Early Stopping for Regression Trees
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909705806282752 |
|---|---|
| author | Miftachov, Ratmir Reiß, Markus |
| author_facet | Miftachov, Ratmir Reiß, Markus |
| contents | We develop early stopping rules for growing regression tree estimators. The fully data-driven stopping rule is based on monitoring the global residual norm. The best-first search and the breadth-first search algorithms together with linear interpolation give rise to generalized projection or regularization flows. A general theory of early stopping is established. Oracle inequalities for the early-stopped regression tree are derived without any smoothness assumption on the regression function, assuming the original CART splitting rule, yet with a much broader scope. The remainder terms are of smaller order than the best achievable rates for Lipschitz functions in dimension $d\ge 2$. In real and synthetic data the early stopping regression tree estimators attain the statistical performance of cost-complexity pruning while significantly reducing computational costs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04709 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Early Stopping for Regression Trees Miftachov, Ratmir Reiß, Markus Statistics Theory We develop early stopping rules for growing regression tree estimators. The fully data-driven stopping rule is based on monitoring the global residual norm. The best-first search and the breadth-first search algorithms together with linear interpolation give rise to generalized projection or regularization flows. A general theory of early stopping is established. Oracle inequalities for the early-stopped regression tree are derived without any smoothness assumption on the regression function, assuming the original CART splitting rule, yet with a much broader scope. The remainder terms are of smaller order than the best achievable rates for Lipschitz functions in dimension $d\ge 2$. In real and synthetic data the early stopping regression tree estimators attain the statistical performance of cost-complexity pruning while significantly reducing computational costs. |
| title | Early Stopping for Regression Trees |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2502.04709 |