Ultra-Strong Machine Learning: comprehensibility of programs learned with ILP

During the 1980s Michie defined Machine Learning in terms of two orthogonal axes of performance: predictive accuracy and comprehensibility of generated hypotheses. Since predictive accuracy was readily measurable and comprehensibility not so, later definitions in the 1990s, such as Mitchell’s, tended to use a one-dimensional approach to Machine Learning based solely on predictive accuracy, ultimately favouring statistical over symbolic Machine Learning approaches. In this paper we provide a definition of comprehensibility of hypotheses which can be estimated using human participant trials. We present two sets of experiments testing human comprehensibility of logic programs. In the first experiment we test human comprehensibility with and without predicate invention. Results indicate comprehensibility is affected not only by the complexity of the presented program but also by the existence of anonymous predicate symbols. In the second experiment we directly test whether any state-of-the-art ILP systems are ultra-strong learners in Michie’s sense, and select the Metagol system for use in humans trials. Results show participants were not able to learn the relational concept on their own from a set of examples but they were able to apply the relational definition provided by the ILP system correctly. This implies the existence of a class of relational concepts which are hard to acquire for humans, though easy to understand given an abstract explanation. We believe improved understanding of this class could have potential relevance to contexts involving human learning, teaching and verbal interaction.