# Classification Trees for Imbalanced and Sparse Data: Surface-to-Volume Regularization

arXiv: https://arxiv.org/abs/2004.12293 · HTML: https://mlsanity.com/paper/2004.12293/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Apr 2020.

## Built on by (most cited first, 2 of 2)

- [Ranking Perspective for Tree-based Methods with Applications to Symbolic Feature Selection](https://mlsanity.com/paper/2410.02623/) (2024)
- [Skew-Probabilistic Neural Networks for Learning from Imbalanced Data](https://mlsanity.com/paper/2312.05878/) (2023)

## Abstract (arXiv)

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.