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arXiv · 2501.07903

Optimal Classification Trees for Continuous Feature Data Using Dynamic Programming with Branch-and-Bound

Catalin E. Brita·Jacobus G. M. van der Linden·Emir Demirović
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Abstract

Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three. Therefore, most methods rely on a coarse binarization of continuous features to maintain scalability. We propose a novel algorithm that optimizes trees directly on the continuous feature data using dynamic programming with branch-and-bound. We develop new pruning techniques that eliminate many sub-optimal splits in the search when similar to previously computed splits and we provide an efficient subroutine for computing optimal depth-two trees. Our experiments demonstrate that these techniques improve runtime by one or more orders of magnitude over state-of-the-art optimal methods and improve test accuracy by 5% over greedy heuristics.

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Catalin E. Brita, Jacobus G. M. van der Linden, Emir Demirović. 2025-01-14. Optimal Classification Trees for Continuous Feature Data Using Dynamic Programming with Branch-and-Bound. https://arxiv.org/abs/2501.07903

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