Neyman-Pearson Paradigm in Binary Classification

• Activity Number: 392
• Type: Topic Contributed
• Date/Time: Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Xin Tong*+
• Companies: Princeton University
• Keywords: binary classification ; Neyman-Pearson paradigm ; anomaly detection ; empirical constraint ; empirical risk minimization

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 $\hat{f}$ that satisfies simultaneously the two following properties with high probability: (\rmnum{1}), type \Rmnum{1} error of $\hat{f}$ is below a pre-specified level $\alpha$; (\rmnum{2}), $\hat{f}$ has type \Rmnum{2} error close to minimum under the type \Rmnum{1} constraint. The classifier $\hat{f}$ is obtained by solving an optimization problem with an empirical objective and an empirical constraint. Moreover, we address the case where we have more observations in one class than the other, as it is in anomaly detection problems.