Neyman-Pearson classification, convexity and stochastic constraints

TL;DR

This paper develops a Neyman-Pearson-based classification method that combines classifiers to control type I error while minimizing type II error, using convex optimization and new chance-constrained techniques.

Contribution

It introduces a novel classifier construction method under the Neyman-Pearson framework with convex loss, handling stochastic constraints effectively.

Findings

Classifier satisfies type I error constraint with high probability

Type II error is close to the minimum achievable

New techniques impact chance constrained programming

Abstract

Motivated by problems of anomaly detection, this paper implements the Neyman-Pearson paradigm to deal with asymmetric errors in binary classification with a convex loss. Given a finite collection of classifiers, we combine them and obtain a new classifier that satisfies simultaneously the two following properties with high probability: (i) its probability of type I error is below a pre-specified level and (ii), it has probability of type II error close to the minimum possible. The proposed classifier is obtained by solving an optimization problem with an empirical objective and an empirical constraint. New techniques to handle such problems are developed and have consequences on chance constrained programming.