A Pathology of Bottom-Up Hill-Climbing in Inductive Rule Learning

In this paper, we close the gap between the simple and straight-forward implementations of top-down hill-climbing that can be found in the literature, and the comparably complex strategies for greedy bottom-up generalization. Our main result is that the simple bottom-up counterpart to the top-down hill-climbing algorithm is unable to learn in domains with comparably dispersed examples. In particular, we show that greedy generalization from a seed example is impossible if it differs from its nearest neighbor in more than one attribute value. We also perform an empirical study of how frequent this case is in popular benchmark datasets, and present average-case and worst-case results for binary domains.