Reducing Examples in Relational Learning with Bounded-Treewidth Hypotheses

Abstract. Feature selection methods often improve the performance of attribute-value learning. We explore whether also in relational learning, examples in the form of clauses can be reduced in size to speed up learning without affecting the learned hypothesis. To this end, we introduce the notion of safe reduction: a safely reduced example cannot be distinguished from the original example under the given hypothesis language bias. Next, we consider the particular, rather permissive bias of bounded treewidth clauses. We show that under this hypothesis bias, examples of arbitrary treewidth can be reduced efficiently. Moreover, they can be reduced at least as much as through the general, NP-complete θ-reduction operation. The bounded threewidth bias can be replaced by other assumptions such as acyclicity with similar benefits. We evaluate our approach on four data sets with the popular system Aleph and the state-of-the-art relational learner nFOIL. On all four data sets we make learning faster for nFOIL, achieving an order-of-magnitude speed up on one of the data sets, and more accurate for Aleph.