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[2503.14381] Optimizing High-Dimensional Oblique Splits
Summary
This article explores the optimization of high-dimensional oblique splits in decision trees, demonstrating their potential to enhance model performance through a novel iterative refinement approach.
Why It Matters
Understanding how to optimize oblique splits in decision trees is crucial for improving machine learning models, especially in complex data scenarios. This research provides insights into balancing statistical accuracy and computational efficiency, which is vital for practitioners in data science and machine learning.
Key Takeaways
- Oblique splits can significantly improve decision tree performance.
- The Sufficient Impurity Decrease (SID) function class expands with increased sparsity, capturing complex data patterns.
- Learning complex functions requires more computational resources, highlighting a trade-off between accuracy and cost.
- Progressive trees optimize oblique splits iteratively, enhancing ensemble models like Random Forests.
- The proposed method outperforms existing oblique tree models in simulations and real-data experiments.
Statistics > Machine Learning arXiv:2503.14381 (stat) [Submitted on 18 Mar 2025 (v1), last revised 21 Feb 2026 (this version, v2)] Title:Optimizing High-Dimensional Oblique Splits Authors:Chien-Ming Chi View a PDF of the paper titled Optimizing High-Dimensional Oblique Splits, by Chien-Ming Chi View PDF Abstract:Evidence suggests that oblique splits can significantly enhance the performance of decision trees. This paper explores the optimization of high-dimensional oblique splits for decision tree construction, establishing the Sufficient Impurity Decrease (SID) convergence that takes into account $s_0$-sparse oblique splits. We demonstrate that the SID function class expands as sparsity parameter $s_0$ increases, enabling the model to capture complex data-generating processes such as the $s_0$-dimensional XOR function. Thus, $s_0$ represents the unknown potential complexity of the underlying data-generating function. Furthermore, we establish that learning these complex functions necessitates greater computational resources. This highlights a fundamental trade-off between statistical accuracy, which is governed by the $s_0$-dependent size of the SID function class, and computational cost. Particularly, for challenging problems, the required candidate oblique split set can become prohibitively large, rendering standard ensemble approaches computationally impractical. To address this, we propose progressive trees that optimize oblique splits through an iterative refinement ...
