# LPCVAE: A Conditional VAE with Long-Term Dependency and Probabilistic Time-Frequency Fusion for Time Series Anomaly Detection

arXiv: https://arxiv.org/abs/2510.10915 · HTML: https://mlsanity.com/paper/2510.10915/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 22 references that are in the map.
- First posted on arXiv 13 Oct 2025.

## Builds on (most cited first, 10 of 10)

- [Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy](https://mlsanity.com/paper/2110.02642/) (2021)
- [TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting](https://mlsanity.com/paper/2405.14616/) (2024)
- [Unsupervised Anomaly Detection via Variational Auto-Encoder for Seasonal KPIs in Web Applications](https://mlsanity.com/paper/1802.03903/) (2018)
- [Time-Series Anomaly Detection Service at Microsoft](https://mlsanity.com/paper/1906.03821/) (2019)
- [DCdetector: Dual Attention Contrastive Representation Learning for Time Series Anomaly Detection](https://mlsanity.com/paper/2306.10347/) (2023)
- [Evaluating Real-time Anomaly Detection Algorithms - the Numenta Anomaly Benchmark](https://mlsanity.com/paper/1510.03336/) (2015)
- [TFAD: A Decomposition Time Series Anomaly Detection Architecture with Time-Frequency Analysis](https://mlsanity.com/paper/2210.09693/) (2022)
- [MEMTO: Memory-guided Transformer for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2312.02530/) (2023)
- [Revisiting VAE for Unsupervised Time Series Anomaly Detection: A Frequency Perspective](https://mlsanity.com/paper/2402.02820/) (2024)
- [Constructing Large-Scale Real-World Benchmark Datasets for AIOps](https://mlsanity.com/paper/2208.03938/) (2022)

## Abstract (arXiv)

Time series anomaly detection(TSAD) is a critical task in signal processing field, ensuring the reliability of complex systems. Reconstruction-based methods dominate in TSAD. Among these methods, VAE-based methods have achieved promising results. Existing VAE-based methods suffer from the limitation of single-window feature and insufficient leveraging of long-term time and frequency information. We propose a Conditional Variational AutoEncoder with Long-term dependency and Probabilistic time-frequency fusion, named LPCVAE. LPCVAE introduces LSTM to capture long-term dependencies beyond windows. It further incorporates a Product-of-Experts (PoE) mechanism for adaptive and distribution-level probabilistic fusion. This design effectively mitigates time-frequency information loss. Extensive experiments on four public datasets demonstrate it outperforms state-of-the-art methods. The results confirm that integrating long-term time and frequency representations with adaptive fusion yields a robust and efficient solution for TSAD.