Provable guarantees for decision tree induction: the agnostic setting

Part of Proceedings of the International Conference on Machine Learning 1 pre-proceedings (ICML 2020)

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Guy Blanc, Jane Lange, Li-Yang Tan


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 $s\in \N$, these heuristics construct a decision tree of size $s^{\tilde{O}((\log s)/\eps^2)}$ that achieves error $\le \opt_s + \eps$, where $\opt_s$ 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.