When children are better learners than adults: Developmental differences in learning the forms of causal relationships

Developmental differences in learning the forms of causal relationships Chris Lucas (clucas@berkeley.edu) Alison Gopnik (gopnik@berkeley.edu) Thomas L. Griffiths (tom griffiths@berkeley.edu) Department of Psychology, University of California Berkeley, CA 94720, USA Abstract Children learn causal relationships quickly, and make far- reaching causal inferences on the basis of what they see. In order to be such efficient learners, they must bring abstract knowledge to bear on their problems. This paper addresses children’s ability to acquire that knowledge. We present evi- dence that children can learn about the abstract properties of causal relationships using only a handful of events, and – con- sistent with a hierarchical Bayesian model of casual inference – children can be more sensitive to evidence than adults. Introduction Recent work suggests that children are skilled at inferring specific causal relationships from patterns of data (Gopnik et al., 2004; Sobel, Tenenbaum, & Gopnik, 2004). For ex- ample, they can infer which blocks will activate a machine based on the contingencies between the blocks and the ma- chine’s activation. But an additional question is whether chil- dren can infer more abstract causal principles from patterns in data, and use those principles to shape their subsequent pre- dictions. For example, can a child infer that a particular type of machine activates reliably, or requires only a single cause to activate? Will those abstract discoveries bias the child’s interpretations of new data? Developmental data suggest that children do have broad in- ductive biases. For example, in language learning the shape bias and the mutual exclusivity principle influence more spe- cific inferences about word meaning (Smith, Jones, Landau, Gershkoff-Stowe, & Samuelson, 2002; Markman & Wachtel, 1988). However there is debate about whether these biases are the result of innate constraints or are themselves the prod- uct of learning (Elman et al., 1996; Leslie, 1994). Recent formal work on hierarchical Bayesian models suggests that, at least in principle, the shape bias may itself be learned as a result of normative inferences from patterns of data (Kemp, Perfors, & Tenenbaum, 2007). Similar high-level biases ap- ply to causal learning, and we know that children can learn about causal types (Schulz, Goodman, Tenenbaum, & Jenk- ins, 2008), and the plausibility of cross-domain relationships (Schulz, Bonawitz, & Griffiths, 2007). In this paper, we ex- plore whether children can learn abstract principles about the forms of causal relationships themselves. The hierarchical Bayesian approach suggests that the na- ture of inductive biases may change as evidence accumu- lates. Absent evidence, a learner without strong built-in bi- ases should assign similar probabilities to a wide range of hypotheses. As data accumulate, the abstract hypotheses con- sistent with those data become more probable, and the learner discounts any hypotheses that fit the current data but are less compatible with past experience. If this is correct, then we might expect to see different patterns of inductive bias in adults and children. In particular, children might rely less on past experience and more on present evidence than adults. This is a possibility that has not previously been explored in the causal learning literature, and one that we examine through head-to-head (or prior-to-prior) comparison of chil- dren and adults in a causal learning task that requires making an abstract generalization about the nature of causal relation- ships. We test the high-level generalizations made by children and adults by contrasting two abstract “overhypotheses” (Goodman, 1955; Kemp et al., 2007) about how a causal sys- tem works. One is a noisy-OR model, in which each object has a certain independent probability of bringing about an ef- fect. This model is pervasive in the literature on adult causal inference (e.g., Cheng, 1997; Griffiths & Tenenbaum, 2005). The other is an AND model in which individual causes are unable to produce an effect, but multiple causes in conjunc- tion can produce an effect. We provided children and adults with evidence for either an AND or OR relationship and then examined how this evidence biased their judgment of a novel, ambiguous pattern of evidence. Would seeing several in- stances of a machine activated by a conjunction of causes lead them to assume that this would be the case for a new set of blocks? By comparing how children and adults respond to data that support these different overhypotheses, we can examine first whether children are capable of forming appro- priate abstract generalizations, and second whether they are more willing to make these generalizations than adults. The plan of the paper is as follows. First, we consider how an ideal Bayesian learner can gather evidence for over- hypotheses relevant to causal induction. We then discuss the specific overhypotheses about the functional form of causal relationships that we contrast in this paper, together with a method that can be used to diagnose whether learners infer these overhypotheses from data. We go on to use this method to compare the abstract generalizations of children and adults in a causal learning task, finding support for the hypothesis that children are more willing to adopt a novel overhypoth- esis than adults. We close by discussing the implications of these results. Causal overhypotheses Children can identify causes using only a handful of observa- tions (Gopnik et al., 2004), but the extent to which they learn