Sequence Outlier Detection and Application of Gated Recurrent Unit Autoencoder Gaussian Mixture Model Based on Various Loss Optimization

Xu, Ting; Tian, Yuzhu; Wu, Chunho; Mian, Zhibao

Abstract

In the era of big data, detecting outliers in time series data is crucial, particularly in fields such as finance and engineering. This article proposes a novel sequence outlier detection method based on the gated recurrent unit autoencoder with Gaussian mixture model (GRU-AE-GMM), which combines gated recurrent unit (GRU), autoencoder (AE), Gaussian mixture model (GMM), and optimization algorithms. The GRU captures long-term dependencies within the sequence, while the AE measures sequence abnormality. Meanwhile, the GMM models the relationship between the original and reconstructed sequences, employing the Expectation–Maximization (EM) algorithm for parameter estimation to calculate the likelihood of each hidden variable belonging to each Gaussian mixture component. In this article, we first train the model with mean-squared error loss (MSEL), and then further enhanced by substituting it with quantile loss (QL), composite quantile loss (CQL), and Huber loss (HL), respectively. Next, we validate the effectiveness and robustness of the proposed model through Monte Carlo experiments conducted under different error terms. Finally, the method is applied to Amazon stock data for 2022, demonstrating its significant potential for application in dynamic and unpredictable market environments.

Citation

Xu, T., Tian, Y., Wu, C., & Mian, Z. (2025). Sequence Outlier Detection and Application of Gated Recurrent Unit Autoencoder Gaussian Mixture Model Based on Various Loss Optimization. Statistical Analysis and Data Mining, 18(1), Article e70001. https://doi.org/10.1002/sam.70001

• Journal Article Type: Article
• Acceptance Date: Dec 5, 2024
• Online Publication Date: Jan 21, 2025
• Publication Date: Feb 1, 2025
• Deposit Date: Dec 6, 2024
• Publicly Available Date: Jan 22, 2026
• Journal: Statistical Analysis and Data Mining
• Print ISSN: 1932-1864
• Electronic ISSN: 1932-1872
• Publisher: John Wiley and Sons
• Peer Reviewed: Peer Reviewed
• Volume: 18
• Issue: 1
• Article Number: e70001
• DOI: https://doi.org/10.1002/sam.70001
• Keywords: Gated recurrent unit; Gaussian mixture model; Loss function; Outlier detection; Quantile loss
• Public URL: https://hull-repository.worktribe.com/output/4960842