A theory of causal learning in children: causal maps and Bayes nets

The authors outline a cognitive and computational account of causal learning in children. They propose that children use specialized cognitive systems that allow them to recover an accurate "causal map" of the world: an abstract, coherent, learned representation of the causal relations among events. This kind of knowledge can be perspicuously understood in terms of the formalism of directed graphical causal models, or Bayes nets. Children's causal learning and inference may involve computations similar to those for learning causal Bayes nets and for predicting with them. Experimental results suggest that 2- to 4-year-old children construct new causal maps and that their learning is consistent with the Bayes net formalism.     

Memory-Based Hypothesis Formation: Heuristic Learning of Commonsense Causal Relations from Text

We present a memory-based approach to learning commonsense causal relations from episodic text. The method relies on dynamic memory that consists of events, event schemata, episodes, causal heuristics, and causal hypotheses. The learning algorithms are based on applying causal heuristics to precedents of new information. The heuristics are derived from principles of causation, and, to a limited extent, from domain-related causal reasoning. Learning is defined as finding—and later augmenting—inter-episodal and intea-episodal causal connections. The learning algorithms enable inductive generalization of causal associations into AND/OR graphs. The methodology has been implemented and tested in the program NEXUS.     

Education and Understanding Structural Causes for Group Inequalities

Group inequalities in the United States are most often attributed to the characteristics of the individuals who belong to these groups; thinking about structural causes of group inequalities is rare. This paper reviews cognitive, cultural, and systemic reasons for this bias. The efficacy of education as a way to increase structural thinking was investigated in two studies of college students' causal thinking about group inequalities. Both studies involved a course on intergroup relations that covered structural sources of racial or ethnic inequalities. Results supported hypotheses that the course would increase structural thinking about racial or ethnic inequality, and that structural thinking would generalize to inequalities not explicitly covered in the course. Both course content and active learning pedagogy were related to structural thinking about inequalities. Active learning was also related to applying structural thinking to targets of change.     

Estimating causal strength: the role of structural knowledge and processing effort.

The strength of causal relations typically must be inferred on the basis of statistical relations between observable events. This article focuses on the problem that there are multiple ways of extracting statistical information from a set of events. In causal structures involving a potential cause, an effect and a third related event, the assumed causal role of this third event crucially determines whether it is appropriate to control for this event when making causal assessments between the potential cause and the effect. Three experiments show that prior assumptions about the causal roles of the learning events affect the way contingencies are assessed with otherwise identical learning input. However, prior assumptions about causal roles is only one factor influencing contingency estimation. The experiments also demonstrate that processing effort affects the way statistical information is processed. These findings provide further evidence for the interaction between bottom-up and top-down influences in the acquisition of causal knowledge. They show that, apart from covariation information or knowledge about mechanisms, abstract assumptions about causal structures also may affect the learning process.     

Rethinking temporal contiguity and the judgement of causality: effects of prior knowledge, experience, and reinforcement procedure.

Time plays a pivotal role in causal inference. Nonetheless most contemporary theories of causal induction do not address the implications of temporal contiguity and delay, with the exception of associative learning theory. Shanks, Pearson, and Dickinson (1989) and several replications (Reed, 1992, 1999) have demonstrated that people fail to identify causal relations if cause and effect are separated by more than two seconds. In line with an associationist perspective, these findings have been interpreted to indicate that temporal lags universally impair causal induction. This interpretation clashes with the richness of everyday causal cognition where people apparently can reason about causal relations involving considerable delays. We look at the implications of cause-effect delays from a computational perspective and predict that delays should generally hinder reasoning performance, but that this hindrance should be alleviated if reasoners have knowledge of the delay. Two experiments demonstrated that (1) the impact of delay on causal judgement depends on participants' expectations about the timeframe of the causal relation, and (2) the free-operant procedures used in previous studies are ill-suited to study the direct influences of delay on causal induction, because they confound delay with weaker evidence for the relation in question. Implications for contemporary causal learning theories are discussed.     

Independence and dependence in human causal reasoning

Causal graphical models (CGMs) are a popular formalism used to model human causal reasoning and learning. The key property of CGMs is the causal Markov condition, which stipulates patterns of independence and dependence among causally related variables. Five experiments found that while adult’s causal inferences exhibited aspects of veridical causal reasoning, they also exhibited a small but tenacious tendency to violate the Markov condition. They also failed to exhibit robust discounting in which the presence of one cause as an explanation of an effect makes the presence of another less likely. Instead, subjects often reasoned “associatively,” that is, assumed that the presence of one variable implied the presence of other, causally related variables, even those that were (according to the Markov condition) conditionally independent. This tendency was unaffected by manipulations (e.g., response deadlines) known to influence fast and intuitive reasoning processes, suggesting that an associative response to a causal reasoning question is sometimes the product of careful and deliberate thinking. That about 60% of the erroneous associative inferences were made by about a quarter of the subjects suggests the presence of substantial individual differences in this tendency. There was also evidence that inferences were influenced by subjects’ assumptions about factors that disable causal relations and their use of a conjunctive reasoning strategy. Theories that strive to provide high fidelity accounts of human causal reasoning will need to relax the independence constraints imposed by CGMs.     

The role of learning data in causal reasoning about observations and interventions

Recent studies have shown that people have the capacity to derive interventional predictions for previously unseen actions from observational knowledge, a finding that challenges associative theories of causal learning and reasoning (e.g., Meder, Hagmayer, & Waldmann, 2008). Although some researchers have claimed that such inferences are based mainly on qualitative reasoning about the structure of a causal system (e.g., Sloman, 2005), we propose that people use both the causal structure and its parameters for their inferences. We here employ an observational trial-by-trial learning paradigm to test this prediction. In Experiment 1, the causal strength of the links within a given causal model was varied, whereas in Experiment 2, base rate information was manipulated while keeping the structure of the model constant. The results show that learners’ causal judgments were strongly affected by the observed learning data despite being presented with identical hypotheses about causal structure. The findings show furthermore that participants correctly distinguished between observations and hypothetical interventions. However, they did not adequately differentiate between hypothetical and counterfactual interventions.     

Causal learning is collaborative: Examining explanation and exploration in social contexts

Causal learning in childhood is a dynamic and collaborative process of explanation and exploration within complex physical and social environments. Understanding how children learn causal knowledge requires examining how they update beliefs about the world given novel information and studying the processes by which children learn in collaboration with caregivers, educators, and peers. The objective of this article is to review evidence for how children learn causal knowledge by explaining and exploring in collaboration with others. We review three examples of causal learning in social contexts, which elucidate how interaction with others influences causal learning. First, we consider children’s explanation-seeking behaviors in the form of “why” questions. Second, we examine parents’ elaboration of meaning about causal relations. Finally, we consider parents’ interactive styles with children during free play, which constrains how children explore. We propose that the best way to understand children’s causal learning in social context is to combine results from laboratory and natural interactive informal learning environments.     

Bayesian generic priors for causal learning

The article presents a Bayesian model of causal learning that incorporates generic priors--systematic assumptions about abstract properties of a system of cause-effect relations. The proposed generic priors for causal learning favor sparse and strong (SS) causes--causes that are few in number and high in their individual powers to produce or prevent effects. The SS power model couples these generic priors with a causal generating function based on the assumption that unobservable causal influences on an effect operate independently (P. W. Cheng, 1997). The authors tested this and other Bayesian models, as well as leading nonnormative models, by fitting multiple data sets in which several parameters were varied parametrically across multiple types of judgments. The SS power model accounted for data concerning judgments of both causal strength and causal structure (whether a causal link exists). The model explains why human judgments of causal structure (relative to a Bayesian model lacking these generic priors) are influenced more by causal power and the base rate of the effect and less by sample size. Broader implications of the Bayesian framework for human learning are discussed.     

Abolishing the effect of reinforcement delay on human causal learning

Associative learning theory postulates two main determinants for human causal learning: contingency and contiguity. In line with such an account, participants in Shanks, Pearson, and Dickinson (1989) failed to discover causal relations involving delays of more than two seconds. More recent research has shown that the impact of contiguity and delay is mediated by prior knowledge about the timeframe of the causal relation in question. Buehner and May (2002, 2003) demonstrated that the detrimental effect of delay can be significantly reduced if reasoners are aware of potential delays. Here we demonstrate for the first time that the negative influence of delay can be abolished completely by a subtle change in the experimental instructions. Temporal contiguity is thus not essential for human causal learning.     

Failures of explaining away and screening off in described versus experienced causal learning scenarios

Causal Bayes nets capture many aspects of causal thinking that set them apart from purely associative reasoning. However, some central properties of this normative theory routinely violated. In tasks requiring an understanding of explaining away and screening off, subjects often deviate from these principles and manifest the operation of an associative bias that we refer to as the rich-get-richer principle. This research focuses on these two failures comparing tasks in which causal scenarios are merely described (via verbal statements of the causal relations) versus experienced (via samples of data that manifest the intervariable correlations implied by the causal relations). Our key finding is that we obtained stronger deviations from normative predictions in the described conditions that highlight the instructed causal model compared to those that presented data. This counterintuitive finding indicate that a theory of causal reasoning and learning needs to integrate normative principles with biases people hold about causal relations.     

Testing Event-Based Forms of Causality

Three fundamental types of causal relations are those of necessity, sufficiency, and necessity and sufficiency. These types are defined in contexts of categorical variables or events. Using statement calculus or Boolean algebra, one can determine which patterns of events are in support of a particular form of causal relation. In this article, we approach the analysis of these forms of causality taking the perspective of the analyst of empirical data. It is proposed using Configural Frequency Analysis (CFA) to test hypotheses about type of causal relation. Models are proposed for two-variable and multi-variable cases. Two CFA approaches are proposed. In the first, individual patterns (configurations) are examined under the question whether they are in support of a particular type of causal relation. In the second, patterns that are in support are compared with corresponding patterns that are not in support. In an empirical example, hypotheses are tested on the prediction of sustainability of change in dietary fat intake habits.     

The tight coupling between category and causal learning

The main goal of the present research was to demonstrate the interaction between category and causal induction in causal model learning. We used a two-phase learning procedure in which learners were presented with learning input referring to two interconnected causal relations forming a causal chain (Experiment 1) or a common-cause model (Experiments 2a, b). One of the three events (i.e., the intermediate event of the chain, or the common cause) was presented as a set of uncategorized exemplars. Although participants were not provided with any feedback about category labels, they tended to induce categories in the first phase that maximized the predictability of their causes or effects. In the second causal learning phase, participants had the choice between transferring the newly learned categories from the first phase at the cost of suboptimal predictions, or they could induce a new set of optimally predictive categories for the second causal relation, but at the cost of proliferating different category schemes for the same set of events. It turned out that in all three experiments learners tended to transfer the categories entailed by the first causal relation to the second causal relation.     

Effect of cue validity on learning of complex rules in probabilistic inference tasks

The effect of cue validity on the learning of positive and negative J-shaped relations in single-cue probability learning was studied. As would be expected from a hypothesis construction model, learning of the J-shaped relations was better when cue validity was high than when it was low. However, the results also showed that positive J-rules were learned more efficiently than negative J-rules. This shows that subjects do not construct their hypotheses on the basis of data from task only. It was concluded that subjects construct their hypotheses from elements stored in memory, and that data are used only to test their hypotheses.     

Assessing interactive causal influence

The discovery of conjunctive causes--factors that act in concert to produce or prevent an effect--has been explained by purely covariational theories. Such theories assume that concomitant variations in observable events directly license causal inferences, without postulating the existence of unobservable causal relations. This article discusses problems with these theories, proposes a causal-power theory that overcomes the problems, and reports empirical evidence favoring the new theory. Unlike earlier models, the new theory derives (a). the conditions under which covariation implies conjunctive causation and (b). functions relating observable events to unobservable conjunctive causal strength. This psychological theory, which concerns simple cases involving 2 binary candidate causes and a binary effect, raises questions about normative statistics for testing causal hypotheses regarding categorical data resulting from discrete variables.     

Can students evaluate their understanding of cause-and-effect relations? The effects of diagram completion on monitoring accuracy

For effective self-regulated study of expository texts, it is crucial that learners can accurately monitor their understanding of cause-and-effect relations. This study aimed to improve adolescents' monitoring accuracy using a diagram completion task. Participants read six texts, predicted performance, selected texts for restudy, and were tested for comprehension. Three groups were compared, in which learners either completed causal diagrams immediately after reading, completed them after a delay, or received no-diagram control instructions. Accuracy of predictions of performance was highest for learning of causal relations following delayed diagram completion. Completing delayed diagrams focused learners specifically on their learning of causal relations, so this task did not improve monitoring of learning of factual information. When selecting texts for restudy, the participants followed their predictions of performance to the same degree, regardless of monitoring accuracy. Fine-grained analyses also showed that, when completing delayed diagrams, learners based judgments on diagnostic cues that indicated actual understanding of connections between events in the text. Most important, delayed diagram completion can improve adolescents' ability to monitor their learning of cause-and-effect relations.     

Preschool children learn about causal structure from conditional interventions

The conditional intervention principle is a formal principle that relates patterns of interventions and outcomes to causal structure. It is a central assumption of experimental design and the causal Bayes net formalism. Two studies suggest that preschoolers can use the conditional intervention principle to distinguish causal chains, common cause and interactive causal structures even in the absence of differential spatiotemporal cues and specific mechanism knowledge. Children were also able to use knowledge of causal structure to predict the patterns of evidence that would result from interventions. A third study suggests that children's spontaneous play can generate evidence that would support such accurate causal learning.     

Determining whether causal order affects cue selection in human contingency learning: Comments on Shanks and Lopez (1996)

Shanks and Lopez (1996) reported three experiments in which they attempted to test whether causal order affects cue selection, and concluded that it does not. Their study provides an opportunity to highlight some basic methodological criteria that must be met in order to test whether and how causal order influences learning. In particular, it is necessary to (1) ensure that participants consistently interpret the learning situation in terms of directed cause-effect relations; (2) measure the causal knowledge they acquire; (3) manipulate causal order; and (4) control the statistical relations between cause and effect. With respect to these criteria, each experiment reported by Shanks and Lopez fails on multiple counts. Moreover, several aspects of the results reported by Shanks and Lopez are explained by causal-model theory, but not by associative accounts. Their study thus adds to a growing body of evidence from different laboratories indicating that human contingency learning can be guided by causal interpretation.     

Effects of information presentation mode on subjects' hypotheses in a probabilistic inference task

The effects of two modes of information-presentation (visual access to an ordered array of cue values vs. no access) on subjects' performance in a two-cue probability learning (MPL) task were investigated.The results showed that the visual access to an ordered array of cue values led to a larger proportion of correct hypotheses and of optimal selection strategies and to a better learning performance. These results were interpreted as supporting the conjecture that the situational variables may affect the subject's hypotheses about the cue-criterion relations. The results were also discussed with respect to their implications for the theory of MPL.