Classification Trees for Imbalanced and Sparse Data: Surface-to-Volume Regularization
This addresses the challenge of irregular decision boundaries in classification trees for imbalanced datasets, which is an incremental improvement for practitioners needing interpretable models.
The paper tackled the problem of poor generalization in classification trees for imbalanced and sparse data by proposing a novel Surface-to-Volume Ratio (SVR) regularization method, resulting in the SVR-Tree algorithm that shows competitive performance in real data applications.
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.