Biometrika Advance Access originally published online on November 19, 2007
Biometrika 2008 95(1):149-167; doi:10.1093/biomet/asm077
Articles |
Probability estimation for large-margin classifiers
School of Statistics, University of Minnesota, Minneapolis, Minnesota 55455, U.S.A. wangjh{at}stat.umn.edu, xshen{at}stat.umn.edu
Department of Statistics and Operations Research, Carolina Center for Genome Sciences, University of North Carolina, Chapel Hill, North Carolina 27599, U.S.A. yfliu{at}email.unc.edu
Received for publication 1 April 2006. Revision received 1 May 2007.
Large margin classifiers have proven to be effective in delivering high predictive accuracy, particularly those focusing on the decision boundaries and bypassing the requirement of estimating the class probability given input for discrimination. As a result, these classifiers may not directly yield an estimated class probability, which is of interest itself. To overcome this difficulty, this article proposes a novel method for estimating the class probability through sequential classifications, by using features of interval estimation of large-margin classifiers. The method uses sequential classifications to bracket the class probability to yield an estimate up to the desired level of accuracy. The method is implemented for support vector machines and 
-learning, in addition to an estimated Kullback–Leibler loss for tuning. A solution path of the method is derived for support vector machines to reduce further its computational cost. Theoretical and numerical analyses indicate that the method is highly competitive against alternatives, especially when the dimension of the input greatly exceeds the sample size. Finally, an application to leukaemia data is described.
Key Words: Function estimation • High dimension and low sample size • Interval estimate • Tuning • Weighting
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