Empirical Study of Relational Learning Algorithms in the Phase Transition Framework

Abstract

Abstract. Relational Learning (RL) has aroused interest to fill the gap between efficient attribute-value learners and growing applications stored in multi-relational databases. However, current systems use generalpurpose problem solvers that do not scale-up well. This is in contrast with the past decade of success in combinatorics communities where studies of random problems, in the phase transition framework, allowed to evaluate and develop better specialised algorithms able to solve real-world applications up to millions of variables. A number of studies have been proposed in RL, like the analysis of the phase transition of a NP-complete sub-problem, the subsumption test, but none has directly studied the phase transition of RL. As RL, in general, is Σ2 − hard, we propose a first random problem generator, which exhibits the phase transition of its decision version, beyond NP. We study the learning cost of several learners on inherently easy and hard instances, and conclude on expected benefits of this new benchmarking tool for RL.

On the Complexity of Inductively Learning Guarded Clauses

“…We first establish that it is sufficient to guess a polynomially bounded hypothesis. Note that this is not true in every setting and previous work has instead regularly considered the bounded ILP consistency problem (Alphonse and Osmani 2009;Gottlob, Leone, and Scarcello 1997), where explicit constraints on the hypothesis size are considered as part of the decision problem.…”