Classification Trees for Imbalanced Data: Surface-to-Volume Regularization

• 成果类型: Article
• 署名作者: Zhu, Yichen; Li, Cheng; Dunson, David B.
• 署名单位: Duke University; National University of Singapore; Duke University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2021.2005609
• 发表日期: 2023
• 页码: 1707-1717
• 关键词: smote; sets

摘要

Classification algorithms face difficulties when one or more classes have limited training data. We are particularly interested in classification trees, due to their interpretability and flexibility. When data are limited in one or more of the classes, the estimated decision boundaries are often irregularly shaped due to the limited sample size, leading to poor generalization error. We propose a novel approach that penalizes the Surface-to-Volume Ratio (SVR) of the decision set, obtaining a new class of SVR-Tree algorithms. We develop a simple and computationally efficient implementation while proving estimation consistency for SVR-Tree and rate of convergence for an idealized empirical risk minimizer of SVR-Tree. SVR-Tree is compared with multiple algorithms that are designed to deal with imbalance through real data applications. Supplementary materials for this article are available online.