Harnessing the Power of Choices in Decision Tree Learning
This addresses a bottleneck in decision tree algorithms for machine learning practitioners, offering a simple yet effective improvement over existing methods.
The paper tackles the problem of greedy decision tree learning by proposing Top-k, which considers the k best attributes for splits instead of just the best, showing it achieves accuracy up to 1-ε compared to 1/2+ε for standard methods and outperforms both greedy and optimal algorithms in accuracy and scalability.
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.