BAYESIAN SPECIAL SECTION: INTRODUCTION Bayesian networks, Bayesian learning and cognitive development

Over the past 30 years we have discovered an enormous amount about what children know and when they know it. But the real question for developmental cognitive science is not so much what children know, when they know it or even whether they learn it. The real question is how they learn it and why they get it right. Developmental ‘theory theorists’ (e.g. Carey, 1985; Gopnik & Meltzoff, 1997; Wellman & Gelman, 1998) have suggested that children’s learning mechanisms are analogous to scientific theory-formation. However, what we really need is a more precise computational specification of the mechanisms that underlie both types of learning, in cognitive development and scientific discovery. The most familiar candidates for learning mechanisms in developmental psychology have been variants of associationism, either the mechanisms of classical and operant conditioning in behaviorist theories (e.g. Rescorla & Wagner, 1972) or more recently, connectionist models (e.g. Rumelhart & McClelland, 1986; Elman, Bates, Johnson & Karmiloff-Smith, 1996; Shultz, 2003; Rogers & McClelland, 2004). Such theories have had difficulty explaining how apparently rich, complex, abstract, rulegoverned representations, such as we see in everyday theories, could be derived from evidence. Typically, associationists have argued that such abstract representations do not really exist, and that children’s behavior can be just as well explained in terms of more specific learned associations between task inputs and outputs. Connectionists often qualify this denial by appealing to the notion of distributed representations in hidden layers of units that relate inputs to outputs (Rogers & McClelland, 2004; Colunga & Smith, 2005). On this view, however, the representations are not explicit, task-independent models of the world’s structure that are responsible for the input–output relations. Instead, they are implicit summaries of the input–output relations for a specific set of tasks that the connectionist network has been trained to perform. Conversely, more nativist accounts of cognitive development endorse the existence of abstract rule-governed representations but deny that their basic structure is learned. Modularity or ‘core knowledge’ theorists, for example, suggest that there are a small number of innate causal schemas designed to fit particular domains of knowledge, such as a belief-desire schema for intuitive psychology or a generic object schema for intuitive physics. Development is either a matter of enriching those innate schemas, or else involves quite sophisticated and culturespecific kinds of learning like those of the social institutions of science (e.g. Spelke, Breinlinger, Macomber & Jacobson, 1992). This has left empirically minded developmentalists, who seem to see both abstract representation and learning in even the youngest children, in an unfortunate theoretical bind. There appears to be a vast gap between the kinds of knowledge that children learn and the mechanisms that could allow them to learn that knowledge. The attempt to bridge this gap dates back to Piagetian ideas about constructivism, of course, but simply saying that there are constructivist learning mechanisms is a way of restating the problem rather than providing a solution. Is there a more precise computational way to bridge this gap? Recent developments in machine learning and artificial intelligence suggest that the answer may be yes. These new approaches to inductive learning are based on sophisticated and rational mechanisms of statistical