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@MISC{Hastie_comment,
author = {Trevor Hastie and Ji Zhu},
title = {Comment},
year = {}
}
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Abstract
We congratulate the authors for a well written and thoughtful survey of some of the literature in this area. They are mainly concerned with the geometry and the computational learning aspects of the support vector machine (SVM). We will therefore complement their review by discussing from the statistical function estimation perspective. In particular, we will elaborate on the following points: • Kernel regularization is essentially a generalized ridge penalty in a certain feature space. • In practice, the effective dimension of the data kernel matrix is not always equal to n, even when the implicit dimension of the feature space is infinite; hence, the training data are not always perfectly separable. • Appropriate regularization plays an important role in the success of the SVM. • The SVM is not fundamentally different from many statistical tools that our statisticians are familiar with, for example, penalized logistic regression. We acknowledge that many of the comments are based
Keyphrases
important role feature space training data support vector machine certain feature space following point generalized ridge penalty data kernel matrix thoughtful survey kernel regularization appropriate regularization many statistical tool logistic regression effective dimension implicit dimension statistical function estimation perspective computational learning aspect
