A Bayesian framework for concept learning

Abstract

This thesis proposes a new computational framework for understanding how people learn concepts from examples, based on. the principles of Bayesian inference. The main contributions of this thesis are as follows. First and foremost, I show how it is possible for people to learn and generalize concepts from just one or a few positive examples (Chapter 2). Building on that understanding, I then present a series of case studies of simple concept learning situations where the Bayesian framework yields both qualitative and quantitative insights into the real behavior of human learners (Chapters 3-5). These cases each focus on a different learning domain. Chapter 3 looks at generalization in continuous feature spaces, a typical representation of objects in psychology and machine learning with the virtues of being analytically tractable and Chapter 4 moves to the more natural domain of learning words for categories of objects and shows the relevance of the same phenomena and explanatory principles learning tasks like this one. In each of these domains, both similarity-like and rule-like generalization emerge as special cases of the Bayesian framework in the limits of very few or very many examples, respectively. However, the transition from similarity to rules occurs much faster in the word learning domain than in the continuous feature space domain. I propose a Bayesian explanation of this difference in learning curves that places crucial importance on the density or sparsity of overlapping hypotheses in the learner's hypothesis space. To test this proposal, a third case study (Chapter 5) returns to the domain of number concepts, in which human learners possess a more complex body of prior knowledge that leads to a hypothesis space with both sparse and densely overlapping components. In each of these case studies, I confront some of the classic questions of concept learning and induction. Finally, Chapter 6 summarizes the major contributions in more detailed form and discusses how this work fits into the larger picture of contemporary research on human learning, thinking, and reasoning. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.) (Abstract shortened by UMI.) (PsycINFO Database Record (c) 2006 APA, all rights reserved)