Decision Tree Induction: How Effective is the Greedy Heuristic?

Most existing decision tree systems use a greedy approach to induce trees — locally optimal splits are induced at every node of the tree. Although the greedy approach is suboptimal, it is believed to produce reasonably good trees. In the current work, we attempt to verify this belief. We quantify the goodness of greedy tree induction empirically, using the popular decision tree algorithms, C4.5 and CART. We induce decision trees on thousands of synthetic data sets and compare them to the corresponding optimal trees, which in turn are found using a novel map coloring idea. We measure the effect on greedy induction of variables such as the underlying concept complexity, training set size, noise and dimensionality. Our experiments show, among other things, that the expected classification cost of a greedily induced tree is consistently very close to that of the optimal tree.