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.     

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.     

Uncovering deterministic causal structures: a Boolean approach

While standard procedures of causal reasoning as procedures analyzing causal Bayesian networks are custom-built for (non-deterministic) probabilistic structures, this paper introduces a Boolean procedure that uncovers deterministic causal structures. Contrary to existing Boolean methodologies, the procedure advanced here successfully analyzes structures of arbitrary complexity. It roughly involves three parts: first, deterministic dependencies are identified in the data; second, these dependencies are suitably minimalized in order to eliminate redundancies; and third, one or—in case of ambiguities—more than one causal structure is assigned to the minimalized deterministic dependencies.     

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.     

Cognitive biases in human causal learning

The main aim of this work was to look for cognitive biases in human inference of causal relationships in order to emphasize the psychological processes that modulate causal learning. From the effect of the judgment frequency, this work presents subsequent research on cue competition (overshadowing, blocking, and super-conditioning effects) showing that the strength of prior beliefs and new evidence based upon covariation computation contributes additively to predict causal judgments, whereas the balance between the reliability of both, beliefs and covariation knowledge, modulates their relative weight. New findings also showed "inattentional blindness" for negative or preventative causal relationships but not for positive or generative ones, due to failure in codifying and retrieving the necessary information for its computation. Overall results unveil the need of three hierarchical levels of a whole architecture for human causal learning: the lower one, responsible for codifying the events during the task; the second one, computing the retrieved information; finally, the higher level, integrating this evidence with previous causal knowledge. In summary, whereas current theoretical frameworks on causal inference and decision-making usually focused either on causal beliefs or covariation information, the present work shows how both are required to be able to explain the complexity and flexibility involved in human causal learning.     

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.     

The role of mechanism and covariation information in causal belief updating

The present study is aimed at identifying how prior causal beliefs and covariation information contribute to belief updating when evidence, either compatible or contradictory with those beliefs, is provided. Participants were presented with a cover story with which it was intended to activate or generate a causal belief. Variables related to the prior belief (the type of information, the strength of the cause-effect causal link, and how confident the participant was that the link existed) were assessed. Subsequently, participants were presented with covariational information and were asked to update their beliefs in light of the new evidence. Information reliability, prior belief's causal influence magnitude, and the cause-effect level of contingency portrayed by the new information--but not the type of the prior belief--are shown to directly determine belief updating.     

Inferring action structure and causal relationships in continuous sequences of human action

In the real world, causal variables do not come pre-identified or occur in isolation, but instead are embedded within a continuous temporal stream of events. A challenge faced by both human learners and machine learning algorithms is identifying subsequences that correspond to the appropriate variables for causal inference. A specific instance of this problem is action segmentation: dividing a sequence of observed behavior into meaningful actions, and determining which of those actions lead to effects in the world. Here we present a Bayesian analysis of how statistical and causal cues to segmentation should optimally be combined, as well as four experiments investigating human action segmentation and causal inference. We find that both people and our model are sensitive to statistical regularities and causal structure in continuous action, and are able to combine these sources of information in order to correctly infer both causal relationships and segmentation boundaries.     

Rationales in children’s causal learning from others’ actions

Shown commensurate actions and information by an adult, preschoolers’ causal learning was influenced by the pedagogical context in which these actions occurred. Four-year-olds who were provided with a reason for an experimenter’s action relevant to learning causal structure showed more accurate causal learning than children exposed to the same action and data accompanied by an inappropriate rationale or accompanied by no explanatory information. These results suggest that children’s accurate causal learning is influenced by contextual factors that specify the instructional value of others’ actions.     

Causal judgements about two causal candidates: Accounting for occurrences,estimating strength,and the importance of interaction judgements

When two possible causes of an outcome are under consideration, contingency information concerns each possible combination of presence and absence of the two causes with occurrences and nonoccurrences of the outcome. White (2008) proposed that such judgements could be predicted by a weighted averaging model integrating these kinds of contingency information. The weights in the model are derived from the hypothesis that causal judgements seek to meet two main aims, accounting for occurrences of the outcome and estimating the strengths of the causes. Here it is shown that the model can explain many but not all relevant published findings. The remainder can be explained by reasoning about interactions between the two causes, by scenario-specific effects, and by variations in cell weight depending on quantity of available information. An experiment is reported that supports this argument. The review and experimental results support the case for a cognitive model of causal judgement in which different kinds of contingency information are utilised to satisfy particular aims of the judgement process.     

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.     

Causal powers and preventers: An explanatory account of cue interaction effects in human causal judgement

According to the causal powers theory, all causal relations are understood in terms of causal powers of one thing producing an effect by acting on liability of another thing. Powers can vary in strength, and their operation also depends on the presence of preventers. When an effect occurs, there is a need to account for the occurrence by assigning sufficient strength to produce it to its possible causes. Contingency information is used to estimate strengths of powers and preventers and the extent to which they account for occurrences and nonoccurrences of the outcome. People make causal judgements from contingency information by processes of inference that interpret evidence in terms of this fundamental understanding. From this account it is possible to derive a computational model based on a common set of principles that involve estimating strengths, using these estimates to interpret ambiguous information, and integrating the resultant evidence in a weighted averaging model. It is shown that the model predicts cue interaction effects in human causal judgement, including forward and backward blocking, second and third order backward blocking, forward and backward conditioned inhibition, recovery from overshadowing, superlearning, and backward superlearning.     

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.     

Children’s causal inferences from indirect evidence: Backwards blocking and Bayesian reasoning in preschoolers

Previous research suggests that children can infer causal relations from patterns of events. However, what appear to be cases of causal inference may simply reduce to children recognizing relevant associations among events, and responding based on those associations. To examine this claim, in Experiments 1 and 2, children were introduced to a “blicket detector,” a machine that lit up and played music when certain objects were placed upon it. Children observed patterns of contingency between objects and the machine’s activation that required them to use indirect evidence to make causal inferences. Critically, associative models either made no predictions, or made incorrect predictions about these inferences. In general, children were able to make these inferences, but some developmental differences between 3- and 4-year-olds were found. We suggest that children’s causal inferences are not based on recognizing associations, but rather that children develop a mechanism for Bayesian structure learning. Experiment 3 explicitly tests a prediction of this account. Children were asked to make an inference about ambiguous data based on the base rate of certain events occurring. Four-year-olds, but not 3-year-olds were able to make this inference.     

Semantic emphasis in causal sentences

A shift in emphasis can change the truth-value of a singular causal sentence. This poses a challenge to the view that singular sentences predicate a relation. I argue that emphasized causal sentences conjoin predication of a causal relation between events with predication of a relation of causal relevance between states of affairs (or perhaps facts). This is superior to the treatments of such sentences offered by Achinstein, Dretske, Kim, Sanford, Bennett, and Levin. My proposal affords clarity regarding logical structure, at least at a certain level of detail. It makes the relation between the content of an emphasized causal sentence and the unemphasized version clear. It answers some questions about the ontological requirements of the truth of emphasized causal sentences, without introducing new entities (as do some other accounts) or unacceptable consequences for identity and individuation of events.     

Diagnostic causal reasoning with verbal information

In diagnostic causal reasoning, the goal is to infer the probability of causes from one or multiple observed effects. Typically, studies investigating such tasks provide subjects with precise quantitative information regarding the strength of the relations between causes and effects or sample data from which the relevant quantities can be learned. By contrast, we sought to examine people’s inferences when causal information is communicated through qualitative, rather vague verbal expressions (e.g., “X occasionally causes A”). We conducted three experiments using a sequential diagnostic inference task, where multiple pieces of evidence were obtained one after the other. Quantitative predictions of different probabilistic models were derived using the numerical equivalents of the verbal terms, taken from an unrelated study with different subjects. We present a novel Bayesian model that allows for incorporating the temporal weighting of information in sequential diagnostic reasoning, which can be used to model both primacy and recency effects. On the basis of 19,848 judgments from 292 subjects, we found a remarkably close correspondence between the diagnostic inferences made by subjects who received only verbal information and those of a matched control group to whom information was presented numerically. Whether information was conveyed through verbal terms or numerical estimates, diagnostic judgments closely resembled the posterior probabilities entailed by the causes’ prior probabilities and the effects’ likelihoods. We observed interindividual differences regarding the temporal weighting of evidence in sequential diagnostic reasoning. Our work provides pathways for investigating judgment and decision making with verbal information within a computational modeling framework.     

Models of causation and the semantics of causal verbs

This research examines the relationship between the concept of CAUSE as it is characterized in psychological models of causation and the meaning of causal verbs, such as the verb cause itself. According to focal set models of causation (; ), the concept of CAUSE should be more similar to the concepts of ENABLE and PREVENT than either is to each other. According to a model based on theory of force dynamics, the force dynamic model, the concepts of CAUSE, ENABLE, and PREVENT should be roughly equally similar to one another. The relationship between these predictions and the meaning of causal verbs was examined by having participants sort causal verbs and rate them with respect to the dimensions specified by the two models. The results from five experiments indicated that the force dynamic model provides a better account of the meaning of causal verbs than do focal set models of causation. Implications for causal inference and induction are discussed.     

Time and order effects on causal learning

Five experiments were conducted to explore trial order and retention interval effects upon causal predictive judgments. Experiment 1 found that participants show a strong effect of trial order when a stimulus was sequentially paired with two different outcomes compared to a condition where both outcomes were presented intermixed. Experiment 2 found that a 48-h retention interval eliminates the trial order effect, so that participants gave a global judgment about the relationship between the stimulus and the two outcomes equivalent to the one given by participants that received the two phases intermixed. This result was replicated in Experiment 3 in a situation in which the probability of the outcome in the presence of the cue was changed from .5 for both outcomes (Experiments 1, 2, 4, and 5) to .75 and .25 for outcomes 1 and 2, respectively. Experiment 4 found that retention intervals ranging from 45 min to 48 h eliminated the trial order effect similarly. Experiment 5 found that a 10-min retention interval replicated the effect of time upon sequential training found in precedent experiments, regardless of whether participants remained within the laboratory during the retention interval or spent it outside. The combined results of this experimental series suggest that retention intervals reduce retroactive interference in causal learning by allowing participants to use all the information presented across phases, rather than differentially increasing or decreasing retrieval of information about each of them.