Tuning Support Vector Machines for Minimax and Neyman-Pearson Classification

Authors:
Mark A. Davenport;Richard G. Baraniuk;Clayton D. Scott
Affiliations:
Stanford University, Stanford;Rice University, Houston;University of Michigan, Ann Arbor
Venue:
IEEE Transactions on Pattern Analysis and Machine Intelligence
Year:
2010

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Abstract

This paper studies the training of support vector machine (SVM) classifiers with respect to the minimax and Neyman-Pearson criteria. In principle, these criteria can be optimized in a straightforward way using a cost-sensitive SVM. In practice, however, because these criteria require especially accurate error estimation, standard techniques for tuning SVM parameters, such as cross-validation, can lead to poor classifier performance. To address this issue, we first prove that the usual cost-sensitive SVM, here called the 2C-SVM, is equivalent to another formulation called the 2\nu-SVM. We then exploit a characterization of the 2\nu-SVM parameter space to develop a simple yet powerful approach to error estimation based on smoothing. In an extensive experimental study, we demonstrate that smoothing significantly improves the accuracy of cross-validation error estimates, leading to dramatic performance gains. Furthermore, we propose coordinate descent strategies that offer significant gains in computational efficiency, with little to no loss in performance.