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

Abstract

Using problem-speci®c background knowledge, computer programs developed within theframework of Inductive Logic Programming (ILP) have been used to construct restricted®rst-order logic solutions to scienti®c problems. However, their approach to the analysis ofdata with substantial numerical content has been largely limited to constructing clauses that:(a) provide qualitative descriptions (high'', low'' etc.) of the values of response variables;and (b) contain simple inequalities restricting the ranges of predictor variables. This has precludedthe application of such techniques to scienti®c and engineering problems requiring amore sophisticated approach. A number of specialised methods have been suggested to remedythis. In contrast, we have chosen to take advantage of the fact that the existing theoreticalframework for ILP places very few restrictions of the nature of the background knowledge.We describe two issues of implementation that make it possible to use background predicatesthat implement well-established statistical and numerical analysis procedures. Any improvementsin analytical sophistication that result are evaluated empirically using arti®cial andreal-life data. Experiments utilising arti®cial data are concerned with extracting constraintsfor response variables in the text-book problem of balancing a pole on a cart. They illustratethe use of clausal de®nitions of arithmetic and trigonometric functions, inequalities, multiplelinear regression, and numerical derivatives. A non-trivial problem concerning the predictionof mutagenic activity of nitroaromatic molecules is also examined. In this case, expert chemistshave been unable to devise a model for explaining the data. The result demonstrates the combineduse by an ILP program of logical and numerical capabilities to achieve an analysis thatincludes linear modelling, clustering and classi®cation. In all experiments, the predictions obtainedcompare favourably against benchmarks set by more traditional methods of quantitativemethods, namely, regression and neural-network.