Abstract:This work formalizes the new framework for anomaly detection, called active anomaly detection. This framework has, in practice, the same cost of unsupervised anomaly detection but with the possibility of much better results. We show that unsupervised anomaly detection is an undecidable problem and that a prior needs to be assumed for the anomalies probability distribution in order to have performance guarantees. Finally, we also present a new layer that can be attached to any deep learning model designed for unsupervised anomaly detection to transform it into an active anomaly detection method, presenting results on both synthetic and real anomaly detection datasets.