Christopher G. Lucas

Learning the Form of Causal Relationships Using Hierarchical Bayesian Models

People learn quickly when reasoning about causal relationships, making inferences from limited data and avoiding spurious inferences. Efficient learning depends on abstract knowledge, which is often domain or context specific, and much of it must be learned. While such knowledge effects are well documented, little is known about exactly how we acquire knowledge that constrains learning. This work focuses on knowledge of the functional form of causal relationships; there are many kinds of relationships that can apply between causes and their effects, and knowledge of the form such a relationship takes is important in order to quickly identify the real causes of an observed effect. We developed a hierarchical Bayesian model of the acquisition of knowledge of the functional form of causal relationships and tested it in five experimental studies, considering disjunctive and conjunctive relationships, failure rates, and cross-domain effects. The Bayesian model accurately predicted human judgments and outperformed several alternative models.

When children are better (or at least more open-minded) learners than adults: Developmental differences in learning the forms of causal relationships

Children learn causal relationships quickly and make far-reaching causal inferences from what they observe. Acquiring abstract causal principles that allow generalization across different causal relationships could support these abilities. We examine childrens ability to acquire abstract knowledge about the forms of causal relationships and show that in some cases they learn better than adults. Adults and 4- and 5-year-old children saw events suggesting that a causal relationship took one of two different forms, and their generalization to a new set of objects was then tested. One form was a more typical disjunctive relationship; the other was a more unusual conjunctive relationship. Participants were asked to both judge the causal efficacy of the objects and to design actions to generate or prevent an effect. Our results show that children can learn the abstract properties of causal relationships using only a handful of events. Moreover, children were more likely than adults to generalize the unusual conjunctive relationship, suggesting that they are less biased by prior assumptions and pay more attention to current evidence. These results are consistent with the predictions of a hierarchical Bayesian model.

When Younger Learners Can Be Better (or at Least More Open-Minded) Than Older Ones

We describe a surprising developmental pattern we found in studies involving three different kinds of problems and age ranges. Younger learners are better than older ones at learning unusual abstract causal principles from evidence. We explore two factors that might contribute to this counterintuitive result. The first is that as our knowledge grows, we become less open to new ideas. The second is that younger minds and brains are intrinsically more flexible and exploratory, although they are also less efficient as a result.

The Child as Econometrician: A Rational Model of Preference Understanding in Children

Recent work has shown that young children can learn about preferences by observing the choices and emotional reactions of other people, but there is no unified account of how this learning occurs. We show that a rational model, built on ideas from economics and computer science, explains the behavior of children in several experiments, and offers new predictions as well. First, we demonstrate that when children use statistical information to learn about preferences, their inferences match the predictions of a simple econometric model. Next, we show that this same model can explain childrens ability to learn that other people have preferences similar to or different from their own and use that knowledge to reason about the desirability of hidden objects. Finally, we use the model to explain a developmental shift in preference understanding.

Non-Bayesian Inference: Causal Structure Trumps Correlation

The study tests the hypothesis that conditional probability judgments can be influenced by causal links between the target event and the evidence even when the statistical relations among variables are held constant. Three experiments varied the causal structure relating three variables and found that (a) the target event was perceived as more probable when it was linked to evidence by a causal chain than when both variables shared a common cause; (b) predictive chains in which evidence is a cause of the hypothesis gave rise to higher judgments than diagnostic chains in which evidence is an effect of the hypothesis; and (c) direct chains gave rise to higher judgments than indirect chains. A Bayesian learning model was applied to our data but failed to explain them. An explanation-based hypothesis stating that statistical information will affect judgments only to the extent that it changes beliefs about causal structure is consistent with the results.

Inferring Hidden Causal Structure

We used a new method to assess how people can infer unobserved causal structure from patterns of observed events. Participants were taught to draw causal graphs, and then shown a pattern of associations and interventions on a novel causal system. Given minimal training and no feedback, participants in Experiment 1 used causal graph notation to spontaneously draw structures containing one observed cause, one unobserved common cause, and two unobserved independent causes, depending on the pattern of associations and interventions they saw. We replicated these findings with less-informative training (Experiments 2 and 3) and a new apparatus (Experiment 3) to show that the pattern of data leads to hidden causal inferences across a range of prior constraints on causal knowledge.

A rational model of function learning

Theories of how people learn relationships between continuous variables have tended to focus on two possibilities: one, that people are estimating explicit functions, or two that they are performing associative learning supported by similarity. We provide a rational analysis of function learning, drawing on work on regression in machine learning and statistics. Using the equivalence of Bayesian linear regression and Gaussian processes, which provide a probabilistic basis for similarity-based function learning, we show that learning explicit rules and using similarity can be seen as two views of one solution to this problem. We use this insight to define a rational model of human function learning that combines the strengths of both approaches and accounts for a wide variety of experimental results.

Changes in cognitive flexibility and hypothesis search across human life history from childhood to adolescence to adulthood

How was the evolution of our unique biological life history related to distinctive human developments in cognition and culture? We suggest that the extended human childhood and adolescence allows a balance between exploration and exploitation, between wider and narrower hypothesis search, and between innovation and imitation in cultural learning. In particular, different developmental periods may be associated with different learning strategies. This relation between biology and culture was probably coevolutionary and bidirectional: life-history changes allowed changes in learning, which in turn both allowed and rewarded extended life histories. In two studies, we test how easily people learn an unusual physical or social causal relation from a pattern of evidence. We track the development of this ability from early childhood through adolescence and adulthood. In the physical domain, preschoolers, counterintuitively, perform better than school-aged children, who in turn perform better than adolescents and adults. As they grow older learners are less flexible: they are less likely to adopt an initially unfamiliar hypothesis that is consistent with new evidence. Instead, learners prefer a familiar hypothesis that is less consistent with the evidence. In the social domain, both preschoolers and adolescents are actually the most flexible learners, adopting an unusual hypothesis more easily than either 6-y-olds or adults. There may be important developmental transitions in flexibility at the entry into middle childhood and in adolescence, which differ across domains.

An improved probabilistic account of counterfactual reasoning

When people want to identify the causes of an event, assign credit or blame, or learn from their mistakes, they often reflect on how things could have gone differently. In this kind of reasoning, one considers a counterfactual world in which some events are different from their real-world counterparts and considers what else would have changed. Researchers have recently proposed several probabilistic models that aim to capture how people do (or should) reason about counterfactuals. We present a new model and show that it accounts better for human inferences than several alternative models. Our model builds on the work of Pearl (2000), and extends his approach in a way that accommodates backtracking inferences and that acknowledges the difference between counterfactual interventions and counterfactual observations. We present 6 new experiments and analyze data from 4 experiments carried out by Rips (2010), and the results suggest that the new model provides an accurate account of both mean human judgments and the judgments of individuals. (PsycINFO Database Record

People learn other people’s preferences through inverse decision-making

People are capable of learning other peoples preferences by observing the choices they make. We propose that this learning relies on inverse decision-making-inverting a decision-making model to infer the preferences that led to an observed choice. In Experiment 1, participants observed 47 choices made by others and ranked them by how strongly each choice suggested that the decision maker had a preference for a specific item. An inverse decision-making model generated predictions that were in accordance with participants inferences. Experiment 2 replicated and extended a previous study by Newtson (1974) in which participants observed pairs of choices and made judgments about which choice provided stronger evidence for a preference. Inverse decision-making again predicted the results, including a result that previous accounts could not explain. Experiment 3 used the same method as Experiment 2 and found that participants did not expect decision makers to be perfect utility-maximizers.