Inducing causal relationships from observations is a classic problem in scientific inference, statistics, and machine learning. It is also a central part of human learning, and a task that people perform remarkably well given its notorious difficulties. People can learn causal structure in various settings, from diverse forms of data: observations of the co-occurrence frequencies between causes and effects, interactions between physical objects, or patterns of spatial or temporal coincidence. These different modes of learning are typically thought of as distinct psychological processes and are rarely studied together, but at heart they present the same inductive challenge—identifying the unobservable mechanisms that generate observable relations between variables, objects, or events, given only sparse and limited data. We present a computational-level analysis of this inductive problem and a framework for its solution, which allows us to model all these forms of causal learning in a common language. In this framework, causal induction is the product of domain-general statistical inference guided by domain-specific prior knowledge, in the form of an abstract causal theory. We identify 3 key aspects of abstract prior knowledge—the ontology of entities, properties, and relations that organizes a domain; the plausibility of specific causal relationships; and the functional form of those relationships—and show how they provide the constraints that people need to induce useful causal models from sparse data.

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.

The very early appearance of abstract knowledge is often taken as evidence for innateness. We explore the relative learning speeds of abstract and specific knowledge within a Bayesian framework, and the role for innate structure. We focus on knowledge about causality, seen as a domain-general intuitive theory, and ask whether this knowledge can be learned from cooccurrence of events. We begin by phrasing the causal Bayes nets theory of causality, and a range of alternatives, in a logical language for relational theories. This allows us to explore simultaneous inductive learning of an abstract theory of causality and a causal model for each of several causal systems. We find that the correct theory of causality can be learned relatively quickly, often becoming available before specific causal theories have been learned—an effect we term the blessing of abstraction. We then explore the effect of providing a variety of auxiliary evidence, and find that a collection of simple “perceptual input analyzers ” can help to bootstrap abstract knowledge. Together these results suggest that the most efficient route to causal knowledge may be to build in not an abstract notion of causality, but a powerful inductive learning mechanism and a variety of perceptual supports. While these results are purely computational, they have implications for cognitive development, which we explore in the conclusion. Pre-print June 2010—to appear in Psych. Review.

Two experiments examined the impact of causal relations between features on categorization by adults and 5-6-year-old children. Participants learned about artificial categories containing instances with two causally related features and two non-causal 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 and centrality when links were probabilistic (Experiment 2). Children’s classification was based primarily on causal coherence in both cases. These results suggest that the generative model [Rehder, B. (2003). A causalmodel theory of conceptual representation and categorization. Journal of Experimental Psychology: Learning, Memory, and Cognition, 29, 1141-1159] provides a good account of causal categorization in both children and adults. Children’s Causal Categorization 3 It is well established that causal knowledge plays an important role in adult categorization and

Learning to understand a single causal system can be an achievement, but humans must learn about multiple causal systems over the course of a lifetime. We present a hierarchical Bayesian framework that helps to explain how learning about several causal systems can accelerate learning about systems that are subsequently encountered. Given experience with a set of objects our framework learns a causal model for each object and a causal schema that captures commonalities among these causal models. The schema organizes the objects into categories and specifies the causal powers and characteristic features of these categories and the characteristic causal interactions between categories. A schema of this kind allows causal models for subsequent objects to be rapidly learned, and we explore this accelerated learning in four experiments. Our results confirm that humans learn rapidly about the causal powers of novel objects, and we show that our framework accounts better for our data than alternative models of causal learning.

Previous work showed that people‟s causal judgments are modeled better as estimates of the probability that a causal relationship exists (a qualitative inference) than as estimates of the strength of that relationship (a quantitative inference). Here, using a novel task, we present experimental evidence in support of the importance of qualitative causal inference. Our findings cannot be explained through the use of parameter estimation and related quantitative inference. These findings suggest the role of qualitative inference in causal reasoning has been understudied despite its unique role in cognition. Further, we suggest these findings open interesting questions about the role of qualitative inference in many domains.

Blocking is a well-studied learning phenomenon in which previous learning inhibits subsequent learning about novel cues. Existing models provide different explanations for blocking and predict different beliefs about novel cues early in the second phase of blocking. Two experiments examined learners ’ beliefs when first encountering novel cues. The results suggest that the introduction of the novel cue in the second phase of a blocking paradigm adds uncertainty and that learners entertain the possibility that novel cues are preventative. A novel computational account is proposed to explain people’s beliefs, because existing models cannot fully account for these findings.

Our main goal in the present set of studies was to re-visit the question whether people are capable of inducing causal models from covariation data alone without further cues, such as temporal order. In the literature there has been a debate between bottom-up and top-down learning theories in causal learning. Whereas top-down theorists claim that in structure induction, covariation information plays none or only a secondary role, bottom-up theories, such as causal Bayes net theory, assert that people are capable of inducing structure from conditional dependence and independence information alone. Our three experiments suggest that both positions are wrong. In simple three-variable domains people are indeed often capable of reliably picking the right model. However, this can be achieved by simple heuristics that do not require complex statistics.

Causal graphical models (CGMs) have become popular in numerous domains of psychological research for representing people’s causal knowledge. Unfortunately, however, the CGMs typically used in cognitive models prohibit representations of causal cycles. Building on work in machine learning, we propose an extension of CGMs that allows cycles and apply that representation to one real-world reasoning task, namely, classification. Our model’s predictions were assessed in experiments that tested both probabilistic and deterministic causal relations. The results were qualitatively consistent with the predictions of our model and inconsistent with those of an alternative model. We naturally reason about causally related events that occur in cycles. In economics, we expect that an increase in corporate hiring may increase consumers ’ income and thus their demand for products, leading to a further increase in hiring. In meteorology, we expect that melting tundra due to global warming may release the greenhouse gas methane, leading to yet further warming. In psychology, we expect that clinicians will affect (hopefully help) their clients but also recognize the clients often affect the clinicians. Many psychologists investigate causal reasoning using a formalism known as Bayesian networks or causal graphical models (hereafter, CGMs). CGMs are one hypothesis for how people reason with causal knowledge. There are claims that causal learning amounts to acquiring the structure and/or parameters of a CGM (Cheng, 1997; Gopnik et al.,

Bayesian models of human causal induction rely on assumptions about people’s priors that have not been extensively tested. We empirically estimated human priors on the strength of causal relationships using iterated learning, an experimental method where people make inferences from data generated based on their own responses in previous trials. This method produced a prior on causal strength that was quite different from priors previously proposed in the literature on causal induction. The predictions of Bayesian models using different priors were then compared against human judgments of strength of causal relationships. The empirical priors estimated via iterated learning resulted in the best predictions.