Anomaly detection is a key technique for ensuring the reliability and stability of systems across various industrial domains. Autoencoder-based reconstruction models are particularly effective in learning normal patterns and detecting deviations. However, conventional loss functions such as Mean Squared Error (MSE) and Mean Absolute Error (MAE) are limited in capturing anomalies that follow heavy-tailed or asymmetric distributions, which are commonly observed in real-world industrial settings. To address this limitation, we propose a Mixture Negative Log-Likelihood (Mixture NLL) loss function based on a combination of Gaussian, Laplace, and Student-t distributions. The loss is constructed using the probability density functions of each distribution, with key parameters such as standard deviation, scale, and degrees of freedom learned during training. The mixture weights representing the contribution of each distribution are also jointly optimized. Experimental results on real-world time-series anomaly detection datasets demonstrate that the proposed MixtureLoss consistently outperforms conventional loss-based Autoencoder models, particularly in detecting tail-end anomalies.

1. 서 론
2. Related Work
3. Proposed Method
    3.1 Mixture NLL Loss Function
    3.2 Trainable Parameters and Learning Mechanism
    3.3 Anomaly Scoring
    3.4 Visualization of Mixture Behavior
    3.5 Experimental Setup
4. Experiments
    4.1 Performance Comparison across LossFunctions
    4.2 Distribution Contribution per Epoch
5. Limitations and Future Work
    5.1 Limitations
    5.2 Future Work
References

• Kwanghyun Lee(Department of Industrial Engineering, Kongju National University ) | 이광현 (공주대학교 산업공학과)
• Dongju Lee(Department of Industrial Engineering, Kongju National University ) | 이동주 (공주대학교 산업공학과) Corresponding author