  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.
