Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.03576 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929742887780352 |
|---|---|
| author | Harviainen, Juha Sommer, Frank Sorge, Manuel Szeider, Stefan |
| author_facet | Harviainen, Juha Sommer, Frank Sorge, Manuel Szeider, Stefan |
| contents | We present a comprehensive classical and parameterized complexity analysis of decision tree pruning operations, extending recent research on the complexity of learning small decision trees. Thereby, we offer new insights into the computational challenges of decision tree simplification, a crucial aspect of developing interpretable and efficient machine learning models. We focus on fundamental pruning operations of subtree replacement and raising, which are used in heuristics. Surprisingly, while optimal pruning can be performed in polynomial time for subtree replacement, the problem is NP-complete for subtree raising. Therefore, we identify parameters and combinations thereof that lead to fixed-parameter tractability or hardness, establishing a precise borderline between these complexity classes. For example, while subtree raising is hard for small domain size $D$ or number $d$ of features, it can be solved in $D^{2d} \cdot |I|^{O(1)}$ time, where $|I|$ is the input size. We complement our theoretical findings with preliminary experimental results, demonstrating the practical implications of our analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03576 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Decision Tree Pruning Revisited: Algorithms and Complexity Harviainen, Juha Sommer, Frank Sorge, Manuel Szeider, Stefan Machine Learning We present a comprehensive classical and parameterized complexity analysis of decision tree pruning operations, extending recent research on the complexity of learning small decision trees. Thereby, we offer new insights into the computational challenges of decision tree simplification, a crucial aspect of developing interpretable and efficient machine learning models. We focus on fundamental pruning operations of subtree replacement and raising, which are used in heuristics. Surprisingly, while optimal pruning can be performed in polynomial time for subtree replacement, the problem is NP-complete for subtree raising. Therefore, we identify parameters and combinations thereof that lead to fixed-parameter tractability or hardness, establishing a precise borderline between these complexity classes. For example, while subtree raising is hard for small domain size $D$ or number $d$ of features, it can be solved in $D^{2d} \cdot |I|^{O(1)}$ time, where $|I|$ is the input size. We complement our theoretical findings with preliminary experimental results, demonstrating the practical implications of our analysis. |
| title | Optimal Decision Tree Pruning Revisited: Algorithms and Complexity |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2503.03576 |