  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.
