# EntropyStop: Unsupervised Deep Outlier Detection with Loss Entropy

arXiv: https://arxiv.org/abs/2405.12502 · HTML: https://mlsanity.com/paper/2405.12502/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 38 references that are in the map.
- First posted on arXiv 21 May 2024.

## Builds on (most cited first, 12 of 12)

- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
- [Unsupervised Anomaly Detection with Generative Adversarial Networks to Guide Marker Discovery](https://mlsanity.com/paper/1703.05921/) (2017)
- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [Deep Learning for Anomaly Detection: A Survey](https://mlsanity.com/paper/1901.03407/) (2019)
- [Enhancing Graph Neural Network-based Fraud Detectors against Camouflaged Fraudsters](https://mlsanity.com/paper/2008.08692/) (2020)
- [Deep Learning for Anomaly Detection: A Review](https://mlsanity.com/paper/2007.02500/) (2020)
- [Understanding and Improving Early Stopping for Learning with Noisy Labels](https://mlsanity.com/paper/2106.15853/) (2021)
- [Neural Transformation Learning for Deep Anomaly Detection Beyond Images](https://mlsanity.com/paper/2103.16440/) (2021)
- [Generative Adversarial Active Learning for Unsupervised Outlier Detection](https://mlsanity.com/paper/1809.10816/) (2018)
- [Latent Outlier Exposure for Anomaly Detection with Contaminated Data](https://mlsanity.com/paper/2202.08088/) (2022)
- [Unsupervised Representation Learning by Predicting Random Distances](https://mlsanity.com/paper/1912.12186/) (2019)
- [Hyperparameter Sensitivity in Deep Outlier Detection: Analysis and a Scalable Hyper-Ensemble Solution](https://mlsanity.com/paper/2206.07647/) (2022)

## Built on by (most cited first, 4 of 4)

- [Contrastive and Variational Approaches in Self-Supervised Learning for Complex Data Mining](https://mlsanity.com/paper/2504.04032/) (2025)
- [GradStop: Exploring Training Dynamics in Unsupervised Outlier Detection through Gradient](https://mlsanity.com/paper/2412.08501/) (2024)
- [Unsupervised Anomaly Detection Using Flow Matching on Tabular Data](https://mlsanity.com/paper/2608.19801/) (2026)
- [Mitigating Convergence Collapse in Fixed-Target Anomaly Detectors via Kernel-Anchored Locality Regularization](https://mlsanity.com/paper/2610.02345/) (2026)

## Abstract (arXiv)

Unsupervised Outlier Detection (UOD) is an important data mining task. With the advance of deep learning, deep Outlier Detection (OD) has received broad interest. Most deep UOD models are trained exclusively on clean datasets to learn the distribution of the normal data, which requires huge manual efforts to clean the real-world data if possible. Instead of relying on clean datasets, some approaches directly train and detect on unlabeled contaminated datasets, leading to the need for methods that are robust to such conditions. Ensemble methods emerged as a superior solution to enhance model robustness against contaminated training sets. However, the training time is greatly increased by the ensemble. In this study, we investigate the impact of outliers on the training phase, aiming to halt training on unlabeled contaminated datasets before performance degradation. Initially, we noted that blending normal and anomalous data causes AUC fluctuations, a label-dependent measure of detection accuracy. To circumvent the need for labels, we propose a zero-label entropy metric named Loss Entropy for loss distribution, enabling us to infer optimal stopping points for training without labels. Meanwhile, we theoretically demonstrate negative correlation between entropy metric and the label-based AUC. Based on this, we develop an automated early-stopping algorithm, EntropyStop, which halts training when loss entropy suggests the maximum model detection capability. We conduct extensive experiments on ADBench (including 47 real datasets), and the overall results indicate that AutoEncoder (AE) enhanced by our approach not only achieves better performance than ensemble AEs but also requires under 2% of training time. Lastly, our proposed metric and early-stopping approach are evaluated on other deep OD models, exhibiting their broad potential applicability.