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arXiv · 2006.00743

Provable guarantees for decision tree induction: the agnostic setting

Guy Blanc·Jane Lange·Li-Yang Tan
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Abstract

We give strengthened provable guarantees on the performance of widely employed and empirically successful {\sl top-down decision tree learning heuristics}. While prior works have focused on the realizable setting, we consider the more realistic and challenging {\sl agnostic} setting. We show that for all monotone functions~$f$ and parameters $s\in \mathbb{N}$, these heuristics construct a decision tree of size $s^{\tilde{O}((\log s)/\varepsilon^2)}$ that achieves error $\le \mathsf{opt}_s + \varepsilon$, where $\mathsf{opt}_s$ denotes the error of the optimal size-$s$ decision tree for $f$. Previously, such a guarantee was not known to be achievable by any algorithm, even one that is not based on top-down heuristics. We complement our algorithmic guarantee with a near-matching $s^{\tilde{\Omega}(\log s)}$ lower bound.

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Guy Blanc, Jane Lange, Li-Yang Tan. 2020-06-01. Provable guarantees for decision tree induction: the agnostic setting. https://arxiv.org/abs/2006.00743

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