# Bayesian Tensor Autoencoder with Physics-informed Predictive Prior for Multi-dimensional Time Series Anomaly Detection

arXiv: https://arxiv.org/abs/2609.31157 · HTML: https://mlsanity.com/paper/2609.31157/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 51 references that are in the map.
- First posted on arXiv 25 Sep 2026.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Memorizing Normality to Detect Anomaly: Memory-augmented Deep Autoencoder for Unsupervised Anomaly Detection](https://mlsanity.com/paper/1904.02639/) (2019)
- [Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy](https://mlsanity.com/paper/2110.02642/) (2021)
- [Advances in Variational Inference](https://mlsanity.com/paper/1711.05597/) (2017)
- [Deep Learning for Time Series Anomaly Detection: A Survey](https://mlsanity.com/paper/2211.05244/) (2022)
- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [CATCH: Channel-Aware multivariate Time Series Anomaly Detection via Frequency Patching](https://mlsanity.com/paper/2410.12261/) (2024)
- [Importance Sampling for Minibatches](https://mlsanity.com/paper/1602.02283/) (2016)
- [Bayesian Robust Tensor Factorization for Incomplete Multiway Data](https://mlsanity.com/paper/1410.2386/) (2014)
- [TrustMAE: A Noise-Resilient Defect Classification Framework using Memory-Augmented Auto-Encoders with Trust Regions](https://mlsanity.com/paper/2012.14629/) (2020)
- [Noisy Tensor Completion via Low-rank Tensor Ring](https://mlsanity.com/paper/2203.08857/) (2022)
- [FT-AED: Benchmark Dataset for Early Freeway Traffic Anomalous Event Detection](https://mlsanity.com/paper/2406.15283/) (2024)
- [Tensor Train Factorization and Completion under Noisy Data with Prior Analysis and Rank Estimation](https://mlsanity.com/paper/2010.06564/) (2020)
- [HR-Extreme: A High-Resolution Dataset for Extreme Weather Forecasting](https://mlsanity.com/paper/2409.18885/) (2024)

## Abstract (arXiv)

Multi-dimensional time series, inherently tensorial, are common in practice. Despite great progress in time series anomaly detection, most existing methods are confined to uni-/multi-variate time series. When handling multi-dimensional time series using these methods, reshaping operations are required, which inevitably break the intrinsic correlations and thus lead to performance degradation. In uni-/multi-variate time series anomaly detection, AutoEncoders (AEs) are widely adopted and generally categorized into reconstruction-based and prediction-based AEs. The reconstruction-based AE utilizes the current observation for reconstruction, while the prediction-based AE utilizes the historical information to predict the current observation. Thus, the two AEs utilize different information. To bridge the gap between reconstruction-based and prediction-based AEs, so as to fully leverage the available information and thus further enhance performance, we propose a predictive prior and incorporate it into the reconstruction-based AE. It may not be very difficult to conceive this idea, but designing the predictive prior so that it can work for tensor anomaly detection is non-trivial. Specifically, to avoid breaking the intrinsic correlations within the multi-dimensional time series, we use the tensor AE as the backbone. To incorporate the predictive prior into the reconstruction-based AE, we propose a Bayesian fusion approach and our analysis reveals that this approach can enhance the modeling capability of the model for normal data. To mitigate the over-generalization problem of AE, we incorporate physical laws, i.e. tensor low-rank decomposition rules, into the neural networks in the predictive prior, leading to the Physics-informed Predictive Prior Tensor AE (PPPTAE) framework. Experimental results on real-world datasets demonstrate the effectiveness of the proposed method.