Inferences about unobserved causes in human contingency learning

Estimates of the causal efficacy of an event need to take into account the possible presence and influence of other unobserved causes that might have contributed to the occurrence of the effect. Current theoretical approaches deal differently with this problem. Associative theories assume that at least one unobserved cause is always present. In contrast, causal Bayes net theories (including Power PC theory) hypothesize that unobserved causes may be present or absent. These theories generally assume independence of different causes of the same event, which greatly simplifies modelling learning and inference. In two experiments participants were requested to learn about the causal relation between a single cause and an effect by observing their co-occurrence (Experiment 1) or by actively intervening in the cause (Experiment 2). Participants' assumptions about the presence of an unobserved cause were assessed either after each learning trial or at the end of the learning phase. The results show an interesting dissociation. Whereas there was a tendency to assume interdependence of the causes in the online judgements during learning, the final judgements tended to be more in the direction of an independence assumption. Possible explanations and implications of these findings are discussed.     

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.     

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.     

Inferring interventional predictions from observational learning data

Previous research has shown that people are capable of deriving correct predictions for previously unseen actions from passive observations of causal systems (Waldmann & Hagmayer, 2005). However, these studies were limited, since learning data were presented as tabulated data only, which may have turned the task more into a reasoning rather than a learning task. In two experiments, we therefore presented learners with trial-by-trial observational learning input referring to a complex causal model consisting of four events. To test the robustness of the capacity to derive correct observational and interventional inferences, we pitted causal order against the temporal order of learning events. The results show that people are, in principle, capable of deriving correct predictions after purely observational trial-by-trial learning, even with relatively complex causal models. However, conflicting temporal information can impair performance, particularly when the inferences require taking alternative causal pathways into account.     

其它可能原因的呈现方式在因果判断中的作用

研究使用不同方式呈现了其它可能原因,研究了这种不同的呈现方式对被试使用共变信息和经验信息进行因果判断的影响。研究结果表明:(1)其它可能原因的呈现方式对于因果判断有着一定的影响。当这一信息在待判断原因与结果的共变中出现、且永远存在时,被试会排除这一其它可能原因的作用,从而增强判断的信心;(2)当其它可能原因出现于待判断原因与结果的共变中、且永远存在时,被试会在一定程度上忽视经验信息的作用,更多地依赖共变信息做出判断。     

Pretense,Counterfactuals, and Bayesian Causal Models: Why What Is Not Real Really Matters

Young children spend a large portion of their time pretending about non‐real situations. Why? We answer this question by using the framework of Bayesian causal models to argue that pretending and counterfactual reasoning engage the same component cognitive abilities: disengaging with current reality, making inferences about an alternative representation of reality, and keeping this representation separate from reality. In turn, according to causal models accounts, counterfactual reasoning is a crucial tool that children need to plan for the future and learn about the world. Both planning with causal models and learning about them require the ability to create false premises and generate conclusions from these premises. We argue that pretending allows children to practice these important cognitive skills. We also consider the prevalence of unrealistic scenarios in children's play and explain how they can be useful in learning, despite appearances to the contrary.     

An Inferential Model of Scientific Understanding

In this article I argue that two current accounts of scientific understanding are incorrect and I propose an alternative theory. My new account draws on recent research in cognitive psychology which reveals the importance of making causal and logical inferences on the basis of incoming information. To understand a phenomenon we need to make particular kinds of inferences concerning the explanations we are given. Specifically, we come to understand a phenomenon scientifically by developing mental models that incorporate the correct causal and logical properties responsible for the causes or logical properties of the phenomenon being explained.     

The effect of causal knowledge on judgments of the likelihood of unknown features

People frequently infer unknown aspects of an entity based on their knowledge about that entity. The current study reports a novel phenomenon, an inductive bias people have in making such inferences. Upon learning that one symptom causes another in a person, both undergraduate students (Experiment 1) and clinicians (Experiment 2) judged that an unknown feature associated with the cause-symptom was more likely to be present in that person than an unknown feature associated with the effect-symptom. Thus, these findings suggest a specific mechanism in which causal explanations influence one’s representation of and inferences about an entity. Implications for clinical reasoning and associative models of conceptual knowledge are discussed.     

Structure and strength in causal induction

We present a framework for the rational analysis of elemental causal induction-learning about the existence of a relationship between a single cause and effect-based upon causal graphical models. This framework makes precise the distinction between causal structure and causal strength: the difference between asking whether a causal relationship exists and asking how strong that causal relationship might be. We show that two leading rational models of elemental causal induction, DeltaP and causal power, both estimate causal strength, and we introduce a new rational model, causal support, that assesses causal structure. Causal support predicts several key phenomena of causal induction that cannot be accounted for by other rational models, which we explore through a series of experiments. These phenomena include the complex interaction between DeltaP and the base-rate probability of the effect in the absence of the cause, sample size effects, inferences from incomplete contingency tables, and causal learning from rates. Causal support also provides a better account of a number of existing datasets than either DeltaP or causal power.     

Individual differences in causal learning and decision making

In judgment and decision making tasks, people tend to neglect the overall frequency of base-rates when they estimate the probability of an event; this is known as the base-rate fallacy. In causal learning, despite people's accuracy at judging causal strength according to one or other normative model (i.e., Power PC, DeltaP), they tend to misperceive base-rate information (e.g., the cause density effect). The present study investigates the relationship between causal learning and decision making by asking whether people weight base-rate information in the same way when estimating causal strength and when making judgments or inferences about the likelihood of an event. The results suggest that people differ according to the weight they place on base-rate information, but the way individuals do this is consistent across causal and decision making tasks. We interpret the results as reflecting a tendency to differentially weight base-rate information which generalizes to a variety of tasks. Additionally, this study provides evidence that causal learning and decision making share some component processes.     

Identifying expectations about the strength of causal relationships

When we try to identify causal relationships, how strong do we expect that relationship to be? Bayesian models of causal induction rely on assumptions regarding people’s a priori beliefs about causal systems, with recent research focusing on people’s expectations about the strength of causes. These expectations are expressed in terms of prior probability distributions. While proposals about the form of such prior distributions have been made previously, many different distributions are possible, making it difficult to test such proposals exhaustively. In Experiment 1 we used iterated learning—a method in which participants make inferences about data generated based on their own responses in previous trials—to estimate participants’ prior beliefs about the strengths of causes. This method produced estimated prior distributions that were quite different from those previously proposed in the literature. Experiment 2 collected a large set of human judgments on the strength of causal relationships to be used as a benchmark for evaluating different models, using stimuli that cover a wider and more systematic set of contingencies than previous research. Using these judgments, we evaluated the predictions of various Bayesian models. The Bayesian model with priors estimated via iterated learning compared favorably against the others. Experiment 3 estimated participants’ prior beliefs concerning different causal systems, revealing key similarities in their expectations across diverse scenarios.     

An integrated account of generalization across objects and features

Humans routinely make inductive generalizations about unobserved features of objects. Previous accounts of inductive reasoning often focus on inferences about a single object or feature: accounts of causal reasoning often focus on a single object with one or more unobserved features, and accounts of property induction often focus on a single feature that is unobserved for one or more objects. We explore problems where people must make inferences about multiple objects and features, and propose that people solve these problems by integrating knowledge about features with knowledge about objects. We evaluate three computational methods for integrating multiple systems of knowledge: the output combination approach combines the outputs produced by these systems, the distribution combination approach combines the probability distributions captured by these systems, and the structure combination approach combines a graph structure over features with a graph structure over objects. Three experiments explore problems where participants make inferences that draw on causal relationships between features and taxonomic relationships between animals, and we find that the structure combination approach provides the best account of our data.     

Theory-based Bayesian models of inductive learning and reasoning

Inductive inference allows humans to make powerful generalizations from sparse data when learning about word meanings, unobserved properties, causal relationships, and many other aspects of the world. Traditional accounts of induction emphasize either the power of statistical learning, or the importance of strong constraints from structured domain knowledge, intuitive theories or schemas. We argue that both components are necessary to explain the nature, use and acquisition of human knowledge, and we introduce a theory-based Bayesian framework for modeling inductive learning and reasoning as statistical inferences over structured knowledge representations.     

A causal model theory of the meaning of cause, enable, and prevent

The verbs cause , enable , and prevent express beliefs about the way the world works. We offer a theory of their meaning in terms of the structure of those beliefs expressed using qualitative properties of causal models, a graphical framework for representing causal structure. We propose that these verbs refer to a causal model relevant to a discourse and that "A causes B" expresses the belief that the causal model includes a link from A to B. "A enables/allows B" entails that the model includes a link from A to B, that A represents a category of events necessary for B, and that an alternative cause of B exists. "A prevents B" entails that the model includes a link from A to B and that A reduces the likelihood of B. This theory is able to account for the results of four experiments as well as a variety of existing data on human reasoning.     

其它可能原因对于因果共变信息作用的影响

研究使用相继呈现信息的方法控制了被试获得信息的顺序,将其它可能原因在因果判断过程中所起到的作用分离了出来,并按照其对不同共变信息的影响进行了分析。研究结果表明：(1)其它可能原因会影响到被试利用因果共变信息而进行的因果推断。(2)其它可能原因与待判断原因共同存在的程度在很大程度上影响着其它可能原因所起到的作用。(3)其它可能原因对于不同共变信息的影响有着明显的差别。     

The influence of the number of relevant causes on the processing of covariation information in causal reasoning

Research on causal reasoning has focused on the influence of covariation between candidate causes and effects on causal judgments. We suggest that the type of covariation information to which people attend is affected by the task being performed. For this, we manipulated the test questions for the evaluation of contingency information and observed its influence on both contingency learning and subsequent causal selections. When people select one cause related to an effect, they focus on conditional contingencies assuming the absence of alternative causes. When people select two causes related to an effect, they focus on conditional contingencies assuming the presence of alternative causes. We demonstrated this use of contingency information in four experiments.     

Time and Singular Causation—A Computational Model

Causal queries about singular cases, which inquire whether specific events were causally connected, are prevalent in daily life and important in professional disciplines such as the law, medicine, or engineering. Because causal links cannot be directly observed, singular causation judgments require an assessment of whether a co-occurrence of two events c and e was causal or simply coincidental. How can this decision be made? Building on previous work by Cheng and Novick (2005) and Stephan and Waldmann (2018), we propose a computational model that combines information about the causal strengths of the potential causes with information about their temporal relations to derive answers to singular causation queries. The relative causal strengths of the potential cause factors are relevant because weak causes are more likely to fail to generate effects than strong causes. But even a strong cause factor does not necessarily need to be causal in a singular case because it could have been preempted by an alternative cause. We here show how information about causal strength and about two different temporal parameters, the potential causes' onset times and their causal latencies, can be formalized and integrated into a computational account of singular causation. Four experiments are presented in which we tested the validity of the model. The results showed that people integrate the different types of information as predicted by the new model.     

Causal competition based on generic priors

Although we live in a complex and multi-causal world, learners often lack sufficient data and/or cognitive resources to acquire a fully veridical causal model. The general goal of making precise predictions with energy-efficient representations suggests a generic prior favoring causal models that include a relatively small number of strong causes. Such “sparse and strong” priors make it possible to quickly identify the most potent individual causes, relegating weaker causes to secondary status or eliminating them from consideration altogether. Sparse-and-strong priors predict that competition will be observed between candidate causes of the same polarity (i.e., generative or else preventive) even if they occur independently. For instance, the strength of a moderately strong cause should be underestimated when an uncorrelated strong cause also occurs in the general learning environment, relative to when a weaker cause also occurs. We report three experiments investigating whether independently-occurring causes (either generative or preventive) compete when people make judgments of causal strength. Cue competition was indeed observed for both generative and preventive causes. The data were used to assess alternative computational models of human learning in complex multi-causal situations.     

Analogical and category-based inference: a theoretical integration with Bayesian causal models

A fundamental issue for theories of human induction is to specify constraints on potential inferences. For inferences based on shared category membership, an analogy, and/or a relational schema, it appears that the basic goal of induction is to make accurate and goal-relevant inferences that are sensitive to uncertainty. People can use source information at various levels of abstraction (including both specific instances and more general categories), coupled with prior causal knowledge, to build a causal model for a target situation, which in turn constrains inferences about the target. We propose a computational theory in the framework of Bayesian inference and test its predictions (parameter-free for the cases we consider) in a series of experiments in which people were asked to assess the probabilities of various causal predictions and attributions about a target on the basis of source knowledge about generative and preventive causes. The theory proved successful in accounting for systematic patterns of judgments about interrelated types of causal inferences, including evidence that analogical inferences are partially dissociable from overall mapping quality.     

How two causes are different from one: The use of (un)conditional information in Simpson's paradox

In a causally complex world, two (or more) factors may simultaneously be potential causes of an effect. To evaluate the causal efficacy of a factor, the alternative factors must be controlled for (or conditionalized on). Subjects judged the causal strength of two potential causes of an effect that covaried with each other, thereby setting up a Simpson's paradox--a situation in which causal judgments should vary widely depending on whether or not they are conditionalized on the alternative potential cause. In Experiments 1 (table format) and 2 (trial-by-trial format), the subjects did conditionalize their judgments for one causal factor on a known alternative cause. The subjects also demonstrated that they knew what information was needed to properly make causal judgments when two potential causes are available. In Experiment 3 (trial-by-trial), those subjects who were not told about the causal mechanism by which the alternative cause operated were less likely to conditionalize on it. However, the more a subject recognized the covariation between the alternative cause and the effect, the more the subject conditionalized on it. Such behavior may arise from the interaction between bottom-up and top-down processing.