论文标题
高维度的部分线性支持向量机的学习率
Learning rates for partially linear support vector machine in high dimensions
论文作者
论文摘要
本文分析了高维部分线性支持向量机的新的正规学习方案。所提出的方法包括经验风险和线性部分的套索惩罚，以及非线性部分的标准功能规范。在这里，线性内核用于模型解释和特征选择，而非线性内核则用于增强算法灵活性。在本文中，我们对加权经验过程进行了新的技术分析，并在正规条件下建立了半参数估计量的尖锐学习率。特别是，我们针对半参数SVM的派生学习率不仅取决于样本量和功能复杂性，还取决于稀疏性和边缘参数。
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.
