Numerical reasoning with an ILP system capable of lazy evaluation and customised search

Using problem-specific background knowledge, computer programs developed wi thin the framework of Inductive Logic Programming (ILP) have been used to c onstruct restricted first-order logic solutions to scientific problems. How ever, their approach to the analysis of data with substantial numerical con tent has been largely limited to constructing clauses that: (a) provide qua litative descriptions ("high", "low" etc.) of the values of response variab les; and (b) contain simple inequalities restricting the ranges of predicto r variables. This has precluded the application of such techniques to scien tific and engineering problems requiring a more sophisticated approach. A n umber of specialised methods have been suggested to remedy this. In contras t, we have chosen to take advantage of the fact that the existing theoretic al framework for ILP places very few restrictions of the nature of the back ground knowledge. We describe two issues of implementation that make it pos sible to use background predicates that implement well-established statisti cal and numerical analysis procedures. Any improvements in analytical sophi stication that result are evaluated empirically using artificial and real-l ife data. Experiments utilising artificial data are concerned with extracti ng constraints for response variables in the text-book problem of balancing a pole on a cart. They illustrate the use of clausal definitions of arithm etic and trigonometric functions, inequalities, multiple linear regression, and numerical derivatives. A non-trivial problem concerning the prediction of mutagenic activity of nitroaromatic molecules is also examined. In this case, expert chemists have been unable to devise a model for explaining th e data. The result demonstrates the combined use by an ILP program of logic al and numerical capabilities to achieve an analysis that includes linear m odelling, clustering and classification. In all experiments, the prediction s obtained compare favourably against benchmarks set by more traditional me thods of quantitative methods, namely, regression and neural-network. (C) 1 999 Elsevier Science Inc. All rights reserved.