Neyman-Pearson classification under a strict constraint

Motivated by problems of anomaly detection, this paper implements the Neyman-Pearson paradigm to deal with asymmetric errors in binary classication with a convex loss. Given a nite collection of classiers, we combine them and obtain a new classier that satises simultaneously the two following properties with high probability: (i), its probability of type I error is below a pre-specied level and (ii), it has probability of type II error close to the minimum possible. The proposed classier is obtained by minimizing an empirical objective subject to an empirical constraint. The novelty of the method is that the classier output by this problem is shown to satisfy the original constraint on type I error. This strict enforcement of the constraint has interesting consequences on the control of the type II error and we develop new techniques to handle this situation. Finally, connections with chance constrained optimization are evident and are investigated.