On the Connection Between the Phase Transition of the Covering Test and the Learning Success Rate

Abstract

To investigate the impact of the occurrence of a phase transition (PT) in the covering test on the learning success rate, systematic experiments with several learning algorithms have been conducted on a large set of artificially generated problems by Botta et al. [3]. The authors generated a set of 451 problems by choosing each target concept according to its location in the (m,L) plane with respect to the PT. The “yes”, “no” and “pt” regions are uniformly visited by varying (m,L) pairs without replacement (m ranges in [5,30] and L ranges in [12,40]). One important conclusion of their work is that the occurrence of a PT in the covering test is a general problem for all learning algorithms: the PT is viewed as an attractor for the heuristic search of any learning algorithms, which are bound to find a concept definition in the PT. Moreover, for all tested learners, there exists a failure region, starting from the “pt” region to the beginning of the “no” region, where the learnt theories are seemingly randomly constructed, with no better predictive accuracy than random guessing.