用可视觉化的形状函数提升决策树的非线性建模能力
Empowering Decision Trees via Shape Function Branching
- 每个节点用可学习的形状函数替代简单切分，实现复杂非线性分割
- 在多个数据集上性能更优且模型规模更小，减少深度树结构
- 适合需要解释性的表格数据场景，尤其关注决策过程可视化
决策树因其可解释性和在表格数据上的良好表现而备受青睐。然而，其依赖简单的轴对齐线性切分，常需构建深层复杂结构来捕捉非线性特征效应，削弱了人类对树结构的理解。为此，我们提出一种新的决策树泛化形式——形状广义树（SGT），其中每个内部节点对单个特征应用可学习的轴对齐形状函数，实现一次切分即完成丰富非线性划分。由于用户可直观可视化每个节点的形状函数，SGTs具有天然可解释性，并能提供模型决策机制的直观视觉解释。为从数据中学习SGTs，我们提出高效归纳算法ShapeCART。进一步将SGT框架扩展至双变量形状函数（S²GT）和多路树（SGT_K），并分别提出Shape²CART和ShapeCART_K。在多种数据集上的实验表明，SGTs在保持更小模型规模的同时，性能优于传统轴对齐线性树。
原文摘要 · Abstract (English)
Decision trees are prized for their interpretability and strong performance on tabular data. Yet, their reliance on simple axis-aligned linear splits often forces deep, complex structures to capture non-linear feature effects, undermining human comprehension of the constructed tree. To address this limitation, we propose a novel generalization of a decision tree, the Shape Generalized Tree (SGT), in which each internal node applies a learnable axis-aligned shape function to a single feature, enabling rich, non-linear partitioning in one split. As users can easily visualize each node's shape function, SGTs are inherently interpretable and provide intuitive, visual explanations of the model's decision mechanisms. To learn SGTs from data, we propose ShapeCART, an efficient induction algorithm for SGTs. We further extend the SGT framework to bivariate shape functions (S$^2$GT) and multi-way trees (SGT$_K$), and present Shape$^2$CART and ShapeCART$_K$, extensions to ShapeCART for learning S$^2$GTs and SGT$_K$s, respectively. Experiments on various datasets show that SGTs achieve superior performance with reduced model size compared to traditional axis-aligned linear trees.
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