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 1\% of training time. Lastly, our proposed metric and
early-stopping approach are evaluated on other deep OD models, exhibiting their
broad potential applicability.

研究旨在研究异常值对训练阶段的影响，并提出了一种名为 Loss Entropy 的零标签熵度量来推断训练的最佳停止点，然后基于此开发了一种自动化的早停算法 EntropyStop，该算法通过在最大模型检测能力时停止训练来提升 AutoEncoder（AE）的性能。

EntropyStop: 无监督深度异常检测与损失熵

EntropyStop: Unsupervised Deep Outlier Detection with Loss Entropy

Outlier detection (OD) has received continuous research interests due to its
wide applications. With the development of deep learning, increasingly deep OD
algorithms are proposed. Despite the availability of numerous deep OD models,
existing research has reported that the performance of deep models is extremely
sensitive to the configuration of hyperparameters (HPs). However, the selection
of HPs for deep OD models remains a notoriously difficult task due to the lack
of any labels and long list of HPs. In our study. we shed light on an essential
factor, training time, that can introduce significant variation in the
performance of deep model. Even the performance is stable across other HPs,
training time itself can cause a serious HP sensitivity issue. Motivated by
this finding, we are dedicated to formulating a strategy to terminate model
training at the optimal iteration. Specifically, we propose a novel metric
called loss entropy to internally evaluate the model performance during
training while an automated training stopping algorithm is devised. To our
knowledge, our approach is the first to enable reliable identification of the
optimal training iteration during training without requiring any labels. Our
experiments on tabular, image datasets show that our approach can be applied to
diverse deep models and datasets. It not only enhances the robustness of deep
models to their HPs, but also improves the performance and reduces plenty of
training time compared to naive training.

通过引入一个新的名为 loss entropy 的指标，本文针对深度离群点检测模型中的超参选择问题进行研究，提出了一种能够在训练过程中自动识别最佳停止时机而无需标签的新算法，实验证明该算法不仅能够提高模型对超参的稳健性，而且可以优化模型性能并减少训练时间。