Stable Optimization With Application To Syntactic Learning

Abstract

The recent development of an algebra for the manipulation of decision trees has allowed the implementation of an algorithm for generating all the irreducible forms of a decision tree. An irreducible is a syntactic form for a decision tree which is guaranteed to be optimal for some cost criterion (for example, an expected testing cost). However, each irreducible is optimal only under certain stability conditions. Thus, in the absence of specific costing information, the more demanding the stability conditions for an irreducible, the less generally useful the tree. This paper illustrates, by means of an example, a syntactic approach to decision tree inference in which all the irreducible decision trees which are consistent with respect to a given set of training examples are generated, and a test for stability is used to narrow down the selection of a reasonable inference model.