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This paper analyzes a new regularized learning scheme for high dimensionalpartially linear support vector machine. The proposed approach consists of anempirical risk and the Lasso-type penalty for linear part, as well as thestandard functional norm for nonlinear part. Here the linear kernel is used formodel interpretation and feature selection, while the nonlinear kernel isadopted to enhance algorithmic flexibility. In this paper, we develop a newtechnical analysis on the weighted empirical process, and establish the sharplearning rates for the semi-parametric estimator under the regularizedconditions. Specially, our derived learning rates for semi-parametric SVMdepend on not only the sample size and the functional complexity, but also thesparsity and the margin parameters.

Learning rates for partially linear support vector machine in high dimensions