Robust chance-constrained support vector machines with second-order moment information

Ximing Wang, Neng Fan, Panos M. Pardalos

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

Support vector machines (SVM) is one of the well known supervised classes of learning algorithms. Basic SVM models are dealing with the situation where the exact values of the data points are known. This paper studies SVM when the data points are uncertain. With some properties known for the distributions, chance-constrained SVM is used to ensure the small probability of misclassification for the uncertain data. As infinite number of distributions could have the known properties, the robust chance-constrained SVM requires efficient transformations of the chance constraints to make the problem solvable. In this paper, robust chance-constrained SVM with second-order moment information is studied and we obtain equivalent semidefinite programming and second order cone programming reformulations. The geometric interpretation is presented and numerical experiments are conducted. Three types of estimation errors for mean and covariance information are studied in this paper and the corresponding formulations and techniques to handle these types of errors are presented.

Original languageEnglish (US)
Pages (from-to)45-68
Number of pages24
JournalAnnals of Operations Research
Volume263
Issue number1-2
DOIs
StatePublished - Apr 1 2018

Keywords

  • Estimation errors
  • Robust chance constraints
  • Second order cone programming
  • Second-order moment information
  • Semidefinite programming
  • Support vector machines

ASJC Scopus subject areas

  • Decision Sciences(all)
  • Management Science and Operations Research

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