/) (2024)
- [Interdependency Matters: Graph Alignment for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2410.08877/) (2024)
- [ScatterAD: Temporal-Topological Scattering Mechanism for Time Series Anomaly Detection](https://mlsanity.com/paper/2509.24414/) (2025)
- [OrionBench: Benchmarking Time Series Generative Models in the Service of the End-User](https://mlsanity.com/paper/2310.17748/) (2023)
- [TreeMIL: A Multi-instance Learning Framework for Time Series Anomaly Detection with Inexact Supervision](https://mlsanity.com/paper/2401.11235/) (2024)
- [FANFOLD: Graph Normalizing Flows-driven Asymmetric Network for Unsupervised Graph-Level Anomaly Detection](https://mlsanity.com/paper/2407.00383/) (2024)
- [A Problem-Oriented Taxonomy of Evaluation Metrics for Time Series Anomaly Detection](https://mlsanity.com/paper/2511.18739/) (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)

## Abstract (arXiv)

Anomaly detection is a widely studied task for a broad variety of data types; among them, multiple time series appear frequently in applications, including for example, power grids and traffic networks. Detecting anomalies for multiple time series, however, is a challenging subject, owing to the intricate interdependencies among the constituent series. We hypothesize that anomalies occur in low density regions of a distribution and explore the use of normalizing flows for unsupervised anomaly detection, because of their superior quality in density estimation. Moreover, we propose a novel flow model by imposing a Bayesian network among constituent series. A Bayesian network is a directed acyclic graph (DAG) that models causal relationships; it factorizes the joint probability of the series into the product of easy-to-evaluate conditional probabilities. We call such a graph-augmented normalizing flow approach GANF and propose joint estimation of the DAG with flow parameters. We conduct extensive experiments on real-world datasets and demonstrate the effectiveness of GANF for density estimation, anomaly detection, and identification of time series distribution drift.