Note on the use of statistical procedures as background predicates in ILP

Abstract

Procedures, broadly under the umbrella of statistical modelling, construct robust and powerful models from sample data. Examples include parametric techniques for regression, and non-parametric ones like classification and regression trees. The techniques are essentially propositional, and a first-order model constructor embodied by an Inductive Logic Programming (ILP) system should, in theory, be able to utilise them by simply providing appropriate (background) predicates. By "utilise", we mean here constructing an appropriate statistical model (estimating relevant parameters) and using it as part of a first-order hypothesis (for prediction). An example is the incorporation of a regression equation as a literal in a hypothesised clause. Nevertheless, the representation adopted by most ILP systems (logic programs) results in some special difficulties in both parameter estimation and prediction. This report presents the principal difficulties and some solutions.