Fast Rates for Support Vector Machines
Fast Rates for Support Vector Machines
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DOI：
10.1007/11503415_19
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发表时间：
2005-06
期刊：
影响因子：
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通讯作者：
Ingo Steinwart;C. Scovel
中科院分区：
文献类型：
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作者：
Ingo Steinwart;C. Scovel
我们使用正则化序列为支持向量机（SVM）建立贝叶斯风险的学习率，其中（0，1）是任意的。在Tsybakov最近提出的噪声条件下，这些速率可以比n坦恩-1/2更快。为了处理近似误差，我们提出了一个一般概念，称为近似误差函数，它描述了所考虑的支持向量机的无限样本版本如何近似数据生成分布。此外，我们还详细讨论了“经典”逼近误差与逼近误差函数之间的关系。最后，对于满足几何噪声假设的分布，当所用的RKHS是Sobolev空间时，我们建立了一些学习率。
We establish learning rates to the Bayes risk for support vector machines (SVMs) using a regularization sequence, where(0,1) is arbitrary. Under a noise condition recently proposed by Tsybakov these rates can become faster thann− 1/2. In order to deal with the approximation error we present a general concept called the approximation error function which describes how well the infinite sample versions of the considered SVMs approximate the data-generating distribution. In addition we discuss in some detail the relation between the “classical” approximation error and the approximation error function. Finally, for distributions satisfying a geometric noise assumption we establish some learning rates when the used RKHS is a Sobolev space.