Error Bounds of L1 Penalized Estimator for High-Dimensional Support Vector Machine

• Activity Number: 353
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Genomics and Genetics
• Author(s): Bo Peng* and Lan Wang and Yichao Wu
• Companies: University of Minnesota and University of Minnesota and North Carolina State University
• Keywords: Lasso ; Nonconvexity penalty ; Oracle property ; Support Vector Machine ; Variable Selection ; High-Dimensional Data

Abstract

The support vector machine (SVM) is a powerful binary classification tool widely used in medical and biological science. Since redundant features will severely affect the performance of SVM, penalized regression methods, especially those based on the lasso of Tibshirani (1996), have been utilized on its objective function for simultaneous variable selection and coefficient estimation. In this work, we investigate a general class of penalized SVMs under high dimensional settings. Properties such as variable consistency, estimator error bounds have been studied, and are achieved under mild conditions. Our analysis reveals that the method achieves nearly oracle performance, i.e. with large probability, the l2 norm of the estimation error is of order O(?klogp/n) under lasso penalty. The proposed algorithm can identify the oracle solution among potential local minimizers under some sufficient conditions. Simulation studies are provided as support for penalized support vector machine including other non-convex penalties.