Linear Space Induction in First Order Logic with RELIEFF

Current ILP algorithms typically use variants and extensions of the greedy search. This prevents them to detect signiicant relationships between the training objects. Instead of myopic impurity functions, we propose the use of the heuristic based on RELIEF for guidance of ILP algorithms. At each step, in our ILP-R system, this heuristic is used to determine a beam of candidate literals. The beam is then used in an exhaustive search for a potentially good conjunction of literals. From the eeciency point of view we introduce interesting declarative bias which enables us to keep the growth of the training set, when introducing new variables, within linear bounds (linear with respect to the clause length). This bias prohibits cross-referencing of variables in variable dependency tree. The resulting system has been tested on various artiicial problems. The advantages and deeciencies of our approach are discussed.