What are you trying to tell me? A Bayesian model of how toddlers can simultaneously infer property extension and sampling processes

What are you trying to tell me? A Bayesian model of how toddlers can simultaneously infer property extension and sampling processes Hyowon Gweon, Joshua B. Tenenbaum, and Laura E. Schulz (hyora, jbt, lschulz@mit.edu) Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology Cambridge, MA 02139 USA Abstract Young human learners possess a remarkable ability to make inductive inferences from sparse data. Recent research suggests that children‟s generalizations are sensitive to the process by which data are generated (i.e., teacher-driven vs. learner-driven sampling; Xu & Tenenbaum, 2007). In general, sampling process and properties of objects are tightly coupled; knowing how the data were sampled can inform your inference about property extensions, and vice versa. In real- world situations, however, both the extension of novel properties and the sampling process may be ambiguous. These situations commonly arise when children are learning socially from adults. How do children confront the challenge of simultaneously inferring both the property extension and the sampling process from a small amount of data? Here we present a Bayesian model showing how this joint inference problem can be solved. Consistent with the predictions of the model, two behavioral experiments suggest that toddlers (mean: 16 months) can use the relationship between a sample and a population to infer both the sampling process and the extent to which a non-obvious object property should be generalized. Keywords: Sampling process; property induction; Bayesian model, cognitive development; toddlers Previous developmental research suggests that young children have a remarkable ability to make inferences from small amounts of data. Children can learn object kinds, causal properties, and word meanings from just a few trials of evidence (Carey & Bartlett, 1978; Gopnik, Sobel, Schulz, & Glymour, 2001; Mandler & McDonough, 1996). Indeed, even infants can generalize a non-obvious property of an object (e.g., squeaking) to a similar-looking object after just a single exposure (Baldwin, Markman, & Melartin, 1993). However, the process by which data are generated can influence the learner‟s inferences. Strikingly, even 8-month- olds are sensitive to sampling processes: they expect that a blind-folded draw from a bin of balls should result in a sample representative of the population (Xu & Garcia, 2008). Recent research suggests different sampling contexts are particularly important when learning in social contexts. For example, three- and four-year olds generalize a label for a novel object more conservatively when the exemplars are sampled by a knowledgeable teacher than when they are chosen by the learners themselves (Xu & Tenenbaum, 2007). Another recent study showed that children can even make sophisticated inferences about mental states of others given a goal-directed, non-random sampling process. When an agent (i.e., a squirrel puppet) deliberately draws a non- representative sample of toys from the population, preschoolers infer that the agent has a preference for the sampled objects (Kushnir, Xu, & Wellman, 2008). Recent modeling work on preference learning shows that children can make these inferences by assuming that the agent selects the samples based on their subjective utility of each example (Lucas, Griffiths, Xu, & Fawcett, 2008). Note, however, that in these studies, the sampling process was specified by information about the person drawing the sample: the agent drawing the sample was either a knowledgeable adult or the child herself (Xu & Tenenbaum, 2007), was blindfolded or had visual access (Xu & Garcia, 2008), or was clearly intentionally selecting specific objects (Kushnir et al., 2008) Frequently however, the sampling process may be less obvious; the learner may need to make inferences about both the sampling process and the properties of objects. Consider an example where mom pulls a few blue toys out of a box of blue and yellow toys and squeaks the blue toys. Did she select just the blue ones because only the blue toys squeak? Or did she sample from the whole box and just happened to pull out all blue toys that squeak? How can the child tell, and how is this inference about the sampling process linked to their inference about the property of the yellow toy? Problems of this nature are much more difficult, because inferences about sampling process and property extension are tightly coupled: inferences about one should affect inferences about the other, but you need to infer both simultaneously. This chicken-and-egg problem comes up particularly in social contexts, where children are learning from other people. Because the cues to the appropriate sampling process may be ambiguous or too subtle for young learners to catch, they might not be able to use information about the sampling process to learn the extension of a demonstrated property from a few samples of evidence. This challenge poses an interesting question: how do young children confront a situation in which both variables need to be inferred? Here we provide a simple Bayesian model that captures how this joint inference problem can be solved. We then present the first empirical evidence that toddlers (mean: 16 months) can engage in these joint inferences to determine both the nature of the sampling process and the extension of non-obvious object properties.