Meta-Interpretive Learning as Metarule Specialisation

TL;DR

This paper demonstrates that in Meta-Interpretive Learning, metarules can be automatically learned through a hierarchy of specialisation, reducing the need for manual definition while maintaining accuracy and efficiency.

Contribution

The work introduces a method to learn metarules automatically in MIL by specialisation, replacing manual user-defined metarules with learned ones, and implements this in the TOIL system.

Findings

Automated metarule learning maintains predictive accuracy.

Training times are comparable when replacing user-defined metarules.

The cardinality of metarule language is polynomial in punch metarules literals.

Abstract

In Meta-Interpretive Learning (MIL) the metarules, second-order datalog clauses acting as inductive bias, are manually defined by the user. In this work we show that second-order metarules for MIL can be learned by MIL. We define a generality ordering of metarules by $\theta$-subsumption and show that user-defined \emph{sort metarules} are derivable by specialisation of the most-general \emph{matrix metarules} in a language class; and that these matrix metarules are in turn derivable by specialisation of third-order \emph{punch metarules} with variables quantified over the set of atoms and for which only an upper bound on their number of literals need be user-defined. We show that the cardinality of a metarule language is polynomial in the number of literals in punch metarules. We re-frame MIL as metarule specialisation by resolution. We modify the MIL metarule specialisation operator to return new metarules rather than first-order clauses and prove the correctness of the new operator. We implement the new operator as TOIL, a sub-system of the MIL system Louise. Our experiments show that as user-defined sort metarules are progressively replaced by sort metarules learned by TOIL, Louise's predictive accuracy and training times are maintained. We conclude that automatically derived metarules can replace user-defined metarules.