Abstract
We investigate practical selection of meta-parameters for SVM regression (that is,
ε -insensitive zone and regularization parameter C). The proposed methodology advocates analytic
parameter selection directly from the training data, rather than resampling approaches commonly
used in SVM applications. Good generalization performance of the proposed parameter selection is
demonstrated empirically using several low-dimensional and high-dimensional regression
problems. Further, we point out the importance of Vapnik’s ε -insensitive loss for regression
problems with finite samples. To this end, we compare generalization performance of SVM
regression (with optimally chosen ε ) with regression using ‘least-modulus’ loss (ε =0). These
comparisons indicate superior generalization performance of SVM regression, for finite sample
settings.
Keywords: Complexity Control; Parameter Selection; Support Vector Machine; VC theory
1. Introduction
This study is motivated by a growing popularity of support vector machines (SVM) for
regression problems [3,6-14]. Their practical successes can be attributed to solid
theoretical foundations based on VC-theory [13,14], since SVM generalization
performance does not depend on the dimensionality of the input space. However, many
SVM regression application studies are performed by ‘expert’ users having good
understanding of SVM methodology. Since the quality of SVM models depends on a
proper setting of SVM meta-parameters, the main issue for practitioners trying to apply
SVM regression is how to set these parameter values (to ensure good generalization
performance) for a given data set. Whereas existing sources on SVM regression

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