Performance Measures for Neyman–Pearson Classification

In the Neyman-Pearson (NP) classification paradigm, the goal is to learn a classifier from labeled training data such that the probability of a false negative is minimized while the probability of a false positive is below a user-specified level alpha isin (0,1). This work addresses the question of how to evaluate and compare classifiers in the NP setting. Simply reporting false positives and false negatives leaves some ambiguity about which classifier is best. Unlike conventional classification, however, there is no natural performance measure for NP classification. We cannot reject classifiers whose false positive rate exceeds a since, among other reasons, the false positive rate must be estimated from data and hence is not known with certainty. We propose two families of performance measures for evaluating and comparing classifiers and suggest one criterion in particular for practical use. We then present general learning rules that satisfy performance guarantees with respect to these criteria. As in conventional classification, the notion of uniform convergence plays a central role, and leads to finite sample bounds, oracle inequalities, consistency, and rates of convergence. The proposed performance measures are also applicable to the problem of anomaly prediction.