Harnessing the Power of Choices in Decision Tree Learning

TL;DR

This paper introduces Top-k, a decision tree learning algorithm that considers multiple top attributes at each split, leading to improved accuracy and scalability over traditional greedy and optimal methods.

Contribution

The paper presents Top-k, a simple yet powerful generalization of decision tree algorithms, with theoretical guarantees and empirical evidence of its superiority.

Findings

Top-k can significantly outperform single-attribute greedy algorithms.

Top-k achieves accuracy close to optimal decision trees in experiments.

Top-k scales better than optimal algorithms, handling larger datasets.

Abstract

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.