Relational learning: Hard problems and Phase transition

Marco Botta (1) , Attilio Giordana (2) , Lorenza Saitta (2) , Michèle Sebag (3)

1 UNITO - Università degli studi di Torino = University of Turin
2 DISTA - Dipartimento di Scienze e Tecnologie Avanzate
3 LMS - Laboratoire de mécanique des solides

This paper focuses on a major step of machine learning, namely checking whether an example matches a candidate hypothesis. In relational learning, matching can be viewed as a Constraint Satisfaction Problem (CSP). The complexity of the task is analyzed in the Phase Transition framework, investigating the impact on the effectiveness of two relational learners: FOIL and G-NET. The critical factors of complexity, and their critical values, are experimentally investigated on artificial problems. This leads to distinguish several kinds of learning domains, depending on whether the target concept lies in the “mushy” region or not. Interestingly, experiments done with FOIL and G-NET show that both learners tend to induce hypotheses generating matching problems located inside the phase transition region, even if the constructed target concept lies far outside. Moreover, target concepts constructed too close to the phase transition are hard and both learners fail. The paper offers an explanation for this fact, and proposes a classification of learning domains and their hardness.

Domaines: Mécanique des solides [physics.class-ph]

Marco Botta, Attilio Giordana, Lorenza Saitta, Michèle Sebag. Relational learning: Hard problems and Phase transition. AI*IA: Congress of the Italian Association for Artificial Intelligence, 1999, Bologne, Italy. pp.178-189, ⟨10.1007/3-540-46238-4_16⟩. ⟨hal-00116119⟩