Learning Overhypotheses

Inductive learning is impossible without overhypotheses, or constraints on the hypotheses considered by the learner. Some of these overhypotheses must be innate, but we suggest that hierarchical Bayesian models help explain how the rest can be acquired. The hierarchical approach also addresses a common question about Bayesian models of cognition: where do the priors come from? To illustrate our claims, we consider two specific kinds of overhypotheses — overhypotheses about feature variability (e.g. the shape bias in word learning) and overhypotheses about the grouping of categories into ontological kinds like objects and substances. Compared to machine-learning algorithms, humans are remarkable for doing so much with so little. A single labelled example is enough for children to learn the meanings of some words, and children develop grammatical constructions that are rarely found in the sentences they hear [2]. These inductive leaps appear even more impressive when we consider the many interpretations of the data that are logically possible but apparently never entertained by human learners [5]. Several authors have proposed that the apparent ease of human learning depends on constraints that guide induction. This view has been applied to many cognitive problems: the M-constraint and the shape bias help explain concept acquisition, universal grammar guides the acquisition of linguistic knowledge [2], and the development of folk biology is guided by the idea that living kinds can be organized hierarchically. Constraints like these may be called framework theories or schemata, but we will borrow a term of Goodman’s and refer to them as overhypotheses. Some overhypotheses must be innate, but others are probably learned. For at least two reasons the acquisition of overhypotheses has received less attention than it deserves. First, the authors who have argued most convincingly for the importance of overhypotheses often suggest that these overhypotheses are innate [2]. Second, the study of overhypothesis acquisition raises some formidable methodological challenges. Designing adult experiments to address the problem is difficult, since Other authors distinguish between theories, schemata, scripts, and overhypotheses. There are important differences between these varieties of abstract knowledge, but it is useful to have a single term (for us, overhypothesis) that includes them all. adults bring a lifetime of learning experience to any experiment and have already distilled overhypotheses that help them deal with most novel tasks. Infant experiments are challenging for different reasons, but worth pursuing because they can address the acquisition of some of the most fundamental overhypotheses. For instance, Smith and colleagues have explored the development of the shape bias [9, 3], and Piaget and colleagues have explored how abstract kinds of knowledge (such as the concrete operations) can be acquired and used to support many different learning tasks. This paper argues that hierarchical Bayesian modelling [4] is a formal approach that should help to explain the acquisition of overhypotheses in many different domains. Hierarchical Bayesian models (HBMs) include representations at many levels of abstraction, and show how knowledge can be acquired at levels that are quite remote from the data given by experience. To illustrate our general claim, we describe one of the simplest possible HBMs and use it to suggest how overhypotheses about feature-variability are acquired and used to support categorization. One such overhypothesis is the shape bias, the expectation that shape is a feature that is homogeneous within object categories. We also present an extension of the basic model that groups categories into ontological kinds (e.g. objects and substances) and discovers the features and the patterns of feature variability that are characteristic of each kind. The problem of overhypothesis acquisition is closely related to a problem raised by Bayesian models of cognition. These models usually rely on a prior distribution chosen by the modeller, and a natural response is to wonder where the prior comes from. HBMs address this question: in the framework we adopt, learning an overhypothesis amounts to learning a prior distribution. The two models we consider provide concrete examples of how priors can be learned from data. Overhypotheses and HBMs Goodman introduces the idea of overhypotheses using bags of colored marbles [5]. Suppose that S is a stack containing many bags of marbles. We empty several bags and discover that some bags contain black marbles, others contain white marbles, but that each bag is uniform in color. We now choose a new bag — bag n — and draw a single black marble from the bag. This observation may lead us to endorse the following hypothesis: