In classification problems, the goal is often to maximize the probability of a true positive while satisfying a system design constraint on the number of false alarms. Current classifiers, which are based on minimizing classification error, achieve this goal indirectly by either shifting the bias of the resulting solution or via tuning of an asymmetry parameter. While these approaches may be used to satisfy a false alarm constraint, they may produce classifiers with suboptimal target classification performance at the desired operating point. We propose a large margin classifier that directly maximizes true positive classifications at a desired false alarm rate via the inclusion of an optimization constraint on the estimated probability of false alarms. Unlike existing false alarm constrained classifiers (also called Neyman-Pearson or minimax classifiers) our approach allows the use of an arbitrary loss function and is applicable to nonlinear datasets that exhibit a high degree of class imbalance. Our technique achieves a robust solution in small-sample training scenarios via the use of tail-estimation techniques to predict the probability of false alarms when estimates based on training error may be unreliable.
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