Macro-Operators in Multirelational Learning: A Search-Space Reduction Technique

Peña‐Castillo, Lourdes; Wrobel, Stefan

doi:10.1007/3-540-36755-1_30

Cited by 7 publications

(5 citation statements)

References 10 publications

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“…As known by all ILPers, the predicate structure (arity, links) strongly influences learning performances. Better predicates can be introduced dynamically through refinement operators, as for instance in Lachiche and Flach (2003) and Peña-Castillo and Wrobel (2002). But the adequacy of a hypothesis language can also be experimentally assessed through systematic θ -subsumption tests, prior to learning.…”

Section: Discussionmentioning

confidence: 99%

Fast Theta-Subsumption with Constraint Satisfaction Algorithms

Maloberti

Sebag

2004

Machine Learning

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Relational learning and Inductive Logic Programming (ILP) commonly use as covering test the θ-subsumption test defined by Plotkin. Based on a reformulation of θ-subsumption as a binary constraint satisfaction problem, this paper describes a novel θ-subsumption algorithm named Django, 1 which combines well-known CSP procedures and θ-subsumption-specific data structures. Django is validated using the stochastic complexity framework developed in CSPs, and imported in ILP by Giordana et Saitta. Principled and extensive experiments within this framework show that Django improves on earlier θ-subsumption algorithms by several orders of magnitude, and that different procedures are better at different regions of the stochastic complexity landscape. These experiments allow for building a control layer over Django, termed Meta-Django, which determines the best procedures to use depending on the order parameters of the θ-subsumption problem instance. The performance gains and good scalability of Django and Meta-Django are finally demonstrated on a real-world ILP task (emulating the search for frequent clauses in the mutagenesis domain) though the smaller size of the problems results in smaller gain factors (ranging from 2.5 to 30).

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Section: Discussionmentioning

confidence: 99%

Fast Theta-Subsumption with Constraint Satisfaction Algorithms

Maloberti

Sebag

2004

Machine Learning

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“…Although, propositionalisation approaches have been successfully applied to various problems but are still considered as ad hoc approaches. These approaches are studied in the larger context of macro-operators [45], which are approaches to improve the heuristic search in ILP systems and extract higherlevel or meta-rules [46]. Pioneering work on the combination of neural-networks and symbolic features has been done by d'Avila Garcez and Zaverucha [47] and extended in França et al [43,48].…”

Section: Related Workmentioning

confidence: 99%

Incorporating Symbolic Domain Knowledge into Graph Neural Networks

Dash,

Srinivasan,

Vig

2020

Preprint

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Our interest is in scientific problems with the following characteristics:(1) Data are naturally represented as graphs; (2) The amount of data available is typically small; and (3) There is significant domain-knowledge, usually expressed in some symbolic form (rules, taxonomies, constraints and the like). These kinds of problems have been addressed effectively in the past by symbolic machine learning methods like Inductive Logic Programming (ILP), by virtue of 2 important characteristics: (a) The use of a representation language that easily captures the relation encoded in graph-structured data, and (b) The inclusion of prior information encoded as domain-specific relations, that can alleviate problems of data scarcity, and construct new relations. Recent advances have seen the emergence of deep neural networks specifically developed for graph-structured data (Graphbased Neural Networks, or GNNs). While GNNs have been shown to be able to handle graph-structured data, less has been done to investigate the inclusion of domain-knowledge. Here we investigate this aspect of GNNs empirically by employing an operation we term vertex-enrichment and denote the corresponding GNNs as V EGN N s. Using over 70 real-world datasets and substantial amounts of symbolic domain-knowledge, we examine the result of vertex-enrichment across 5 different variants of GNNs. Our results provide support for the following: (a) Inclusion of domain-knowledge by vertex-enrichment can significantly improve the performance of a GNN. That is, the performance V EGN N s is significantly better than GN N s across all GNN variants; (b) The inclusion of domain-specific relations constructed using ILP improves the performance of V EGN N s, across all GNN variants. Taken together, the results provide evidence that it is possible to incorporate symbolic domain knowledge into a GNN, and that ILP can play an

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“…Macros are automatically created based on a list of (user declared or automatically determined) dependent providers. The macros construction algorithm we use differs from the one presented in (Peña Castillo & Wrobel, 2002) in the generation of macros with more than one dependent provider. 2 By employing a macro-based refinement operator (ρ M ) in step 2(b)i of Algorithm 1, we obtain macro-based hill-climbing.…”

Section: Macro-operatorsmentioning

confidence: 99%

“…As proposed by Peña Castillo and Wrobel (2002), literals can be classified in providers and consumers. A literal p is a consumer of literal q if p has at least one input variable bound to an output argument value of q; conversely, q is a provider of p. Notice that these relations apply as well to the head literal.…”

Section: Reducing Hill-climbing's Myopiamentioning

confidence: 99%

“…In this paper, we integrate macro-operators, which have recently been shown to reduce the search space explored by exhaustive search (Peña Castillo & Wrobel, 2002), in a hill-climbing learner and empirically show that a greedy system using macros performs significantly better than current systems involving other techniques for reducing myopia.…”

Section: Introductionmentioning

confidence: 98%

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A comparative study on methods for reducing myopia of hill-climbing search in multirelational learning

Peña‐Castillo

Wrobel²

2004

Twenty-First International Conference on Machine Learning - ICML '04

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Hill-climbing search is the most commonly used search algorithm in ILP systems because it permits the generation of theories in short running times. However, a well known drawback of this greedy search strategy is its myopia. Macro-operators (or macros for short), a recently proposed technique to reduce the search space explored by exhaustive search, can also be argued to reduce the myopia of hill-climbing search by automatically performing a variable-depth look-ahead in the search space. Surprisingly, macros have not been employed in a greedy learner. In this paper, we integrate macros into a hill-climbing learner. In a detailed comparative study in several domains, we show that indeed a hillclimbing learner using macros performs significantly better than current state-of-the-art systems involving other techniques for reducing myopia, such as fixed-depth look-ahead, template-based look-ahead, beam-search, or determinate literals. In addition, macros, in contrast to some of the other approaches, can be computed fully automatically and do not require user involvement nor special domain properties such as determinacy.

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Macro-Operators in Multirelational Learning: A Search-Space Reduction Technique

Cited by 7 publications

References 10 publications

Fast Theta-Subsumption with Constraint Satisfaction Algorithms

Fast Theta-Subsumption with Constraint Satisfaction Algorithms

Incorporating Symbolic Domain Knowledge into Graph Neural Networks

A comparative study on methods for reducing myopia of hill-climbing search in multirelational learning

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