Decision tree reduction

Abstract

The reduction algorithm is a technique for improving a decision tree in the abseence of aproecise cost criterion. The result of applying the algorithm is an irreducible tree that is no less efficient than the original, and may be more efficient. Irreducible trees arise in discrete decision theory as an algebraic form for decision trees. This form has significant computational properties. In fact, every irreducible is optimal with respect to some expected testing cost criterion and is strictly better than any given distinct tree with respect to some criterion. Many irreducibles are decision equivalent to a given tree; onely some of these are reductions of the tree. The reduction algorithm is a particular way of finding one of these. It tends to preserve the overall structure of the tree by reducing the subtrees first. A bound on the complexity of this algorithm with input tree t is O (hgt9 t ) 2 ). usize( t ) is the uniform size of the tree (the number of leaves less one) and hgt( t ) is the height of the tree. This means that decision tree reduction has the same worst-case order of complexity as most heuristic methods for building suboptimal trees. While the purpose of using heuristics is often rather different, such comparisons are an indication of the efficiency of the reduction algorithms.