We propose a supervised anomaly detection method for data with inexact anomaly labels, where each label, which is assigned to a set of instances, indicates that at least one instance in the set is anomalous. Although many anomaly detection methods have been proposed, they cannot handle inexact anomaly labels. To measure the performance with inexact anomaly labels, we define the inexact AUC, which is our extension of the area under the ROC curve (AUC) for inexact labels. The proposed method trains an anomaly score function so that the smooth approximation of the inexact AUC increases while anomaly scores for non-anomalous instances become low. We model the anomaly score function by a neural network-based unsupervised anomaly detection method, e.g., autoencoders. The proposed method performs well even when only a small number of inexact labels are available by incorporating an unsupervised anomaly detection mechanism with inexact AUC maximization. Using various datasets, we experimentally demonstrate that our proposed method improves the anomaly detection performance with inexact anomaly labels, and outperforms existing unsupervised and supervised anomaly detection and multiple instance learning methods.

中文翻译：

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带有不精确标签的异常检测

我们为具有不精确异常标签的数据提出了一种有监督的异常检测方法，其中分配给一组实例的每个标签表明该集合中至少有一个实例是异常的。尽管已经提出了许多异常检测方法，但它们无法处理不精确的异常标签。为了用不精确的异常标签衡量性能，我们定义了不精确的 AUC，这是我们对不精确标签的 ROC 曲线下面积 (AUC) 的扩展。所提出的方法训练异常评分函数，以便不精确 AUC 的平滑近似增加，而非异常实例的异常评分变低。我们通过基于神经网络的无监督异常检测方法（例如自动编码器）对异常评分函数进行建模。通过将无监督的异常检测机制与不精确的 AUC 最大化相结合，即使只有少量不精确的标签可用，所提出的方法也能很好地执行。使用各种数据集，我们通过实验证明我们提出的方法通过不精确的异常标签提高了异常检测性能，并且优于现有的无监督和有监督的异常检测以及多实例学习方法。