ILP Through Propositionalization and Stochastic k-Term DNF Learning

ILP has been successfully applied to a variety of tasks. Nevertheless, ILP systems have huge time and storage requirements, owing to a large search space of possible clauses. Therefore, clever search strategies are needed. One promising family of search strategies is that of stochastic local search methods. These methods have been successfully applied to propositional tasks, such as satisfiability, substantially improving their efficiency. Following the success of such methods, a promising research direction is to employ stochastic local search within ILP, to accelerate the runtime of the learning process. An investigation in that direction was recently performed within ILP [Železný et al., 2004]. Stochastic local search algorithms for propositional satisfiability benefit from the ability to quickly test whether a truth assignment satisfies a formula. As a result, many possible solutions (assignments) can be tested and scored in a short time. In contrast, the analogous test within ILP—testing whether a clause covers an example—takes much longer, so that far fewer possible solutions can be tested in the same time. Therefore, motivated by both the sucess and limitations of the previous work, we also apply stochastic local search to ILP but in a different manner. Instead of directly applying stochastic local search to the space of firstorder Horn clauses, we use a propositionalization approach that transforms the ILP task into an attribute-value learning task. In this alternative search space, we can take advantage of fast testing as in propositional satisfiability. Our primary aim in this paper is to reduce ILP run-time. The standard greedy covering algorithm employed by most ILP systems is another shortcoming of typical ILP search. There is no guarantee that greedy covering will yield the globally optimal hypothesis; consequently, greedy covering often gives rise to problems such as unnecessarily long hypothesis with too