Fast Theta-Subsumption with Constraint Satisfaction Algorithms

Relational learning and Inductive Logic Programming (ILP) commonly use as covering test the -subsumption test defined by Plotkin. Based on a reformulation of -subsumption as a binary constraint satisfaction problem, this paper describes a novel -subsumption algorithm named Django,¹ which combines well-known CSP procedures and -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 -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 -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).