Complexity-Based Induction

Abstract

A central problem in inductive logic programming is theory evaluation. Without some sort of preference criterion, any two theories that explain a set of examples are equally acceptable. This paper presents a scheme for evaluating alternative inductive theories based on an objective preference criterion. It strives to extract maximal redundancy from examples, transforming structure into randomness. A major strength of the method is its application to learning problems where negative examples of concepts are scarce or unavailable. A new measure called model complexity is introduced, and its use is illustrated and compared with a proof complexity measure on relational learning tasks. The complementarity of model and proof complexity parallels that of model and proof-theoretic semantics. Model complexity, where applicable, seems to be an appropriate measure for evaluating inductive logic theories.