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：我们提出对标准且经实证成功的决策树学习算法（如ID3、C4.5和CART）的一种简单泛化。这些算法数十年来一直是机器学习领域的核心，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$k$个最佳属性作为可能的分裂点，而非仅选择单个最佳属性。我们从理论和实证两方面展示了这一简单泛化的强大之处。首先，我们证明了一个{\sl 贪心层次定理}，表明对每个$k \in \mathbb{N}$，Top-$(k+1)$可能比Top-$k$强大得多：存在数据分布使得前者达到精度$1-\varepsilon$，而后者只能达到$\frac1{2}+\varepsilon$。随后，通过大量实验，我们展示了Top-$k$优于两种主要的决策树学习方法：经典的贪心算法和更新的“最优决策树”算法。一方面，在广泛的基准测试中，Top-$k$相较于贪心算法始终取得显著的精度提升。另一方面，Top-$k$在可扩展性上明显优于最优决策树算法，能够处理这些算法仍远无法企及的数据集和特征集规模。