Top program construction and reduction for polynomial time Meta-Interpretive learning

Patsantzis, Stassa; Muggleton, Stephen

doi:10.1007/s10994-020-05945-w

Cited by 3 publications

(7 citation statements)

References 31 publications

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“…Top-down and bottom-up approaches refine and revise a single hypothesis. A third approach has recently emerged called meta-level ILP (Inoue et al, 2013;Muggleton et al, 2015;Inoue, 2016;Law et al, 2020b;Cropper & Morel, 2021a;Patsantzis & Muggleton, 2021). There is no standard definition for meta-level ILP.…”

Section: Meta-levelmentioning

confidence: 99%

Inductive logic programming at 30

et al. 2021

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Inductive logic programming (ILP) is a form of logic-based machine learning. The goal is to induce a hypothesis (a logic program) that generalises given training examples and background knowledge. As ILP turns 30, we review the last decade of research. We focus on (i) new meta-level search methods, (ii) techniques for learning recursive programs, (iii) new approaches for predicate invention, and (iv) the use of different technologies. We conclude by discussing current limitations of ILP and directions for future research.

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Section: Meta-levelmentioning

confidence: 99%

Inductive logic programming at 30

et al. 2021

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“…While the number of specialisations of third order punch metarules can grow very large, they can be derived efficiently by Top Program Construction (TPC) (Patsantzis and Muggleton, 2021), a polynomial -time MIL algorithm that forms the basis of the MIL system Louise (Patsantzis and Muggleton, 2019a). We implement metarule learning by TPC in Louise as a new sub-system called TOIL.…”

Section: Rd-ordermentioning

confidence: 99%

“…Our implementation extends the Top Program Construction algorithm (Patsantzis and Muggleton, 2021) that avoids an expensive search of a potentially large hypothesis space and instead constructs all clauses that entail an example with respect to background knowledge. We extend this earlier work with the ability to construct second-order clauses without compromising efficiency.…”

Section: Related Workmentioning

confidence: 99%

“…We reuse the datasets described in (Patsantzis and Muggleton, 2021). These comprise: a) Grid World, a grid-world generator for robot navigation problems; b) 7 summarises the MIL problem elements of the three datasets.…”

Section: Experiments Datasetsmentioning

confidence: 99%

“…These comprise: a) Grid World, a grid-world generator for robot navigation problems; b) 7 summarises the MIL problem elements of the three datasets. We refer the reader to (Patsantzis and Muggleton, 2021) for a full description of the three datasets. Instead of the metarules defined in the experiment datasets we start each experiment by initialising M to the set of 14 H 2 2 metarules in (Cropper and Muggleton, 2015), listed in Table 2, which we call the canonical H 2 2 set.…”

Section: Experiments Datasetsmentioning

confidence: 99%

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Meta-Interpretive Learning as Metarule Specialisation

Patsantzis¹,

Muggleton²

2021

Preprint

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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 θ-subsumption and show that user-defined sort metarules are derivable by specialisation of the most-general matrix metarules in a language class; and that these matrix metarules are in turn derivable by specialisation of third-order punch metarules with variables that range over the set of second-order literals 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 is maintained at the cost of a small increase in training times. We conclude that automatically derived metarules can replace user-defined metarules. IntroductionMeta-Interpretive Learning (MIL) (Muggleton et al., 2014;Muggleton and Lin, 2015) is a new approach to Inductive Logic Programming (ILP) (Muggleton and de Raedt, 1994) capable of learning logic programs with recursive clauses and invented predicates from examples, background knowledge and a declarative bias,

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Meta-interpretive learning as metarule specialisation

Patsantzis

Muggleton

2022

Mach Learn

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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 $$\theta$$ θ -subsumption and show that user-defined sort metarules are derivable by specialisation of the most-general matrix metarules in a language class; and that these matrix metarules are in turn derivable by specialisation of third-order 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.

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Top program construction and reduction for polynomial time Meta-Interpretive learning

Cited by 3 publications

References 31 publications

Inductive logic programming at 30

Inductive logic programming at 30

Meta-Interpretive Learning as Metarule Specialisation

Meta-interpretive learning as metarule specialisation

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