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

Hanchang Cheng, Weimin Mu, Fan Liu, Weilin Zhu, Can Ma

TL;DR

LPCVAE addresses key limitations in reconstruction-based TSAD by modeling long-term temporal dependencies with an LSTM-based LTDB and by fusing time- and frequency-domain representations via a CVAE-based Product of Experts. The approach leverages Time Embedding and FFT-derived features, with a CM-ELBO training objective and an anomaly-score metric grounded in reconstruction likelihood. Across four public datasets, LPCVAE achieves state-of-the-art F1 scores and demonstrates strong ablation-supported gains, while remaining memory-efficient and scalable. The work provides a practical, robust solution for real-world TSAD that effectively exploits both temporal history and frequency structure.

Abstract

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.

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

TL;DR

LPCVAE addresses key limitations in reconstruction-based TSAD by modeling long-term temporal dependencies with an LSTM-based LTDB and by fusing time- and frequency-domain representations via a CVAE-based Product of Experts. The approach leverages Time Embedding and FFT-derived features, with a CM-ELBO training objective and an anomaly-score metric grounded in reconstruction likelihood. Across four public datasets, LPCVAE achieves state-of-the-art F1 scores and demonstrates strong ablation-supported gains, while remaining memory-efficient and scalable. The work provides a practical, robust solution for real-world TSAD that effectively exploits both temporal history and frequency structure.

Abstract

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.

Paper Structure

This paper contains 17 sections, 12 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. METHODOLOGY
  3. Problem Formulation
  4. Network Architecture
  5. Long-term Time Domain Branch(LTDB)
  6. Frequency Domain Branch(FDB)
  7. CVAE Based Product of Experts
  8. Training and Testing
  9. EXPERIMENT
  10. Datasets
  11. Baselines
  12. Implementation
  13. Performance Comparison
  14. Ablation Study
  15. Hyper-Parameter Sensitivity
  16. ...and 2 more sections

Figures (5)

  • Figure 1: (a) Long-term historical information cannot be propagated across input windows. (b)VAE-based Methods comparison: i) Time-only architecture. ii) Time-Frequency concatenation architecture. iii) Our LPCVAE architecture. Here, © denotes concatenation, and Freq represents the frequency.
  • Figure 2: LPCVAE Model Architecture.
  • Figure 3: F1 Score of different settings."w/o" denotes "without"; e.g., "w/o LSTM" means LPCVAE without LSTM module.
  • Figure 4: F1 Score of different Hyper-Parameters.
  • Figure 5: Computation Efficiency Comparison on NAB Dataset.