# Anomaly Detection of Time Series with Smoothness-Inducing Sequential Variational Auto-Encoder

arXiv: https://arxiv.org/abs/2102.01331 · HTML: https://mlsanity.com/paper/2102.01331/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 62 references that are in the map.
- First posted on arXiv 2 Feb 2021.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Unsupervised Anomaly Detection via Variational Auto-Encoder for Seasonal KPIs in Web Applications](https://mlsanity.com/paper/1802.03903/) (2018)
- [Sequential Neural Models with Stochastic Layers](https://mlsanity.com/paper/1605.07571/) (2016)
- [Bias and Generalization in Deep Generative Models: An Empirical Study](https://mlsanity.com/paper/1811.03259/) (2018)
- [Learning Stochastic Recurrent Networks](https://mlsanity.com/paper/1411.7610/) (2014)
- [Variational Recurrent Auto-Encoders](https://mlsanity.com/paper/1412.6581/) (2014)
- [Variational Inference for On-line Anomaly Detection in High-Dimensional Time Series](https://mlsanity.com/paper/1602.07109/) (2016)

## Built on by (most cited first, 30 of 39)

- [Deep Learning for Time Series Anomaly Detection: A Survey](https://mlsanity.com/paper/2211.05244/) (2022)
- [Data Augmentation techniques in time series domain: A survey and taxonomy](https://mlsanity.com/paper/2206.13508/) (2022)
- [Advancements in Generative AI: A Comprehensive Review of GANs, GPT, Autoencoders, Diffusion Model, and Transformers](https://mlsanity.com/paper/2311.10242/) (2023)
- [Navigating the Metric Maze: A Taxonomy of Evaluation Metrics for Anomaly Detection in Time Series](https://mlsanity.com/paper/2303.01272/) (2023)
- [SSD-TS: Exploring the Potential of Linear State Space Models for Diffusion Models in Time Series Imputation](https://mlsanity.com/paper/2410.13338/) (2024)
- [Deep Learning Advancements in Anomaly Detection: A Comprehensive Survey](https://mlsanity.com/paper/2503.13195/) (2025)
- [Are we certain it's anomalous?](https://mlsanity.com/paper/2211.09224/) (2022)
- [Clustering Aided Weakly Supervised Training to Detect Anomalous Events in Surveillance Videos](https://mlsanity.com/paper/2203.13704/) (2022)
- [PatchAD: A Lightweight Patch-based MLP-Mixer for Time Series Anomaly Detection](https://mlsanity.com/paper/2401.09793/) (2024)
- [Harnessing Vision-Language Models for Time Series Anomaly Detection](https://mlsanity.com/paper/2506.06836/) (2025)
- [DyEdgeGAT: Dynamic Edge via Graph Attention for Early Fault Detection in IIoT Systems](https://mlsanity.com/paper/2307.03761/) (2023)
- [Enhancing Unsupervised Anomaly Detection with Score-Guided Network](https://mlsanity.com/paper/2109.04684/) (2021)
- [Conditional Generative Modeling for High-dimensional Marked Temporal Point Processes](https://mlsanity.com/paper/2305.12569/) (2023)
- [FedTADBench: Federated Time-Series Anomaly Detection Benchmark](https://mlsanity.com/paper/2212.09518/) (2022)
- [Few-Shot Anomaly Detection via Category-Agnostic Registration Learning](https://mlsanity.com/paper/2406.08810/) (2024)
- [Online Model-based Anomaly Detection in Multivariate Time Series: Taxonomy, Survey, Research Challenges and Future Directions](https://mlsanity.com/paper/2408.03747/) (2024)
- [Deep Anomaly Detection on Tennessee Eastman Process Data](https://mlsanity.com/paper/2303.05904/) (2023)
- [MA-VAE: Multi-head Attention-based Variational Autoencoder Approach for Anomaly Detection in Multivariate Time-series Applied to Automotive Endurance Powertrain Testing](https://mlsanity.com/paper/2309.02253/) (2023)
- [MTS-DVGAN: Anomaly Detection in Cyber-Physical Systems using a Dual Variational Generative Adversarial Network](https://mlsanity.com/paper/2311.02378/) (2023)
- [DTAAD: Dual Tcn-Attention Networks for Anomaly Detection in Multivariate Time Series Data](https://mlsanity.com/paper/2302.10753/) (2023)
- [ReAugment: Model Zoo-Guided RL for Few-Shot Time Series Augmentation and Forecasting](https://mlsanity.com/paper/2409.06282/) (2024)
- [STREAM-VAE: Dual-Path Routing for Slow and Fast Dynamics in Vehicle Telemetry Anomaly Detection](https://mlsanity.com/paper/2511.15339/) (2025)
- [TeVAE: A Variational Autoencoder Approach for Discrete Online Anomaly Detection in Variable-state Multivariate Time-series Data](https://mlsanity.com/paper/2407.06849/) (2024)
- [Dynamical modeling of nonlinear latent factors in multiscale neural activity with real-time inference](https://mlsanity.com/paper/2512.12462/) (2025)
- [Deep learning and differential equations for modeling changes in individual-level latent dynamics between observation periods](https://mlsanity.com/paper/2202.07403/) (2022)
- [From MIM-Based GAN to Anomaly Detection:Event Probability Influence on Generative Adversarial Networks](https://mlsanity.com/paper/2203.13464/) (2022)
- [PATH: A Discrete-sequence Dataset for Evaluating Online Unsupervised Anomaly Detection Approaches for Multivariate Time Series](https://mlsanity.com/paper/2411.13951/) (2024)
- [A Joint Learning Framework with Feature Reconstruction and Prediction for Incomplete Satellite Image Time Series in Agricultural Semantic Segmentation](https://mlsanity.com/paper/2505.19159/) (2025)
- [Surprised by Attention: Predictable Query Dynamics for Time Series Anomaly Detection](https://mlsanity.com/paper/2603.12916/) (2026)
- [On the Tradeoffs of On-Device Generative Models in Federated Predictive Maintenance Systems](https://mlsanity.com/paper/2605.07860/) (2026)

## Abstract (arXiv)

Deep generative models have demonstrated their effectiveness in learning latent representation and modeling complex dependencies of time series. In this paper, we present a Smoothness-Inducing Sequential Variational Auto-Encoder (SISVAE) model for robust estimation and anomaly detection of multi-dimensional time series. Our model is based on Variational Auto-Encoder (VAE), and its backbone is fulfilled by a Recurrent Neural Network to capture latent temporal structures of time series for both generative model and inference model. Specifically, our model parameterizes mean and variance for each time-stamp with flexible neural networks, resulting in a non-stationary model that can work without the assumption of constant noise as commonly made by existing Markov models. However, such a flexibility may cause the model fragile to anomalies. To achieve robust density estimation which can also benefit detection tasks, we propose a smoothness-inducing prior over possible estimations. The proposed prior works as a regularizer that places penalty at non-smooth reconstructions. Our model is learned efficiently with a novel stochastic gradient variational Bayes estimator. In particular, we study two decision criteria for anomaly detection: reconstruction probability and reconstruction error. We show the effectiveness of our model on both synthetic datasets and public real-world benchmarks.