Semi-supervised novelty detection

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