The Paradox of Time in Dynamic Causal Systems.

Recent work has shown that people use temporal information including order, delay, and variability to infer causality between events. In this study, we build on this work by investigating the role of time in dynamic systems, where causes take continuous values and also continually influence their effects. Recent studies of learning in these systems explored short interactions in a setting with rapidly evolving dynamics and modeled people as relying on simpler, resource-limited strategies to grapple with the stream of information. A natural question that arises from such an account is whether interacting with systems that unfold more slowly might reduce the systematic errors that result from these strategies. Paradoxically, we find that slowing the task indeed reduced the frequency of one type of error, albeit at the cost of increasing the overall error rate. To explain these results we posit that human learners analyze continuous dynamics into discrete events and use the observed relationships between events to draw conclusions about causal structure. We formalize this intuition in terms of a novel Causal Event Abstraction model and show that this model indeed captures the observed pattern of errors. We comment on the implications these results have for causal cognition.

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 Structure Learning in Continuous Systems.

Real causal systems are complicated. Despite this, causal learning research has traditionally emphasized how causal relations can be induced on the basis of idealized events, i.e., those that have been mapped to binary variables and abstracted from time. For example, participants may be asked to assess the efficacy of a headache-relief pill on the basis of multiple patients who take the pill (or not) and find their headache relieved (or not). In contrast, the current study examines learning via interactions with continuous dynamic systems, systems that include continuous variables that interact over time (and that can be continuously observed in real time by the learner). To explore such systems, we develop a new framework that represents a causal system as a network of stationary Gauss-Markov ("Ornstein-Uhlenbeck") processes and show how such OU networks can express complex dynamic phenomena, such as feedback loops and oscillations. To assess adult's abilities to learn such systems, we conducted an experiment in which participants were asked to identify the causal relationships of a number of OU networks, potentially carrying out multiple, temporally-extended interventions. We compared their judgments to a normative model for learning OU networks as well as a range of alternative and heuristic learning models from the literature. We found that, although participants exhibited substantial learning of such systems, they committed certain systematic errors. These successes and failures were best accounted for by a model that describes people as focusing on pairs of variables, rather than evaluating the evidence with respect to the full space of possible structural models. We argue that our approach provides both a principled framework for exploring the space of dynamic learning environments as well as new algorithmic insights into how people interact successfully with a continuous causal world.

Beyond Markov: Accounting for independence violations in causal reasoning.

Although many theories of causal cognition are based on causal graphical models, a key property of such models-the independence relations stipulated by the Markov condition-is routinely violated by human reasoners. This article presents three new accounts of those independence violations, accounts that share the assumption that people's understanding of the correlational structure of data generated from a causal graph differs from that stipulated by causal graphical model framework. To distinguish these models, experiments assessed how people reason with causal graphs that are larger than those tested in previous studies. A traditional common cause network (Y1←X→Y2) was extended so that the effects themselves had effects (Z1←Y1←X→Y2→Z2). A traditional common effect network (Y1→X←Y2) was extended so that the causes themselves had causes (Z1→Y1→X←Y2←Z2). Subjects' inferences were most consistent with the beta-Q model in which consistent states of the world-those in which variables are either mostly all present or mostly all absent-are viewed as more probable than stipulated by the causal graphical model framework. Substantial variability in subjects' inferences was also observed, with the result that substantial minorities of subjects were best fit by one of the other models (the dual prototype or a leaky gate models). The discrepancy between normative and human causal cognition stipulated by these models is foundational in the sense that they locate the error not in people's causal reasoning but rather in their causal representations. As a result, they are applicable to any cognitive theory grounded in causal graphical models, including theories of analogy, learning, explanation, categorization, decision-making, and counterfactual reasoning. Preliminary evidence that independence violations indeed generalize to other judgment types is presented.

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.

Reasoning With Causal Cycles.

This article assesses how people reason with categories whose features are related in causal cycles. Whereas models based on causal graphical models (CGMs) have enjoyed success modeling category-based judgments as well as a number of other cognitive phenomena, CGMs are only able to represent causal structures that are acyclic. A number of new formalisms that allow cycles are introduced and evaluated. Dynamic Bayesian networks (DBNs) represent cycles by unfolding them over time. Chain graphs augment CGMs by allowing the presence of undirected links that model feedback relations between variables. Unfolded chain graphs are chain graphs that unfold over time. An existing model of causal cycles (alpha centrality) is also evaluated. Four experiments in which subjects reason about categories with cyclically related features provided evidence against DBNs and alpha centrality and for the two types of chain graphs. Chain graphs-a mechanism for representing the equilibrium distribution of a dynamic system-may thus be good candidates for modeling how people reason causally with complex systems. Applications of chain graphs to areas of cognition other than category-based judgments are discussed.

Strategies to intervene on causal systems are adaptively selected.

How do people choose interventions to learn about causal systems? Here, we considered two possibilities. First, we test an information sampling model, information gain, which values interventions that can discriminate between a learner's hypotheses (i.e. possible causal structures). We compare this discriminatory model to a positive testing strategy that instead aims to confirm individual hypotheses. Experiment 1 shows that individual behavior is described best by a mixture of these two alternatives. In Experiment 2 we find that people are able to adaptively alter their behavior and adopt the discriminatory model more often after experiencing that the confirmatory strategy leads to a subjective performance decrement. In Experiment 3, time pressure leads to the opposite effect of inducing a change towards the simpler positive testing strategy. These findings suggest that there is no single strategy that describes how intervention decisions are made. Instead, people select strategies in an adaptive fashion that trades off their expected performance and cognitive effort.

The role of functional form in causal-based categorization.

Two experiments tested how the functional form of the causal relations that link features of categories affects category-based inferences. Whereas independent causes can each bring about an effect by themselves, conjunctive causes all need to be present for an effect to occur. The causal model view of category representations is extended to include a representation of conjunctive causes and then predictions are derived for 3 category-based judgments: classification, conditional feature predictions, and feature likelihoods. Experiment 1 revealed that subjects' judgments on all 3 tasks were not only sensitive to whether causes were independent or conjunctive but also conformed to the causal model predictions, albeit with an important exception. Experiment 2 revealed that inferences with independent and conjunctive causes were affected quite differently by a manipulation of the strengths of the causal relations (and in the manner predicted by the model). This is the 1st study to show how a single representation of a category's causal knowledge can account for 3 category-based judgments with the same model parameters. Other models of causal-based categories are unable to account for the observed effects.

The role of causal models in multiple judgments under uncertainty.

Two studies examined a novel prediction of the causal Bayes net approach to judgments under uncertainty, namely that causal knowledge affects the interpretation of statistical evidence obtained over multiple observations. Participants estimated the conditional probability of an uncertain event (breast cancer) given information about the base rate, hit rate (probability of a positive mammogram given cancer) and false positive rate (probability of a positive mammogram in the absence of cancer). Conditional probability estimates were made after observing one or two positive mammograms. Participants exhibited a causal stability effect: there was a smaller increase in estimates of the probability of cancer over multiple positive mammograms when a causal explanation of false positives was provided. This was the case when the judgments were made by different participants (Experiment 1) or by the same participants (Experiment 2). These results show that identical patterns of observed events can lead to different estimates of event probability depending on beliefs about the generative causes of the observations.

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.

Differences in the weighting and choice of evidence for plausible versus implausible causes.

Individuals have difficulty changing their causal beliefs in light of contradictory evidence. We hypothesized that this difficulty arises because people facing implausible causes give greater consideration to causal alternatives, which, because of their use of a positive test strategy, leads to differential weighting of contingency evidence. Across 4 experiments, participants learned about plausible or implausible causes of outcomes. Additionally, we assessed the effects of participants' ability to think of alternative causes of the outcomes. Participants either saw complete frequency information (Experiments 1 and 2) or chose what information to see (Experiments 3 and 4). Consistent with the positive test account, participants given implausible causes were more likely to inquire about the occurrence of the outcome in the absence of the cause (Experiments 3 and 4) than those given plausible causes. Furthermore, they gave less weight to Cells A and B in a 2 × 2 contingency table and gave either equal or less weight to Cells C and D (Experiments 1 and 2). These effects were inconsistently modified by participants' ability to consider alternative causes of the outcome. The total of the observed effects are not predicted by either dominant models of normative causal inference or by the particular positive test account proposed here, but they may be commensurate with a more broadly construed positive test account.

The hazards of explanation: overgeneralization in the face of exceptions.

Seeking explanations is central to science, education, and everyday thinking, and prompting learners to explain is often beneficial. Nonetheless, in 2 category learning experiments across artifact and social domains, we demonstrate that the very properties of explanation that support learning can impair learning by fostering overgeneralizations. We find that explaining encourages learners to seek broad patterns, hindering learning when patterns involve exceptions. By revealing how effects of explanation depend on the structure of what is being learned, these experiments simultaneously demonstrate the hazards of explaining and provide evidence for why explaining is so often beneficial. For better or for worse, explaining recruits the remarkable human capacity to seek underlying patterns that go beyond individual observations.

Functions in biological kind classification.

Biological traits that serve functions, such as a zebra's coloration (for camouflage) or a kangaroo's tail (for balance), seem to have a special role in conceptual representations for biological kinds. In five experiments, we investigate whether and why functional features are privileged in biological kind classification. Experiment 1 experimentally manipulates whether a feature serves a function and finds that functional features are judged more diagnostic of category membership as well as more likely to have a deep evolutionary history, be frequent in the current population, and persist in future populations. Experiments 2-5 reveal that these inferences about history, frequency, and persistence account for nearly all the effect of function on classification. We conclude that functional features are privileged because their relationship with the kind is viewed as stable over time and thus as especially well suited for establishing category membership, with implications for theories of classification and folk biological understanding.

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.

How prior knowledge affects selective attention during category learning: an eyetracking study.

Research has shown that category learning is affected by (a) attention, which selects which aspects of stimuli are available for further processing, and (b) the existing semantic knowledge that learners bring to the task. However, little is known about how knowledge affects what is attended. Using eyetracking, we found that (a) knowledge indeed changes what features are attended, with knowledge-relevant features being fixated more often than irrelevant ones, (b) this effect was not due to an initial attentional bias toward relevant dimensions but rather emerged gradually as a result of observing category members, and (c) this effect grew even after a learning criterion was reached, that is, despite the absence of negative feedback. We argue that models of knowledge-based learning will remain incomplete until they specify mechanisms that dynamically select prior knowledge in response to observed category members and which then directs attention to knowledge-relevant dimensions and away from irrelevant ones.

Causal status and coherence in causal-based categorization.

Research has documented two effects of interfeature causal knowledge on classification. A causal status effect occurs when features that are causes are more important to category membership than their effects. A coherence effect occurs when combinations of features that are consistent with causal laws provide additional evidence of category membership. In this study, we found that stronger causal relations led to a weaker causal status effect and a stronger coherence effect (Experiment 1), that weaker alternative causes led to stronger causal status and coherence effects (Experiment 2), and that "essentialized" categories led to a stronger causal status effect (Experiment 3), albeit only for probabilistic causal links (Experiment 4). In addition, the causal status effect was mediated by features' subjective category validity, the probability they occur in category members. These findings were consistent with a generative model of categorization but inconsistent with an alternative model.

The costs of supervised classification: The effect of learning task on conceptual flexibility.

Research has shown that learning a concept via standard supervised classification leads to a focus on diagnostic features, whereas learning by inferring missing features promotes the acquisition of within-category information. Accordingly, we predicted that classification learning would produce a deficit in people's ability to draw novel contrasts--distinctions that were not part of training--compared with feature inference learning. Two experiments confirmed that classification learners were at a disadvantage at making novel distinctions. Eye movement data indicated that this conceptual inflexibility was due to (a) a narrower attention profile that reduces the encoding of many category features and (b) learned inattention that inhibits the reallocation of attention to newly relevant information. Implications of these costs of supervised classification learning for views of conceptual structure are discussed.

Classification as diagnostic reasoning.

An ongoing goal in the field of categorization has been to determine how objects' features provide evidence of membership in one category versus another. Well-known findings include that feature diagnosticity is a function of how often the feature appears in category members versus nonmembers, their perceptual salience, how features are used in support of inferences, and how observable features are related to other observable features. We tested how diagnosticity is affected by causal relations between observable and unobserved features. Consistent with our view of classification as diagnostic reasoning, we found that observable features are more diagnostic to the extent that they are caused by underlying features that define category membership, because the presence of the latter can be (causally) inferred from the former. Implications of these results for current views of conceptual structure and models of categorization are discussed.

Causal-based property generalization.

A central question in cognitive research concerns how new properties are generalized to categories. This article introduces a model of how generalizations involve a process of causal inference in which people estimate the likely presence of the new property in individual category exemplars and then the prevalence of the property among all category members. Evidence in favor of this causal-based generalization (CBG) view included effects of an existing feature's base rate (Experiment 1), the direction of the causal relations (Experiments 2 and 4), the number of those relations (Experiment 3), and the distribution of features among category members (Experiments 4 and 5). The results provided no support for an alternative view that generalizations are promoted by the centrality of the to-be-generalized feature. However, there was evidence that a minority of participants based their judgments on simpler associative reasoning processes.

Prior knowledge and exemplar frequency.

New concepts can be learned by statistical associations, as well as by relevant existing knowledge. We examined the interaction of these two processes by manipulating exemplar frequency and thematic knowledge and considering their interaction through computational modeling. Exemplar frequency affects category learning, with high-frequency items learned more quickly than low-frequency items, and prior knowledge usually speeds category learning. In two experiments in which both of these factors were manipulated, we found that the effects of frequency are greatly reduced when stimulus features are linked by thematic prior knowledge and that frequency effects on single stimulus features can actually be reversed by knowledge. We account for these results with the knowledge resonance model of category learning (Rehder & Murphy, 2003) and conclude that prior knowledge may change representations so that empirical effects, such as those caused by frequency manipulations, are modulated.