用自适应分段编码提升回归模型的可解释性与非线性捕捉能力
SplitWise Regression: Stepwise Modeling with Adaptive Dummy Encoding
- 通过浅层决策树将数值变量转为阈值二元特征，仅在提升拟合度时启用
- 在真实和合成数据上均比传统逐步回归更简洁且泛化性能更好
- 适合需要可解释性又需处理非线性关系的统计建模场景
在保持可解释性的前提下捕捉非线性关系仍是回归建模中的持续挑战。我们提出SplitWise框架，增强逐步回归方法。该方法利用浅层决策树自适应地将数值预测变量转换为基于阈值的二元特征，但仅当转换能改善模型拟合度（以AIC或BIC评估）时才执行。此方法在保留线性模型透明性的同时，灵活捕捉非线性效应。SplitWise已实现为易用的R包，在合成及真实世界数据集上进行了评估。结果表明，其始终生成比传统逐步回归和惩罚回归更简洁、泛化能力更强的模型。
原文摘要 · Abstract (English)
Capturing nonlinear relationships without sacrificing interpretability remains a persistent challenge in regression modeling. We introduce SplitWise, a novel framework that enhances stepwise regression. It adaptively transforms numeric predictors into threshold-based binary features using shallow decision trees, but only when such transformations improve model fit, as assessed by the Akaike Information Criterion (AIC) or Bayesian Information Criterion (BIC). This approach preserves the transparency of linear models while flexibly capturing nonlinear effects. Implemented as a user-friendly R package, SplitWise is evaluated on both synthetic and real-world datasets. The results show that it consistently produces more parsimonious and generalizable models than traditional stepwise and penalized regression techniques.
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