Relational Learning as Search in a Critical Region

Marco Botta, Attilio Giordana, Lorenza Saitta, Michèle Sebag; 4(Aug):431-463, 2003.


Machine learning strongly relies on the covering test to assess whether a candidate hypothesis covers training examples. The present paper investigates learning relational concepts from examples, termed relational learning or inductive logic programming. In particular, it investigates the chances of success and the computational cost of relational learning, which appears to be severely affected by the presence of a phase transition in the covering test. To this aim, three up-to-date relational learners have been applied to a wide range of artificial, fully relational learning problems. A first experimental observation is that the phase transition behaves as an attractor for relational learning; no matter which region the learning problem belongs to, all three learners produce hypotheses lying within or close to the phase transition region. Second, a failure region appears. All three learners fail to learn any accurate hypothesis in this region. Quite surprisingly, the probability of failure does not systematically increase with the size of the underlying target concept: under some circumstances, longer concepts may be easier to accurately approximate than shorter ones. Some interpretations for these findings are proposed and discussed.