论文标题
关于支持向量机的精确误差分析
On the Precise Error Analysis of Support Vector Machines
论文作者
论文摘要
本文研究了从高斯混合物分布中从高斯混合物分布中绘制的，调查了软化和硬利润支持矢量机（SVM）分类器的渐近分类器（SVM）分类器（同时具有高维和大量数据（大$ n $和$ n/p \toΔ$）的大型$ n $和$ n/p \toΔ$）。提供了对硬利润和软边缘SVM的分类错误率的尖锐预测，以及作为重要参数（例如边缘和偏置）的渐近限制。作为进一步的结果，该分析允许识别Hard-Margin SVM能够分离的最大训练样品数量。我们结果的确切性质允许对硬利润和软边缘SVM进行准确的性能比较，并更好地了解分类性能的涉及参数（例如测量值和余量参数）。我们的分析通过一组数值实验确认，建立在凸高斯Min-Max定理的基础上，并将其范围扩展到该框架以前从未研究过的新问题。
This paper investigates the asymptotic behavior of the soft-margin and hard-margin support vector machine (SVM) classifiers for simultaneously high-dimensional and numerous data (large $n$ and large $p$ with $n/p\toδ$) drawn from a Gaussian mixture distribution. Sharp predictions of the classification error rate of the hard-margin and soft-margin SVM are provided, as well as asymptotic limits of as such important parameters as the margin and the bias. As a further outcome, the analysis allow for the identification of the maximum number of training samples that the hard-margin SVM is able to separate. The precise nature of our results allow for an accurate performance comparison of the hard-margin and soft-margin SVM as well as a better understanding of the involved parameters (such as the number of measurements and the margin parameter) on the classification performance. Our analysis, confirmed by a set of numerical experiments, builds upon the convex Gaussian min-max Theorem, and extends its scope to new problems never studied before by this framework.
