Support vector machines based on convex risk functions and general norms
Support vector machines based on convex risk functions and general norms
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DOI：
10.1007/s10479-016-2326-x
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发表时间：
2016-09
影响因子：
4.8
通讯作者：
Jun-ya Gotoh;S. Uryasev
中科院分区：
文献类型：
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作者：
Jun-ya Gotoh;S. Uryasev
基于凸分析，特别是近年来在金融优化领域发展起来的凸风险函数理论，研究了支持向量机（SVM）二元分类的统一形式。使用凸经验风险和凸正则化的概念，一对原始和对偶公式的支持向量机的一般方式进行了描述。与广义公式，我们讨论了合理的选择的经验风险和正则化的风险函数的性质的基础上，这是众所周知的金融环境。特别是，我们使用的风险函数的双重表示的属性，以获得多种解释。我们提供了两个观点的鲁棒优化建模，加强已知的事实：（1）原始配方可以被视为一个强大的经验风险最小化;（2）对偶配方是兼容的分布鲁棒建模。
This paper studies unified formulations of support vector machines (SVMs) for binary classification on the basis of convex analysis, especially, convex risk functions theory, which is recently developed in the context of financial optimization. Using the notions of convex empirical risk and convex regularizer, a pair of primal and dual formulations of the SVMs are described in a general manner. With the generalized formulations, we discuss reasonable choices for the empirical risk and the regularizer on the basis of the risk function’s properties, which are well-known in the financial context. In particular, we use the properties of the risk function’s dual representations to derive multiple interpretations. We provide two perspectives on robust optimization modeling, enhancing the known facts: (1) the primal formulation can be viewed as a robust empirical risk minimization; (2) the dual formulation is compatible with the distributionally robust modeling.