A Plug-In Approach to Supervised Binary Classification Problems in High-Dimensional Space Under the Neyman-Pearson Paradigm

• Activity Number: 215
• Type: Topic Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: WNAR
• Author(s): Anqi Zhao*+ and Xin Tong and Yang Feng and Lie Wang
• Companies: Harvard and University of Southern California and Columbia University and MIT
• Keywords: plug-in approach ; Neyman-Pearson paradigm ; NP oracle inequality ; Naive Bayes classifier ; screening

Abstract

Most existing binary classification algorithms target on optimizing the overall classification error and may fail to fully serve the purpose of some real-world applications in which users care more about bounding or optimizing a specific type of error (i.e. false positive/ false negative). Neyman-Pearson (NP) paradigm is introduced in this context as a novel statistical framework for asymmetric risk control. It seeks classifiers that minimize one type of risk while keeping the other under a user specified level. In this paper, we propose a plug-in approach to constructing NP-type classifiers based on the Neyman-Pearson Lemma. Theoretical properties of the resulting classifiers are derived in terms of oracle inequalities. Two types of Neyman-Pearson Naive Bayes (NNB) classifiers in specific, together with their screening-based variants, are then implemented under independence rule and sparsity independence assumption for binary classification in high and ultra-high dimensional spaces. Simulation studies and real data analysis support our theoretical results and demonstrate the advantages of NNB classifiers in controlling a specific type of risk under a variety of circumstances.