Transductive anomaly detection

One formulation of the anomaly detection problem is to build a detector based on a training sample consisting only on nominal data. The standard approach to this problem has been to declare anomalies where the nominal density is low, which reduces the problem to density level set estimation. This approach is inductive in the sense that the detector is constructed before any test data are observed. In this paper, we consider the transductive setting where the unlabeled and possibly contaminated test sample is also available at learning time. We argue that anomaly detection in this transductive setting is naturally solved by a general reduction to a binary classification problem. In particular, an anomaly detector with a desired false positive rate can be achieved through a reduction to Neyman-Pearson classification. Unlike the inductive approach, the transductive approach yields detectors that are optimal (e.g., statistically consistent) regardless of the distribution on anomalies. Therefore, in anomaly detection, unlabeled data can have a substantial impact on the theoretical properties of the decision rule.