Set-Valued Support Vector Machine with Bounded Error Rates

• 成果类型: Article
• 署名作者: Wang, Wenbo; Qiao, Xingye
• 署名单位: State University of New York (SUNY) System; Binghamton University, SUNY
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2089573
• 发表日期: 2023
• 页码: 2847-2859
• 关键词: neyman-pearson classification; convexity; TUTORIAL; kernel

摘要

This article concerns cautious classification models that are allowed to predict a set of class labels or reject to make a prediction when the uncertainty in the prediction is high. This set-valued classification approach is equivalent to the task of acceptance region learning, which aims to identify subsets of the input space, each of which guarantees to cover observations in a class with at least a predetermined probability. We propose to directly learn the acceptance regions through risk minimization, by making use of a truncated hinge loss and a constrained optimization framework. Collectively our theoretical analyses show that these acceptance regions, with high probability, satisfy simultaneously two properties: (a) they guarantee to cover each class with a noncoverage rate bounded from above; (b) they give the least ambiguous predictions among all the acceptance regions satisfying (a). An efficient algorithm is developed and numerical studies are conducted using both simulated and real data. for this article are available online.