Abstract
Meta-Interpretive Learning (MIL) is an ILP technique which uses higher-order meta-rules to support predicate invention and learning of recursive definitions. In MIL the selection of meta-rules is analogous to the choice of refinement operators in a refinement graph search. The meta-rules determine the structure of permissible rules which in turn defines the hypothesis space. On the other hand, the hypothesis space can be shown to increase rapidly in the number of meta-rules. However, methods for reducing the set of meta-rules have so far not been explored within MIL. In this paper we demonstrate that irreducible, or minimal sets of meta-rules can be found automatically by applying Plotkin’s clausal theory reduction algorithm. When this approach is applied to a set of meta-rules consisting of an enumeration of all meta-rules in a given finite hypothesis language we show that in some cases as few as two meta-rules are complete and sufficient for generating all hypotheses. In our experiments we compare the effect of using a minimal set of meta-rules to randomly chosen subsets of the maximal set of meta-rules. In general the minimal set of meta-rules leads to lower runtimes and higher predictive accuracies than larger randomly selected sets of meta-rules.
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Notes
- 1.
\(H^{i}_{j}\) consists of definite datalog logic programs with predicates of arity at most i and at most j atoms in the body of each clause.
- 2.
It should be noted that MIL uses example driven test-incorporation for finding consistent programs as opposed to the generate-and-test approach of clause refinement.
- 3.
- 4.
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Acknowledgements
The first author acknowledges the support of the BBSRC and Syngenta in funding his PhD Case studentship. The second author would like to thank the Royal Academy of Engineering and Syngenta for funding his present 5 year Research Chair.
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Cropper, A., Muggleton, S.H. (2015). Logical Minimisation of Meta-Rules Within Meta-Interpretive Learning. In: Davis, J., Ramon, J. (eds) Inductive Logic Programming. Lecture Notes in Computer Science(), vol 9046. Springer, Cham. https://doi.org/10.1007/978-3-319-23708-4_5
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