We propose a simple generalization of standard and empirically successful decision tree learning algorithms such as ID3, C4.5, and CART. These algorithms, which have been central to machine learning for decades, are greedy in nature: they grow a decision tree by iteratively splitting on the best attribute. Our algorithm, Top-$k$, considers the $k$ best attributes as possible splits instead of just the single best attribute. We demonstrate, theoretically and empirically, the power of this simple generalization. We first prove a {\sl greediness hierarchy theorem} showing that for every $k \in \mathbb{N}$, Top-$(k+1)$ can be dramatically more powerful than Top-$k$: there are data distributions for which the former achieves accuracy $1-\varepsilon$, whereas the latter only achieves accuracy $\frac1{2}+\varepsilon$. We then show, through extensive experiments, that Top-$k$ outperforms the two main approaches to decision tree learning: classic greedy algorithms and more recent "optimal decision tree" algorithms. On one hand, Top-$k$ consistently enjoys significant accuracy gains over greedy algorithms across a wide range of benchmarks. On the other hand, Top-$k$ is markedly more scalable than optimal decision tree algorithms and is able to handle dataset and feature set sizes that remain far beyond the reach of these algorithms.

翻译：我们提出一种对标准且经验上成功的决策树学习算法（如ID3、C4.5和CART）的简单泛化。这些算法数十年来一直是机器学习的核心，本质上是贪心的：它们通过迭代地在最佳属性上进行分裂来生长决策树。我们的算法Top-$k$考虑前$k$个最佳属性作为可能的分裂点，而非仅单一最佳属性。我们从理论和经验上证明了这一简单泛化的力量。首先，我们证明了一个{\sl 贪心层次定理}：对于每个$k \in \mathbb{N}$，Top-$(k+1)$可能比Top-$k$强大得多——存在数据分布使得前者能达到精度$1-\varepsilon$，而后者仅能达到精度$\frac1{2}+\varepsilon$。然后，通过大量实验表明，Top-$k$优于决策树学习的两种主要方法：经典贪心算法和更近期的“最优决策树”算法。一方面，在广泛的基准测试中，Top-$k$始终比贪心算法享有显著的精度提升。另一方面，Top-$k$比最优决策树算法具有显著更高的可扩展性，能够处理这些算法目前远无法企及的数据集和特征集规模。