Richness of the Base and Probabilistic Unsupervised Learning in Optimality Theory

Abstract

This paper proposes an unsupervised learning algorithm for Optimality Theoretic grammars, which learns a complete constraint ranking and a lexicon given only unstructured surface forms and morphological relations. The learning algorithm, which is based on the Expectation-Maximization algorithm, gradually maximizes the likelihood of the observed forms by adjusting the parameters of a probabilistic constraint grammar and a probabilistic lexicon. The paper presents the algorithm's results on three constructed language systems with different types of hidden structure: voicing neutralization, stress, and abstract vowels. In all cases the algorithm learns the correct constraint ranking and lexicon. The paper argues that the algorithm's ability to identify correct, restrictive grammars is due in part to its explicit reliance on the Optimality Theoretic notion of Richness of the Base.