Clayton Scott, Robert Nowak
Classiﬁcation trees are one of the most popular types of classiﬁers, with ease of implementation and interpretation being among their attractive features. Despite the widespread use of classiﬁcation trees, theoretical analysis of their performance is scarce. In this paper, we show that a new family of classiﬁcation trees, called dyadic classiﬁcation trees (DCTs), are near optimal (in a minimax sense) for a very broad range of clas- siﬁcation problems. This demonstrates that other schemes (e.g., neural networks, support vector machines) cannot perform signiﬁcantly better than DCTs in many cases. We also show that this near optimal perfor- mance is attained with linear (in the number of training data) complexity growing and pruning algorithms. Moreover, the performance of DCTs on benchmark datasets compares favorably to that of standard CART, which is generally more computationally intensive and which does not possess similar near optimality properties. Our analysis stems from the- oretical results on structural risk minimization, on which the pruning rule for DCTs is based.