Neyman-Pearson (NP) classification algorithms and NP receiver operating characteristics (NP-ROC)

TL;DR

This paper introduces a new umbrella algorithm for implementing Neyman-Pearson classification across various models, along with NP-ROC bands for better classifier evaluation and selection, addressing a gap in controlling type I errors.

Contribution

It develops the first universal umbrella algorithm for Neyman-Pearson classification applicable to all scoring classifiers and introduces NP-ROC bands for data-driven classifier comparison.

Findings

The umbrella algorithm effectively controls type I error below the threshold.

NP-ROC bands assist in selecting optimal significance levels.

The methods are validated through simulations and real data analysis.

Abstract

In many binary classification applications such as disease diagnosis and spam detection, practitioners often face great needs to control type I errors (i.e., the conditional probability of misclassifying a class 0 observation as class 1) so that it remains below a desired threshold. To address this need, the Neyman-Pearson (NP) classification paradigm is a natural choice; it minimizes type II error (i.e., the conditional probability of misclassifying a class 1 observation as class 0) while enforcing an upper bound, $\alpha$, on the type I error. Although the NP paradigm has a century-long history in hypothesis testing, it has not been well recognized and implemented in classification schemes. Common practices that directly limit the empirical type I error to no more than $\alpha$ do not satisfy the type I error control objective because the resulting classifiers are still likely to have type I errors much larger than $\alpha$. As a result, the NP paradigm has not been properly implemented for many classification scenarios in practice. In this work, we develop the first umbrella algorithm that implements the NP paradigm for all scoring-type classification methods, including popular methods such as logistic regression, support vector machines and random forests. Powered by this umbrella algorithm, we propose a novel graphical tool for NP classification methods: NP receiver operating characteristic (NP-ROC) bands, motivated by the popular receiver operating characteristic (ROC) curves. NP-ROC bands will help choose $\alpha$ in a data adaptive way and compare different NP classifiers. We demonstrate the use and properties of the NP umbrella algorithm and NP-ROC bands, available in the R package nproc, through simulation and real data case studies.