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.

The ability to derive predictions for the outcomes of potential actions from observational data is one of the hallmarks of true causal reasoning. We present four learning experiments with deterministic and probabilistic data showing that people indeed make different predictions from causal models, whose parameters were learned in a purely observational learning phase, depending on whether learners believe that an event within the model has been merely observed (“seeing”) or was actively manipulated (“doing”). The predictions reflect sensitivity both to the structure of the causal models and to the size of their parameters. This competency is remarkable because the predictions for potential interventions were very different from the patterns that had actually been observed. Whereas associative and probabilistic theories fail, recent developments of causal Bayes net theories provide tools for modeling this competency. Causal knowledge underlies our ability to predict future events, to explain the occurrence of present events, and to achieve goals by means of actions. Thus, causal knowledge belongs to one of our most central cognitive competencies. However, the nature of causal knowledge has been debated. A number of philosophers and

computation. In preparation. Address for correspondence:

Introduction: Characterizing the Questions of causal reasoning This chapter describes the mechanism approach to the study of causal reasoning. We will first offer a characterization of the central issues in human causal reasoning, and will discuss how the mechanism approach addresses these issues. In the course of this presentation, we will frequently compare the mechanism approach with alternative accounts based on analyses of covariation, or what is often termed the regularity view. The aims of this chapter are the following: to explain why covariation and mechanism are different, to discuss why such a distinction is actually a useful tool for our understanding of causal reasoning, and to explicate the complementary nature of the two views. Before presenting these two approaches, it is necessary first to offer a description of the domain or problem itself : namely, what are these alternative approaches to? Although there are a number of different ways of characterizing the study of

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.

Causal knowledge enables us to predict future events, to choose the right actions to achieve our goals, and to envision what would have happened if things had been different. Thus, it allows us to reason about observations, interventions and counterfactual possibilities.

A pervasive feature of the sciences, particularly the applied sciences, is an experimental focus on a few (often only one) possible causal connections. At the same time, scientists often advance and apply relatively broad models that incorporate many different causal mechanisms. We are naturally led to ask whether there are normative rules for integrating multiple local experimental conclusions into models covering many additional variables. In this paper, we provide a positive answer to this question by developing several inference rules that use local causal models to place constraints on the integrated model, given quite general assumptions. We also demonstrate the practical value of these rules by applying them to a case study from ecology. 1 Experimental scope in applied sciences 2 Fusing the results of experiments 3 A concrete example of the inference rules 4 Application to a case study 1 Experimental scope in applied sciences Total photosynthetic material has increased globally in recent years (though with local decreases), and one might naturally wonder why. In a recent paper in Science, Nemani et al. ([2003]) focused on some of the potential causes of global vegetation growth during the past 20 years. Their analysis focused on only four variables: growing season average temperature, vapor pressure deficit, solar radiation, and net primary production (photosynthetic material). Their study considered only a limited variable set because of (a) the global scale of their analysis, and (b) the relatively long study period (18 years). Despite this limited scope (in terms of variables), their study gives substantial support to the hypothesis that the first three variables are causes of the last, and helps to clarify the functional form of those dependencies. At the same time, they explicitly note that there are many causally relevant variables that were ignored in their study, such as vegetation

Competence and performance in causal learning The dominant theoretical approach to causal learning postulates the acquisition of associative weights between cues and outcomes. These associative weights reflect the amount of covariation between the learning events. In the past few years, the associationist approach to causal learning has been criticized by a number of researchers

Information about the structure of a causal system can come in the form of observational data--- random samples of the system's autonomous behavior---or interventional data---samples conditioned on the particular values of one or more variables that have been experimentally manipulated. Here we study people's ability to infer causal structure from both observation and intervention, and to choose informative interventions on the basis of observational data. In three causal inference tasks, participants were to some degree capable of distinguishing between competing causal hypotheses on the basis of purely observational data. Performance improved substantially when participants were allowed to observe the effects of interventions that they performed on the systems. We develop computational models of how people infer causal structure from data and how they plan intervention experiments, based on the representational framework of causal graphical models and the inferential principles of optimal Bayesian decision-making and maximizing expected information gain. These analyses suggest that people can make rational causal inferences, subject to psychologically reasonable representational assumptions and computationally reasonable processing constraints.