$ \nu$ -Support Vector Machine as Conditional Value-at-Risk Minimization
$ \nu$ -Support Vector Machine as Conditional Value-at-Risk Minimization
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发表时间：
2011
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通讯作者：
A. Takeda;Masashi Sugiyama
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作者：
A. Takeda;Masashi Sugiyama
$ \nu$ -支持向量分类（$ \nu$ -SVC）算法被证明工作良好，并提供直观的解释，例如，参数$ \nu$粗略地指定了支持向量的分数。虽然$ \nu$对应的是一个分数，但它不能以原始形式取0 $和1之间的整个范围。这个问题是解决了$ \nu$ -SVC的非凸扩展和扩展的方法，实验证明比原来的v-SVC更好地推广。然而，其良好的推广性能和优化算法的收敛性尚未得到研究。在本文中，我们提供了新的理论见解，这些问题，并提出了一种新的$ \nu$ -SVC算法，有保证的泛化性能和收敛性能。
The $ \nu$ -support vector classification ( $ \nu$ -SVC) algorithm was shown to work well and provide intuitive interpretations, e.g., the parameter $ \nu$ roughly specifies the fraction of support vectors. Although $ \nu$ corresponds to a fraction, it cannot take the entire range between $0$ and 1 in its original form. This problem was settled by a non-convex extension of $ \nu$ -SVC and the extended method was experimentally shown to generalize better than original v-SVC. However, its good generalization performance and convergence properties of the optimization algorithm have not been studied yet. In this paper, we provide new theoretical insights into these issues and propose a novel $ \nu$ -SVC algorithm that has guaranteed generalization performance and convergence properties.