SMART用树结构找断点，再用MARS拟合连续段，提升回归精度。
SMART: A Flexible Approach to Regression using Spline-Based Multivariate Adaptive Regression Trees
- 树结构识别数据断点，分段后由MARS独立拟合连续关系。
- 在含间断的连续关系建模上优于现有方法，尤其适合复杂非线性数据。
- 开源实现，适合需要高精度回归的机器学习实践者。
决策树在预测建模中表现强大，但在处理连续关系时易出现高方差问题。尽管多变量自适应样条回归（MARS）能有效捕捉连续关系，但在建模间断时表现不佳。为此，我们提出基于样条的多变量自适应回归树（SMART），利用决策树识别具有不同连续关系的数据子集，并对每个子集独立使用MARS进行拟合。与依赖树结构建模交互项和高阶项的方法不同，SMART充分利用MARS原生处理这些项的能力，使树结构仅专注于识别关系中的间断点。我们在多个数据集上测试了SMART，结果表明其在类似场景下显著优于当前最优方法。此外，我们还提供了开源实现，供研究人员和从业者使用。
原文摘要 · Abstract (English)
Decision trees are powerful for predictive modeling but often suffer from high variance when modeling continuous relationships. While algorithms like Multivariate Adaptive Regression Splines (MARS) excel at capturing such continuous relationships, they perform poorly when modeling discontinuities. To address the limitations of both approaches, we introduce Spline-based Multivariate Adaptive Regression Trees (SMART), which uses a decision tree to identify subsets of data with distinct continuous relationships and then leverages MARS to fit these relationships independently. Unlike other methods that rely on the tree structure to model interaction and higher-order terms, SMART leverages MARS's native ability to handle these terms, allowing the tree to focus solely on identifying discontinuities in the relationship. We test SMART on various datasets, demonstrating its improvement over state-of-the-art methods in such cases. Additionally, we provide an open-source implementation of our method to be used by practitioners.
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