On the Adaptive Properties of Decision Trees

Part of Advances in Neural Information Processing Systems 17 (NIPS 2004)

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Clayton Scott, Robert Nowak


Decision trees are surprisingly adaptive in three important respects: They automatically (1) adapt to favorable conditions near the Bayes decision boundary; (2) focus on data distributed on lower dimensional manifolds; (3) reject irrelevant features. In this paper we examine a decision tree based on dyadic splits that adapts to each of these conditions to achieve minimax optimal rates of convergence. The proposed classifier is the first known to achieve these optimal rates while being practical and im- plementable.