Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/s10479-016-2326-x | Annals OR |
Keywords | Field | DocType |
Support vector machine, SVM, Binary classification, Convex risk function, Duality, Norm, Robust optimization | Discrete mathematics,Convexity in economics,Mathematical optimization,Empirical risk minimization,Quasiconvex function,Choquet theory,Proper convex function,Convex optimization,Linear matrix inequality,Mathematics,Convex analysis | Journal |
Volume | Issue | ISSN |
249 | 1-2 | 1572-9338 |
Citations | PageRank | References |
1 | 0.36 | 18 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jun-Ya Gotoh | 1 | 117 | 10.17 |
| Stan Uryasev | 2 | 243 | 27.31 |