Classification Trees for Imbalanced Data: Surface-to-Volume Regularization
针对分类树在不平衡数据中因样本少导致决策边界不规则、泛化差的问题，提出一种惩罚决策集表面体积比的新算法SVR-Tree，并证明其估计一致性和收敛速度。
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.