Sparse Distance-Weighted Discrimination and the Oracle Theory

• Activity Number: 382
• Type: Invited
• Date/Time: Tuesday, August 3, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Lingsong Zhang*+ and Xihong Lin
• Companies: Purdue University and Harvard School of Public Health
• Keywords: classification ; variable selection ; high dimension ; oracle theory ; proteomics ; machine learning

Abstract

Distance Weighted Discrimination (DWD) has recently been proposed as an attractive classification method. In this paper, we first show Fisher consistency of the DWD method, which justifies its use when there are sufficient data. However, the DWD classifier is not sparse, which makes the interpretation and prediction performance less attractive. We propose several sparse DWD methods, which incorporate variable selection techniques in classification using penalized loss functions to estimate the true hyperplane. We show that when an appropriate penalty is used, the sparse DWD method is consistent and the estimated normal vector has the oracle property under suitable conditions. We evaluate the finite sample performance of the proposed methods using simulations and illustrate the methods with an application to the Faroe island proteomic biomarker data.