Classification trees with optimal multi-variate splits

Tree classifiers assign an observation to a class through a series of binary questions. This form of classification is very fast and easy to interpret. However, tree classifiers constructed using standard techniques, such as CART (classification and regression trees), have difficulties with multi-modal problems like the parity problem. In particular. CART produces a very inefficient tree for this class of problems, which can occur in a number of important applications. This paper examines the problems with CART and then presents a solution that yields trees that use the optimal multi-variate split at each node