Bayes and blickets: effects of knowledge on causal induction in children and adults

People are adept at inferring novel causal relations, even from only a few observations. Prior knowledge about the probability of encountering causal relations of various types and the nature of the mechanisms relating causes and effects plays a crucial role in these inferences. We test a formal account of how this knowledge can be used and acquired, based on analyzing causal induction as Bayesian inference. Five studies explored the predictions of this account with adults and 4-year-olds, using tasks in which participants learned about the causal properties of a set of objects. The studies varied the two factors that our Bayesian approach predicted should be relevant to causal induction: the prior probability with which causal relations exist, and the assumption of a deterministic or a probabilistic relation between cause and effect. Adults' judgments (Experiments 1, 2, and 4) were in close correspondence with the quantitative predictions of the model, and children's judgments (Experiments 3 and 5) agreed qualitatively with this account.     

The double-edged sword of pedagogy: Instruction limits spontaneous exploration and discovery

Motivated by computational analyses, we look at how teaching affects exploration and discovery. In Experiment 1, we investigated children’s exploratory play after an adult pedagogically demonstrated a function of a toy, after an interrupted pedagogical demonstration, after a naïve adult demonstrated the function, and at baseline. Preschoolers in the pedagogical condition focused almost exclusively on the target function; by contrast, children in the other conditions explored broadly. In Experiment 2, we show that children restrict their exploration both after direct instruction to themselves and after overhearing direct instruction given to another child; they do not show this constraint after observing direct instruction given to an adult or after observing a non-pedagogical intentional action. We discuss these findings as the result of rational inductive biases. In pedagogical contexts, a teacher’s failure to provide evidence for additional functions provides evidence for their absence; such contexts generalize from child to child (because children are likely to have comparable states of knowledge) but not from adult to child. Thus, pedagogy promotes efficient learning but at a cost: children are less likely to perform potentially irrelevant actions but also less likely to discover novel information.     

Sticking to the Evidence? A Behavioral and Computational Case Study of Micro‐Theory Change in the Domain of Magnetism

Constructing an intuitive theory from data confronts learners with a “chicken‐and‐egg” problem: The laws can only be expressed in terms of the theory's core concepts, but these concepts are only meaningful in terms of the role they play in the theory's laws; how can a learner discover appropriate concepts and laws simultaneously, knowing neither to begin with? We explore how children can solve this chicken‐and‐egg problem in the domain of magnetism, drawing on perspectives from computational modeling and behavioral experiments. We present 4‐ and 5‐year‐olds with two different simplified magnet‐learning tasks. Children appropriately constrain their beliefs to two hypotheses following ambiguous but informative evidence. Following a critical intervention, they learn the correct theory. In the second study, children infer the correct number of categories given no information about the possible causal laws. Children's hypotheses in these tasks are explained as rational inferences within a Bayesian computational framework.     

Error probabilities for inference of causal directions

A main message from the causal modelling literature in the last several decades is that under some plausible assumptions, there can be statistically consistent procedures for inferring (features of) the causal structure of a set of random variables from observational data. But whether we can control the error probabilities with a finite sample size depends on the kind of consistency the procedures can achieve. It has been shown that in general, under the standard causal Markov and Faithfulness assumptions, the procedures can only be pointwise but not uniformly consistent without substantial background knowledge. This implies the impossibility of choosing a finite sample size to control the worst case error probabilities. In this paper, I consider the simpler task of inferring causal directions when the skeleton of the causal structure is known, and establish a similarly negative result concerning the possibility of controlling error probabilities. Although the result is negative in form, it has an interesting positive implication for causal discovery methods.     

The development of causal categorization

Two experiments examined the impact of causal relations between features on categorization in 5- to 6-year-old children and adults. Participants learned artificial categories containing instances with causally related features and noncausal features. They then selected the most likely category member from a series of novel test pairs. Classification patterns and logistic regression were used to diagnose the presence of independent effects of causal coherence, causal status, and relational centrality. Adult classification was driven primarily by coherence when causal links were deterministic (Experiment 1) but showed additional influences of causal status when links were probabilistic (Experiment 2). Children's classification was based primarily on causal coherence in both cases. There was no effect of relational centrality in either age group. These results suggest that the generative model (Rehder, 2003a) provides a good account of causal categorization in children as well as adults.     

Children’s developing understanding of the relation between variable causal efficacy and mechanistic complexity

Two experiments investigated 3–4-year-olds’ ability to infer the causal mechanisms for a pair of lights. In both experiments the exterior of the two lights appeared identical. In Experiment 1, one light displayed a stable activation pattern of a single color while the other light displayed a variable pattern of activation by cycling through a series of different colors (i.e., a more varied effect). Children were asked to judge which light had a more complex internal structure. Four-year-olds were more likely to match the light with the more variable effect with a more complex internal mechanism and the light with the more stable effect with a less complex mechanism. Three-year-olds’ responses were at chance. Experiment 2 replicated this finding when the activation patterns of the two lights were described verbally but never demonstrated. Taken together, these results suggest that 4-year-olds appreciate that the variability of an object’s causal efficacy is related to the complexity of its internal mechanistic structure.     

The power of causal beliefs and conflicting evidence on causal judgments and decision making

In two experiments, we investigated the relative impact of causal beliefs and empirical evidence on both decision making and causal judgments, and whether this relative impact could be altered by previous experience. Participants had to decide which of two alternatives would attain a higher outcome on the basis of four cues. After completing the decision task, they were asked to estimate to what extent each cue was a reliable cause of the outcome. Participants were provided with instructions that causally related two of the cues to the outcome, whereas they received neutral information about the other two cues. Two of the four cues—a causal and a neutral cue—had high validity and were both generative. The remaining two cues had low validity, and were generative in Experiment 1, but almost not related to the outcome in Experiment 2. Selected groups of participants in both experiments received pre-training with either causal or neutral cues, or no pre-training was provided. Results revealed that the impact of causal beliefs and empirical evidence depends on both the experienced pre-training and cue validity. When all cues were generative and participants received pre-training with causal cues, they mostly relied on their causal beliefs, whereas they relied on empirical evidence when they received pre-training with neutral cues. In contrast, when some of the cues were almost not related to the outcome, participants’ responses were primarily influenced by validity and—to a lesser extent—by causal beliefs. In either case, however, the influence of causal beliefs was higher in causal judgments than in decision making. While current theoretical approaches in causal learning focus either on the effect of causal beliefs or empirical evidence, the present research shows that both factors are required to explain the flexibility involved in human inferences.     

Own and Others' Prior Experiences Influence Children's Imitation of Causal Acts

Young children learn from others' examples, and they do so selectively. We examine whether the efficacy of prior experiences influences children's imitation. Thirty-six-month-olds had initial experience on a causal learning task either by performing the task themselves or by watching an adult perform it. The nature of the experience was manipulated such that the actor had either an easy or a difficult experience completing the task. Next, a second adult demonstrated an innovative technique for completing it. Children who had a difficult first-person experience, and those who had witnessed another person having difficulty, were significantly more likely to adopt and imitate the adult's innovation than those who had or witnessed an easy experience. Children who observed another were also more likely to imitate than were those who had the initial experience themselves. Imitation is influenced by prior experience, both when it is obtained through one's own hands-on motor manipulation and when it derives from observing the acts of others.     

The mental representation of causal conditional reasoning: mental models or causal models

In this paper, two experiments are reported investigating the nature of the cognitive representations underlying causal conditional reasoning performance. The predictions of causal and logical interpretations of the conditional diverge sharply when inferences involving pairs of conditionals—such as if P₁then Q and if P₂then Q—are considered. From a causal perspective, the causal direction of these conditionals is critical: are the P_icauses of Q; or symptoms caused byQ. The rich variety of inference patterns can naturally be modelled by Bayesian networks. A pair of causal conditionals where Q is an effect corresponds to a “collider” structure where the two causes (P_i) converge on a common effect. In contrast, a pair of causal conditionals where Q is a cause corresponds to a network where two effects (P_i) diverge from a common cause. Very different predictions are made by fully explicit or initial mental models interpretations. These predictions were tested in two experiments, each of which yielded data most consistent with causal model theory, rather than with mental models.     

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.     

Stick to the script: The effect of witnessing multiple actors on children’s imitation

What kinds of cues increase imitative fidelity in early childhood? The effects of multiple models and verbal framing were examined in preschool children (N = 259, 3–6-year-olds). Each participant was presented with one of eight possible combinations of type of modeling and verbal frame. The type of modeling involved: (i) a single model offering two demonstrations, (ii) two successive models each offering a single demonstration, (iii) two synchronous models each offering two demonstrations, or (iv) two synchronous models each offering a single demonstration. The verbal frame preceding the demonstrations emphasized either the instrumental outcome of the actions or their conventionality. Imitative fidelity was highest for the synchronous models (types iii and iv) and lowest for the single model (type i). Imitative fidelity was also higher for the convention-oriented than the outcome-oriented frame and higher for older than younger children. Children also provided more conventional explanations for their actions after viewing the synchronous models and after the convention-oriented framing. The results indicate that children’s imitative fidelity depends on the number of actors and the way the actions are framed.     

Preschoolers use pedagogical cues to guide radical reorganization of category knowledge

In constructing a conceptual understanding of the world, children must actively evaluate what information is idiosyncratic or superficial, and what represents essential, defining information about kinds and categories. Preschoolers observed identical evidence about a novel object’s function (magnetism) produced in subtly different manners: accidentally, intentionally, or demonstrated communicatively and pedagogically. Only when evidence was explicitly demonstrated for their benefit did children reliably go beyond salient perceptual features (color or shape), to infer function to be a defining property on which to base judgments about category membership. Children did not show this pattern when reasoning about a novel perceptual property, suggesting that a pedagogical communicative context may be especially important for children’s learning about artifact functions. Observing functional evidence in a pedagogical context helps children construct fundamentally different conceptions of novel categories as defined not by superficial appearances but by deeper, functional properties.     

The effect of the model's presence and of negative evidence on infants' selective imitation

This study demonstrated selective “rational” imitation in infants in two testing conditions: in the presence or absence of the model during the response phase. In the study, 14-month-olds were more likely to imitate a tool-use behavior when a prior failed attempt emphasized the logical reason and relevance of introducing this novel means, making it cognitively transparent for the infants. Infants also learned imitatively from the cognitively opaque (yet socially communicated) modeling situation, but to a lesser degree. Furthermore, the presence of the model as a social partner during testing influenced the performance of infants in that they were more likely to imitate the novel means when the model was present during testing. These results highlight the important interaction of interpretive schemas (e.g., causality, teleological stance) and social communicative cues in action interpretation guiding imitative learning.     

Influences of credibility of testimony and strength of statistical evidence on children’s and adolescents’ reasoning

According to dual-process models that include analytic and heuristic modes of processing, analytic processing is often expected to become more common with development. Consistent with this view, on reasoning problems, adolescents are more likely than children to select alternatives that are backed by statistical evidence. It is shown here that this pattern depends on the quality of the statistical evidence and the quality of the testimonial that is the typical alternative to statistical evidence. In Experiment 1, 9- and 13-year-olds (N = 64) were presented with scenarios in which solid statistical evidence was contrasted with casual or expert testimonial evidence. When testimony was casual, children relied on it but adolescents did not; when testimony was expert, both children and adolescents relied on it. In Experiment 2, 9- and 13-year-olds (N = 83) were presented with scenarios in which casual testimonial evidence was contrasted with weak or strong statistical evidence. When statistical evidence was weak, children and adolescents relied on both testimonial and statistical evidence; when statistical evidence was strong, most children and adolescents relied on it. Results are discussed in terms of their implications for dual-process accounts of cognitive development.     

Young children's use of statistical sampling evidence to infer the subjectivity of preferences

A crucial task in social interaction involves understanding subjective mental states. Here we report two experiments with toddlers exploring whether they can use statistical evidence to infer the subjective nature of preferences. We found that 2-year-olds were likely to interpret another person’s nonrandom sampling behavior as a cue for a preference different from their own. When there was no alternative in the population or if the sampling was random, 2-year-olds did not ascribe a preference and persisted in their initial beliefs that the person would share their own preference. We found similar but weaker patterns of responses in 16-month-olds. These results suggest that the ability to infer the subjectivity of preferences based on sampling information begins to emerge between 16 months and 2 years. Our findings provide some of the first evidence that from early in development, young children can use statistical evidence to make rational inferences about the social world.     

Cognitive imitation in typically-developing 3- and 4-year olds and individuals with autism

Individuals diagnosed with autism suffer from numerous social, affective and linguistic impairments. It has also been suggested that they have a global imitation deficit. That hypothesis, however, is compromised by the fact that individuals with autism suffer from various motor impairments. Here we describe an experiment on cognitive imitation, a type of imitation that doesn’t require motor learning. Nine male autistic subjects and 20 typically-developing 3- and 4-year olds were trained to respond, in a prescribed order, to different lists of photographs that were displayed simultaneously on a touch-sensitive monitor. Because the position of the photographs varied randomly from trial to trial, sequences could not be learned by motor imitation. In three different imitation treatments, including a ghost control, autistic subjects learned new sequences more rapidly after observing a model execute those sequences than when they had to learn new sequences entirely by trial and error. Moreover, the performance of autistic subjects did not significantly differ from the performance of typically-developing controls. The result of this and other studies suggests that individuals with autism suffer from a specific novel motor imitation deficit.