In the course of development, children change their beliefs, moving from a less to more accurate picture of the world. How do they do this when there are apparently an infinite variety of beliefs from which to choose? And how can we reconcile children's cognitive progress with the apparent irrationality of many of their explanations and predictions? In computer science, probabilistic models have provided a powerful framework for characterizing beliefs, and can tell us when beliefs are justified by the evidence. But they face similar questions: how can one actually get from less warranted beliefs to more accurate ones given a vast space of possibilities? This project brings these threads together, suggesting a possible solution to both challenges. The solution is based on the idea that children may form their beliefs by randomly sampling from a probability distribution of possible hypotheses, testing those sampled hypotheses, and then moving on to sample new possibilities. This "Sampling Hypothesis" provides a natural bridge between understanding how children actually do learn and reason and how computers can be designed to learn and reason optimally. These experiments will provide an important first step in exploring the Sampling Hypothesis: how do evidence and prior beliefs shape the samples of possible beliefs that children generate and evaluate, and how do developmental changes lead to differences in the samples of possible beliefs generated and evaluated.
A relatively immediate contribution of this work will be to connect state-of-the-art methods from machine learning and data analysis in computer science and statistics with accounts of belief acquisition in developmental psychology and educational psychology. In the longer run, the proposed projects have the potential to inform education, early intervention programs, and the study of cognitive deficits; by precisely characterizing how learning should proceed in typically developing children, this project can illustrate when and how developmental limitations impact learning and suggest a framework of ways of helping children with such disorders. The research also supports an ambitious training plan for post-doctoral and graduate student researchers, requiring the development of a nuanced understanding of both computational approaches and developmental experiments.
In this project we explored how very young children can learn as much as they do about the world around them. In particular, how can children learn about causes and effects? To answer this question we used the framework of Bayesian probabilistic models, derived from philosophy of science, machine learning and artificial intelligence. This approach essentially envisions the child as a kind of scientist formulating hypotheses and assessing them against the data. In particular, we discovered earlier that children seem to evaluate the probability of various hypotheses about causes and effects as they accumulate more data from the world around them. One important question about this kind of learning is how children ever decide which hypotheses to consider, since there are an enormous number of possibilities. In this project, we explored the possibility that children use some of the same techniques as machine learning algorithms. In particular, computers can "sample" – that is they can pick out hypotheses to test in a partly random but still systematic way. When a computer (or a brain) conducts this kind of sampling there is a particular signature behavior – in particular, the system will consider more probable hypotheses more often than less probable hypotheses. We demonstrated that children show this signature in their early causal learning. When they are asked to make multiple guesses about how a causal system works, they are more likely to guess more probable hypotheses. In fact, their guesses closely track how likely the various options are. Moreover, we showed that a specific kind of algorithm, which we call a win-stay lose-sample algorithm leads to the right causal answers in the long run. We also showed that adults and children behave in ways that are in accord with this algorithm. We also discovered a surprising developmental pattern across three different domains and age ranges. Younger learners are better than older ones at inferring unusual causal hypotheses from evidence. In one set of experiments, we showed participants new data that suggested that a machine worked in an unusual way. Four-year-olds drew the right conclusions but adults stuck to the most obvious assumption about the machine. In a second set of experiments we showed four-year-olds and six-year-olds data that suggested that a person acted because of their long-standing personality traits or because of the situation they were in. Six-year-olds tended to say that that the person’s actions were caused by traits regardless of the data, four-year-olds were more accurate. Finally, we showed 18-month-olds and three-year-olds data that suggested that an effect was caused by the relationship between two objects rather than by features of individual objects. Again, younger children were better at inferring the relationship than older children. The theoretical explanations we propose for this pattern involve three related ideas from machine learning: Development may proceed from a flatter to a more peaked prior, from high-temperature searches to low-temperature ones, and from exploration to exploitation. As we learn more we may pay less attention to new data and rely more on what we already know. Moreover, children’s brains may be designed to consider an especially wide range of hypotheses, much wider than the range of hypotheses we consider as adults. This work has implications for debates about the early childhood curriculum, Childhood cognition that may look irrational at first. For example, the variability of children’s behavior, their wide-ranging pretense, and their free-ranging unconstrained exploration, all look unlike what we might expect from an adult learner. However, this may actually be exactly what allows young children to learn so much.
