On Stopping Rules and Spatial Adaptation for CART
The popular CART algorithm for regression trees combines a greedy splitting rule with a stopping rule, but while the splitting rule has been well studied, the statistical role of stopping rules is less well understood. Meanwhile, although regression trees fit using Bayesian methods or via empirical risk minimization (ERM) have been shown to be spatially adaptive to local smoothness and anisotropy, it is unknown whether CART can achieve the same adaptation. We address these gaps by proving that, under spatially heterogeneous and anisotropic smoothness and appropriate structural assumptions on the regression function and covariate distribution, CART with the minimum impurity decrease (MID) ...
| Authors | Zineng Xu, Yuchao Cai, Yan Shuo Tan |
|---|---|
| Primary category | stat.ML |
| Published | 16 August 2026 |
| Last updated at source | 16 August 2026 |
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