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.     

Valuing intervention and observation

Understanding causal relations is fundamental to effective action but causal data can be confounded. We examined the value that participants placed on data derived from a hypothetical intervention or observation. Our materials involved a possible cause (“bottled water”), a possible confound (“food”), and a context (“a restaurant”). We supposed that participants seek to draw as specific a causal inference as possible from presented data and value information sources more highly that allow them to do so. On this basis, we predicted that in circumstances where an intervention removed the confounding causal factor but observation did not, participants would prefer data derived from an intervention when the possible cause was present (the bottled water was drunk) but show the reverse preference when the possible cause was absent (the bottled water was not drunk). Experiment 1 confirmed this prediction. Using a between-subjects design, Experiment 2 tested for a difference in confidence in causal judgements given identical data, including data on the confound, as a function of method of data collection (intervention or observation). There was no significant difference in confidence ratings between the two methods but confidence ratings were sensitive to the probability of an effect (illness) given the cause. Using a within-subjects design, Experiment 3 revealed systematic individual differences in preference for the two methods. Participants were divided between those who considered intervention more confounded and those who considered observation more confounded. Our experiments point to the subtleties of participants' evaluation of data from studies of human beings.     

Are Causal Structure and Intervention Judgments Inextricably Linked? A Developmental Study

The application of the formal framework of causal Bayesian Networks to children’s causal learning provides the motivation to examine the link between judgments about the causal structure of a system, and the ability to make inferences about interventions on components of the system. Three experiments examined whether children are able to make correct inferences about interventions on different causal structures. The first two experiments examined whether children’s causal structure and intervention judgments were consistent with one another. In Experiment 1, children aged between 4 and 8 years made causal structure judgments on a three‐component causal system followed by counterfactual intervention judgments. In Experiment 2, children’s causal structure judgments were followed by intervention judgments phrased as future hypotheticals. In Experiment 3, we explicitly told children what the correct causal structure was and asked them to make intervention judgments. The results of the three experiments suggest that the representations that support causal structure judgments do not easily support simple judgments about interventions in children. We discuss our findings in light of strong interventionist claims that the two types of judgments should be closely linked.     

Inferring causal networks from observations and interventions

Information about the structure of a causal system can come in the form of observational data—random samples of the system's autonomous behavior—or interventional data—samples conditioned on the particular values of one or more variables that have been experimentally manipulated. Here we study people's ability to infer causal structure from both observation and intervention, and to choose informative interventions on the basis of observational data. In three causal inference tasks, participants were to some degree capable of distinguishing between competing causal hypotheses on the basis of purely observational data. Performance improved substantially when participants were allowed to observe the effects of interventions that they performed on the systems. We develop computational models of how people infer causal structure from data and how they plan intervention experiments, based on the representational framework of causal graphical models and the inferential principles of optimal Bayesian decision‐making and maximizing expected information gain. These analyses suggest that people can make rational causal inferences, subject to psychologically reasonable representational assumptions and computationally reasonable processing constraints.     

Temporal information and children's and adults' causal inferences

Three experiments examined whether children and adults would use temporal information as a cue to the causal structure of a three-variable system, and also whether their judgements about the effects of interventions on the system would be affected by the temporal properties of the event sequence. Participants were shown a system in which two events B and C occurred either simultaneously (synchronous condition) or in a temporal sequence (sequential condition) following an initial event A. The causal judgements of adults and 6–7-year-olds differed between the conditions, but this was not the case for 4-year-olds' judgements. However, unlike those of adults, 6–7-year-olds' intervention judgements were not affected by condition, and causal and intervention judgements were not reliably consistent in this age group. The findings support the claim that temporal information provides an important cue to causal structure, at least in older children. However, they raise important issues about the relationship between causal and intervention judgements.     

Effects of Causal Structure on Decisions About Where to Intervene on Causal Systems

We investigated how people design interventions to affect the outcomes of causal systems. We propose that the abstract structural properties of a causal system, in addition to people's content and mechanism knowledge, influence decisions about how to intervene. In Experiment 1, participants preferred to intervene at specific locations (immediate causes, root causes) in a causal chain regardless of which content variables occupied those positions. In Experiment 2, participants were more likely to intervene on root causes versus immediate causes when they were presented with a long‐term goal versus a short‐term goal. These results show that the structural properties of a causal system can guide the design of interventions.     

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.     

Do We “do”?

A normative framework for modeling causal and counterfactual reasoning has been proposed by Spirtes, Glymour, and Scheines (1993; cf. Pearl, 2000). The framework takes as fundamental that reasoning from observation and intervention differ. Intervention includes actual manipulation as well as counterfactual manipulation of a model via thought. To represent intervention, Pearl employed the do operator that simplifies the structure of a causal model by disconnecting an intervened-on variable from its normal causes. Construing the do operator as a psychological function affords predictions about how people reason when asked counterfactual questions about causal relations that we refer to as undoing, a family of effects that derive from the claim that intervened-on variables become independent of their normal causes. Six studies support the prediction for causal (A causes B) arguments but not consistently for parallel conditional (if A then B) ones. Two of the studies show that effects are treated as diagnostic when their values are observed but nondiagnostic when they are intervened on. These results cannot be explained by theories that do not distinguish interventions from other sorts of events.     

Compound cue processing within the fast and frugal heuristics approach in nonlinearly separable environments

Three experiments investigated whether participants used Take The Best (TTB) Configural, a fast and frugal heuristic that processes configurations of cues when making inferences concerning which of two alternatives has a higher criterion value. Participants were presented with a compound cue that was nonlinearly separable from its elements. The compound was highly valid in Experiments 1 and 2, but invalid in Experiment 3. Participants’ causal mental models were manipulated via instructions: participants were either told that cues acted through the same causal mechanism (configural causal model), through different causal mechanisms (elemental causal model), or the causal mechanisms were not specified (neutral causal model). A high percentage of participants used TTB-Configural when they had a configural causal model and a highly valid compound existed, suggesting that causal knowledge can be incorporated in otherwise very basic cognitive mechanisms to allow fine-grained adaptation to complex task structures.     

A Process Model of Causal Reasoning

How do we make causal judgments? Many studies have demonstrated that people are capable causal reasoners, achieving success on tasks from reasoning to categorization to interventions. However, less is known about the mental processes used to achieve such sophisticated judgments. We propose a new process model—the mutation sampler—that models causal judgments as based on a sample of possible states of the causal system generated using the Metropolis–Hastings sampling algorithm. Across a diverse array of tasks and conditions encompassing over 1,700 participants, we found that our model provided a consistently closer fit to participant judgments than standard causal graphical models. In particular, we found that the biases introduced by mutation sampling accounted for people's consistent, predictable errors that the normative model by definition could not. Moreover, using a novel experimental methodology, we found that those biases appeared in the samples that participants explicitly judged to be representative of a causal system. We conclude by advocating sampling methods as plausible process-level accounts of the computations specified by the causal graphical model framework and highlight opportunities for future research to identify not just what reasoners compute when drawing causal inferences, but also how they compute it.     

Causal discovery and the problem of psychological interventions

Finding causes is a central goal in psychological research. In this paper, I argue based on the interventionist approach to causal discovery that the search for psychological causes faces great obstacles. Psychological interventions are likely to be fat-handed: they change several variables simultaneously, and it is not known to what extent such interventions give leverage for causal inference. Moreover, due to problems of measurement, the degree to which an intervention was fat-handed, or more generally, what the intervention in fact did, is difficult to reliably estimate. A further complication is that the causal findings in psychology are typically made at the population level, and such findings do not allow inferences to individual-level causal relationships. I also discuss the implications of these problems for research, as well as various ways of addressing them, such as focusing more on the discovery of robust but non-causal patterns.     

Singular Clues to Causality and Their Use in Human Causal Judgment

It is argued that causal understanding originates in experiences of acting on objects. Such experiences have consistent features that can be used as clues to causal identification and judgment. These are singular clues, meaning that they can be detected in single instances. A catalog of 14 singular clues is proposed. The clues function as heuristics for generating causal judgments under uncertainty and are a pervasive source of bias in causal judgment. More sophisticated clues such as mechanism clues and repeated interventions are derived from the 14. Research on the use of empirical information and conditional probabilities to identify causes has used scenarios in which several of the clues are present, and the use of empirical association information for causal judgment depends on the presence of singular clues. It is the singular clues and their origin that are basic to causal understanding, not multiple instance clues such as empirical association, contingency, and conditional probabilities.     

Children Use Temporal Cues to Learn Causal Directionality

The ability to learn the direction of causal relations is critical for understanding and acting in the world. We investigated how children learn causal directionality in situations in which the states of variables are temporally dependent (i.e., autocorrelated). In Experiment 1, children learned about causal direction by comparing the states of one variable before versus after an intervention on another variable. In Experiment 2, children reliably inferred causal directionality merely from observing how two variables change over time; they interpreted Y changing without a change in X as evidence that Y does not influence X. Both of these strategies make sense if one believes the variables to be temporally dependent. We discuss the implications of these results for interpreting previous findings. More broadly, given that many real‐world environments are characterized by temporal dependency, these results suggest strategies that children may use to learn the causal structure of their environments.     

Valuing intervention and observation

Understanding causal relations is fundamental to effective action but causal data can be confounded. We examined the value that participants placed on data derived from a hypothetical intervention or observation. Our materials involved a possible cause ("bottled water"), a possible confound ("food"), and a context ("a restaurant"). We supposed that participants seek to draw as specific a causal inference as possible from presented data and value information sources more highly that allow them to do so. On this basis, we predicted that in circumstances where an intervention removed the confounding causal factor but observation did not, participants would prefer data derived from an intervention when the possible cause was present (the bottled water was drunk) but show the reverse preference when the possible cause was absent (the bottled water was not drunk). Experiment 1 confirmed this prediction. Using a between-subjects design, Experiment 2 tested for a difference in confidence in causal judgements given identical data, including data on the confound, as a function of method of data collection (intervention or observation). There was no significant difference in confidence ratings between the two methods but confidence ratings were sensitive to the probability of an effect (illness) given the cause. Using a within-subjects design, Experiment 3 revealed systematic individual differences in preference for the two methods. Participants were divided between those who considered intervention more confounded and those who considered observation more confounded. Our experiments point to the subtleties of participants' evaluation of data from studies of human beings.     

Categorization as causal reasoning⋆

A theory of categorization is presented in which knowledge of causal relationships between category features is represented in terms of asymmetric and probabilistic causal mechanisms. According to causal‐model theory, objects are classified as category members to the extent they are likely to have been generated or produced by those mechanisms. The empirical results confirmed that participants rated exemplars good category members to the extent their features manifested the expectations that causal knowledge induces, such as correlations between feature pairs that are directly connected by causal relationships. These expectations also included sensitivity to higher‐order feature interactions that emerge from the asymmetries inherent in causal relationships. Quantitative fits of causal‐model theory were superior to those obtained with extensions to traditional similarity‐based models that represent causal knowledge either as higher‐order relational features or “prior exemplars” stored in memory.     

Category transfer in sequential causal learning: the unbroken mechanism hypothesis

The goal of the present set of studies is to explore the boundary conditions of category transfer in causal learning. Previous research has shown that people are capable of inducing categories based on causal learning input, and they often transfer these categories to new causal learning tasks. However, occasionally learners abandon the learned categories and induce new ones. Whereas previously it has been argued that transfer is only observed with essentialist categories in which the hidden properties are causally relevant for the target effect in the transfer relation, we here propose an alternative explanation, the unbroken mechanism hypothesis. This hypothesis claims that categories are transferred from a previously learned causal relation to a new causal relation when learners assume a causal mechanism linking the two relations that is continuous and unbroken. The findings of two causal learning experiments support the unbroken mechanism hypothesis.     

Are People Successful at Learning Sequences of Actions on a Perceptual Matching Task?

We report the results of an experiment in which human subjects were trained to perform a perceptual matching task. Subjects were asked to manipulate comparison objects until they matched target objects using the fewest manipulations possible. An unusual feature of the experimental task is that efficient performance requires an understanding of the hidden or latent causal structure governing the relationships between actions and perceptual outcomes. We use two benchmarks to evaluate the quality of subjects' learning. One benchmark is based on optimal performance as calculated by a dynamic programming procedure. The other is based on an adaptive computational agent that uses a reinforcement-learning method known as Q-learning to learn to perform the task. Our analyses suggest that subjects were successful learners. In particular, they learned to perform the perceptual matching task in a near-optimal manner (i.e., using a small number of manipulations) at the end of training. Subjects were able to achieve near-optimal performance because they learned, at least partially, the causal structure underlying the task. In addition, subjects' performances were broadly consistent with those of model-based reinforcement-learning agents that built and used internal models of how their actions influenced the external environment. We hypothesize that people will achieve near-optimal performances on tasks requiring sequences of action-especially sensorimotor tasks with underlying latent causal structures-when they can detect the effects of their actions on the environment, and when they can represent and reason about these effects using an internal mental model.     

Extinction in human learning and memory

In two experiments, participants were given extinction training in a human causal learning task. In both experiments, three critical experimental cues were paired with different outcomes in a first phase of training and were then extinguished in a second phase. Three control cues were given the same treatment in the first phase of training, but were not then presented in the second phase. Participants' ability to correctly identify the outcome with which each cue had been paired in the first phase was lower for extinguished than for control cues. Causal attributions to the extinguished cues were also lower than those to the control cues, a difference that correlated with outcome memory. These data are consistent with the idea that extinction in causal judgement is due, at least in part, to a failure to remember the cue–outcome relationship encoded in the first phase of training.     

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.     

The role of preschoolers' social understanding in evaluating the informativeness of causal interventions

Preschoolers use information from interventions, namely intentional actions, to make causal inferences. We asked whether children consider some interventions to be more informative than others based on two components of an actor’s knowledge state: whether an actor possesses causal knowledge, and whether an actor is allowed to use their knowledge in a given situation. Three- and four-year-olds saw a novel toy that activated in the presence of certain objects. Two actors, one knowledgeable about the toy and one ignorant, each tried to activate the toy with an object. In Experiment 1, either the actors chose objects or the child chose for them. In Experiment 2, the actors chose objects blindfolded. Objects were always placed on the toy simultaneously, and thus were equally associated with the effect. Preschoolers’ causal inferences favored the knowledgeable actor’s object only when he was allowed to choose it (Experiment 1). Thus, children consider both personal and situational constraints on knowledge when evaluating the informativeness of causal interventions.