Structural Regression Trees 1

In many real-world domains the task of machine learning algorithms is to learn a theory predicting numerical values. In particular several standard test domains used in Inductive Logic Programming (ILP) are concerned with predicting numerical values from examples and relational and mostly non-determinate background knowledge. However, so far no ILP algorithm except one can predict numbers and cope with non-determinate background knowledge. (The only exception is a covering algorithm called FORS.) In this paper we present Structural Regression Trees (SRT), a new algorithm which can be applied to the above class of problems by integrating the statistical method of regression trees into ILP. SRT constructs a tree containing a literal (an atomic formula or its negation) or a conjunction of literals in each node, and assigns a numerical value to each leaf. SRT provides more comprehensible results than purely statistical methods, and can be applied to a class of problems most other ILP systems cannot handle. Experiments in several real-world domains demonstrate that the approach is competitive with existing methods, indicating that the advantages are not at the expense of predictive accuracy.