Abstract
We provide a formulation for Local Support Vector Machines (LSVMs) that generalizes previous formulations, and brings out the explicit connections to local polynomial learning used in nonparametric estimation literature. We investigate the simplest type of LSVMs called Local Linear Support Vector Machines (LLSVMs). For the first time we establish conditions under which LLSVMs make Bayes consistent predictions at each test point $x_0$. We also establish rates at which the local risk of LLSVMs converges to the minimum value of expected local risk at each point $x_0$. Using stability arguments we establish generalization error bounds for LLSVMs.
Abstract (translated by Google)
我们为局部支持向量机（LSVM）提供了一个公式，该公式推广了以前的公式，并引出了与非参数估计文献中使用的局部多项式学习的显式关联。我们研究称为局部线性支持向量机（LLSVM）的最简单类型的LSVM。我们第一次建立了LLSVM在每个测试点$ x_0 $下进行贝叶斯一致预测的条件。我们还建立了LLSVM的局部风险在每个点$ x_0 $收敛到预期局部风险最小值的汇率。使用稳定性参数我们为LLSVMs建立泛化误差界。
URL
https://arxiv.org/abs/1309.3699