Support vector machines based on convex risk functions and general norms

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• 作者：Jun-ya Gotoh ; Stan Uryasev
• 关键词：Support vector machine ; SVM ; Binary classification ; Convex risk function ; Duality ; Norm ; Robust optimization
• 刊名：Annals of Operations Research
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：249
• 期：1-2
• 页码：301-328
• 全文大小：
• 刊物类别：Business and Economics
• 刊物主题：Operation Research/Decision Theory; Combinatorics; Theory of Computation;
• 出版者：Springer US
• ISSN：1572-9338
• 卷排序：249

文摘

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.