  This paper analyzes a new regularized learning scheme for high dimensional
partially linear support vector machine. The proposed approach consists of an
empirical risk and the Lasso-type penalty for linear part, as well as the
standard functional norm for nonlinear part. Here the linear kernel is used for
model interpretation and feature selection, while the nonlinear kernel is
adopted to enhance algorithmic flexibility. In this paper, we develop a new
technical analysis on the weighted empirical process, and establish the sharp
learning rates for the semi-parametric estimator under the regularized
conditions. Specially, our derived learning rates for semi-parametric SVM
depend on not only the sample size and the functional complexity, but also the
sparsity and the margin parameters.
