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The Neyman-Pearson (NP) paradigm in binary classification seeks classifiersthat achieve a minimal type II error while enforcing the prioritized type Ierror controlled under some user-specified level $\alpha$. This paradigm servesnaturally in applications such as severe disease diagnosis and spam detection,where people have clear priorities among the two error types. Recently, Tong,Feng and Li (2018) proposed a nonparametric umbrella algorithm that adapts allscoring-type classification methods (e.g., logistic regression, support vectormachines, random forest) to respect the given type I error upper bound $\alpha$with high probability, without specific distributional assumptions on thefeatures and the responses. Universal the umbrella algorithm is, it demands anexplicit minimum sample size requirement on class $0$, which is often the morescarce class, such as in rare disease diagnosis applications. In this work, weemploy the parametric linear discriminant analysis (LDA) model and propose anew parametric thresholding algorithm, which does not need the minimum samplesize requirements on class $0$ observations and thus is suitable for smallsample applications such as rare disease diagnosis. Leveraging both theexisting nonparametric and the newly proposed parametric thresholding rules, wepropose four LDA-based NP classifiers, for both low- and high-dimensionalsettings. On the theoretical front, we prove NP oracle inequalities for oneproposed classifier, where the rate for excess type II error benefits from theexplicit parametric model assumption. Furthermore, as NP classifiers involve asample splitting step of class $0$ observations, we construct a new adaptivesample splitting scheme that can be applied universally to NP classifiers, andthis adaptive strategy reduces the type II error of these classifiers.

Neyman-Pearson classification: parametrics and sample size requirement