Three ideal observer models for rule learning in simple languages

Children learning the inflections of their native language show the ability to generalize beyond the perceptual particulars of the examples they are exposed to. The phenomenon of "rule learning"--quick learning of abstract regularities from exposure to a limited set of stimuli--has become an important model system for understanding generalization in infancy. Experiments with adults and children have revealed differences in performance across domains and types of rules. To understand the representational and inferential assumptions necessary to capture this broad set of results, we introduce three ideal observer models for rule learning. Each model builds on the next, allowing us to test the consequences of individual assumptions. Model 1 learns a single rule, Model 2 learns a single rule from noisy input, and Model 3 learns multiple rules from noisy input. These models capture a wide range of experimental results--including several that have been used to argue for domain-specificity or limits on the kinds of generalizations learners can make-suggesting that these ideal observers may be a useful baseline for future work on rule learning.