# An Encode-then-Decompose Approach to Unsupervised Time Series Anomaly Detection on Contaminated Training Data--Extended Version

arXiv: https://arxiv.org/abs/2510.18998 · HTML: https://mlsanity.com/paper/2510.18998/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 80 references that are in the map.
- First posted on arXiv 21 Oct 2025.

## Builds on (most cited first, 30 of 32)

- [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)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Temporal Ensembling for Semi-Supervised Learning](https://mlsanity.com/paper/1610.02242/) (2016)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Learning Representations by Maximizing Mutual Information Across Views](https://mlsanity.com/paper/1906.00910/) (2019)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [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)
- [On Mutual Information Maximization for Representation Learning](https://mlsanity.com/paper/1907.13625/) (2019)
- [Graph Neural Network-Based Anomaly Detection in Multivariate Time Series](https://mlsanity.com/paper/2106.06947/) (2021)
- [Unsupervised Anomaly Detection via Variational Auto-Encoder for Seasonal KPIs in Web Applications](https://mlsanity.com/paper/1802.03903/) (2018)
- [TranAD: Deep Transformer Networks for Anomaly Detection in Multivariate Time Series Data](https://mlsanity.com/paper/2201.07284/) (2022)
- [MAD-GAN: Multivariate Anomaly Detection for Time Series Data with Generative Adversarial Networks](https://mlsanity.com/paper/1901.04997/) (2019)
- [DCdetector: Dual Attention Contrastive Representation Learning for Time Series Anomaly Detection](https://mlsanity.com/paper/2306.10347/) (2023)
- [Towards Spatio-Temporal Aware Traffic Time Series Forecasting--Full Version](https://mlsanity.com/paper/2203.15737/) (2022)
- [ImDiffusion: Imputed Diffusion Models for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2307.00754/) (2023)
- [AnomalyBERT: Self-Supervised Transformer for Time Series Anomaly Detection using Data Degradation Scheme](https://mlsanity.com/paper/2305.04468/) (2023)
- [Robust and Explainable Autoencoders for Unsupervised Time Series Outlier Detection---Extended Version](https://mlsanity.com/paper/2204.03341/) (2022)
- [Distributed Anomaly Detection using Autoencoder Neural Networks in WSN for IoT](https://mlsanity.com/paper/1812.04872/) (2018)
- [Pi-NAS: Improving Neural Architecture Search by Reducing Supernet Training Consistency Shift](https://mlsanity.com/paper/2108.09671/) (2021)
- [PAC-Wrap: Semi-Supervised PAC Anomaly Detection](https://mlsanity.com/paper/2205.10798/) (2022)
- [Anomaly Detection for an E-commerce Pricing System](https://mlsanity.com/paper/1902.09566/) (2019)
- [Deep Variational Multivariate Information Bottleneck -- A Framework for Variational Losses](https://mlsanity.com/paper/2310.03311/) (2023)

## Built on by (most cited first, 3 of 3)

- [TimeART: Towards Agentic Time Series Reasoning via Tool-Augmentation](https://mlsanity.com/paper/2601.13653/) (2026)
- [FLAME: Flow Enhanced Legendre Memory Models for General Time Series Forecasting](https://mlsanity.com/paper/2512.14253/) (2025)
- [WPBench: A Comprehensive Benchmark for Wind Power Forecasting](https://mlsanity.com/paper/2609.24444/) (2026)

## Abstract (arXiv)

Time series anomaly detection is important in modern large-scale systems and is applied in a variety of domains to analyze and monitor the operation of diverse systems. Unsupervised approaches have received widespread interest, as they do not require anomaly labels during training, thus avoiding potentially high costs and having wider applications. Among these, autoencoders have received extensive attention. They use reconstruction errors from compressed representations to define anomaly scores. However, representations learned by autoencoders are sensitive to anomalies in training time series, causing reduced accuracy. We propose a novel encode-then-decompose paradigm, where we decompose the encoded representation into stable and auxiliary representations, thereby enhancing the robustness when training with contaminated time series. In addition, we propose a novel mutual information based metric to replace the reconstruction errors for identifying anomalies. Our proposal demonstrates competitive or state-of-the-art performance on eight commonly used multi- and univariate time series benchmarks and exhibits robustness to time series with different contamination ratios.