The authors outline a cognitive and computational account of causal learning in children. They propose that children use specialized cognitive systems that allow them to recover an accurate “causal map ” of the world: an abstract, coherent, learned representation of the causal relations among events. This kind of knowledge can be perspicuously understood in terms of the formalism of directed graphical causal models, or Bayes nets. Children’s causal learning and inference may involve computations similar to those for learning causal Bayes nets and for predicting with them. Experimental results suggest that 2to 4-year-old children construct new causal maps and that their learning is consistent with the Bayes net formalism.

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 routinely make sophisticated causal inferences unconsciously, effortlessly, and from very little data – often from just one or a few observations. We argue that these inferences can be explained as Bayesian computations over a hypothesis space of causal graphical models, shaped by strong top-down prior knowledge in the form of intuitive theories. We present two case studies of our approach, including quantitative models of human causal judgments and brief comparisons with traditional bottom-up models of inference. 1

In the previous chapter (Tenenbaum, Griffiths, & Niyogi, this volume), we introduced a framework for thinking about the structure, function, and acquisition of intuitive theories inspired by an analogy to the research program of generative grammar in linguistics. We argued that a principal function for intuitive theories, just as for grammars for natural

Causal inferences about sparsely observed objects are often supported by causal schemata, or systems of abstract causal knowledge. We present a hierarchical Bayesian framework that learns simple causal schemata given only raw data as input. Given a set of objects and observations of causal events involving some of these objects, our framework simultaneously discovers the causal type of each object, the causal powers of these types, the characteristic features of these types, and the characteristic interactions between these types. Previous behavioral studies confirm that humans are able to discover causal schemata, and we show that our framework accounts for data collected by Lien and Cheng and Shanks and Darby.

Leading accounts of judgment under uncertainty evaluate performance within purely statistical frameworks, holding people to the standards of classical Bayesian (Tversky & Kahneman, 1974) or frequentist (Gigerenzer & Hoffrage, 1995) norms. We argue that these frameworks have limited ability to explain the success and flexibility of people's real-world judgments, and propose an alternative normative framework based on Bayesian inferences over causal models. Deviations from traditional norms of judgment, such as "base-rate neglect", may then be explained in terms of a mismatch between the statistics given to people and the causal models they intuitively construct to support probabilistic reasoning. Four experiments show that when a clear mapping can be established from given statistics to the parameters of an intuitive causal model, people are more likely to use the statistics appropriately, and that when the classical and causal Bayesian norms differ in their prescriptions, people's judgments are more consistent with causal Bayesian norms.

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.

A connectionist model of causal attribution is presented, emphasizing the use of domain-general principles of processing and learning previously employed in models of semantic cognition. The model categorizes objects dependent upon their observed “causal properties ” and is capable of making several types of inferences that four-year-old children have been shown to be capable of. The model gives rise to approximate conformity to normative models of causal inference and gives approximate estimates of the probability that an object presented in an ambiguous situation actually possesses a particular causal power, based on background knowledge and recent observations. It accounts for data from three sets of experimental studies of the causal inferencing abilities of young children. The model provides a base for further efforts to delineate the intuitive mechanisms of causal inference employed by children and adults, without appealing to inherent principles or mechanisms specialized for causal as opposed to other forms of reasoning.

We outline a new computational account of learning in children using the causal Bayes net formalism. We also present evidence that children as young as two years old use something like causal Bayes net learning mechanisms to infer the causal structure of the world around them. This kind of learning may play an important role in the development of intuitive theories. Finally we contrast causal Bayes net and neural net learning mechanisms.

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.