Children's Imitation of Action Sequences is Influenced by Statistical Evidence and Inferred Causal Structure

Children’s Imitation of Action Sequences is Influenced by Statistical Evidence and Inferred Causal Structure Daphna Buchsbaum, Alison Gopnik, Thomas L. Griffiths {daphnab, gopnik, tom_griffiths}@berkeley.edu Department of Psychology, University of California, Berkeley, Berkeley, CA 94720 USA Abstract Children are ubiquitous imitators, but how do they decide which actions to imitate? One possibility is that children might learn which actions are necessary to reproduce by observing the contingencies between action sequences and outcomes across repeated observations. We define a Bayesian model that predicts that children will decide whether to imitate part or all of a sequence based on the pattern of statistical evidence. To test this prediction, we conducted an experi- ment in which preschool children watched an experimenter repeatedly perform sequences of varying actions followed by an outcome. Children’s imitation of sequences that produced the outcome increased, in some cases resulting in production of shorter sequences of actions that the children had never seen performed in isolation. This behavior is consistent with our model’s predictions, and suggests that children attend to statistical evidence in deciding which actions to imitate, rather than obligately imitating successful actions. Keywords: Cognitive development; Imitation; Statistical learning; Causal inference; Bayesian inference Introduction Learning the causal relationships between everyday se- quences of actions and their outcomes is a daunting task. How do you transform a package of bread, a jar of peanut butter and a jar of jelly into a peanut butter and jelly sand- wich? Do you cut the bread in half before or after you put together the sandwich? Can you put the peanut butter on first, or does it always have to be jelly first? In order to achieve desired outcomes – from everyday goals such as eating a tasty sandwich to distinctive human abilities such as making and using tools – children need to solve a challenging causal learning problem: observing that the intentional actions of others lead to outcomes, inferring the causal relations between those actions and outcomes, and then using that knowledge to plan their own actions. To learn from observation in this way, children cannot sim- ply mimic everything they see. Instead, they must segment actions into meaningful sequences, and determine which actions are relevant to outcomes and why. Recent studies of imitation in children have produced varying answers to the question of whether children are capable of solving this problem. While children sometimes selectively reproduce the most obviously causally effective actions (Williamson, Meltzoff, & Markman, 2008; Schulz, Hooppell, & Jenkins, 2008), at other times they will “overimitate”, reproducing apparently unnecessary parts of a causal sequence (Whiten, Custance, Gomez, Teixidor, & Bard, 1996; Lyons, Young, & Keil, 2007), or copying an actor’s precise means, when a more efficient action for accomplishing the same goal is available (Meltzoff, 1995). Sometimes children may produce both kinds of behavior in the same study. In the “rational imitation” studies by Gergely, Bekkering, and Kiraly (2002), children saw an experimenter activate a machine with hands free or hands confined. Children both produced exact imita- tions of the actor (touching their head to a machine to make it go) and produced more obviously causally effective actions (touching the machine with a hand), though the proportion of such actions differed in the different intentional contexts. We suggest that these different results reflect the multiple sources of information that contribute to a rational statistical inference about causally effective actions. Children need to balance their prior knowledge about causal relations, the new evidence that is presented to them by the adult, and their knowledge of the adult’s intentions. Moreover, in the case of imitation there is often no single “right answer” to the question of what to imitate. After all, a longer “overimitation” sequence might actually be necessary to bring about an effect, though that might seem unlikely at first. The imitation problem can be expressed as a problem of Bayesian inference, with Bayes’ rule indicating how children might combine these factors to formulate different causal hypotheses and produce different action sequences based on those hypotheses. It is difficult to test this idea however, without knowing the strength of various causal hypotheses for the children. Since previous studies involved general folk physical and psychological knowledge (such as removing a visibly ineffectual bolt to open a puzzle box) it is difficult to know how strong those hypotheses would be. By giving children statistical information supporting different hypotheses we can normatively determine how probable dif- ferent hypotheses should be, and then see whether children’s imitation reflects those probabilities. It is also independently interesting to explore the role of statistical information in imitation. Recent studies show that children are surprisingly sophisticated in their use of statistical information such as conditional probabilities in a range of domains, from phonology (Saffran, Aslin, & Newport, 1996), to visual perception (Fiser & Aslin, 2002; Kirkham, Slemmer, & Johnson, 2002), to word meaning (Xu & Tenenbaum, 2007). Such information plays a particularly important role in both action processing (Zacks et al., 2001; Baldwin, Andersson, Saffran, & Meyer, 2008; Buchsbaum, Griffiths, Gopnik, & Baldwin, 2009) and causal inference (Gopnik et al., 2004; Gopnik & Schulz, 2007), and allows adults to identify causal subsequences within continuous streams of action (Buchsbaum et al., 2009). Varying the probabilities of events within action sequences may thus provide a way to vary the statistical evidence those sequences provide in favor of different causal hypotheses. Statistical inference might be particularly important to