Using Physical Theories to Infer Hidden Causal Structure

Using Physical Theories to Infer Hidden Causal Structure Thomas L. Griﬃths Elizabeth R. Baraﬀ & Joshua B. Tenenbaum gruffydd@psych.stanford.edu Department of Psychology Stanford University {liz b,jbt}@mit.edu Department of Brain and Cognitive Sciences Massachusetts Institute of Technology some, 2003) turns on this issue. Causal graphical models provide a language in which the problem of causal induction can be formally expressed. How- ever, conventional algorithms for inducing causal structure (e.g., Pearl, 2000; Spirtes et al., 1993) do not provide a satisfying account of either the roles of causal knowledge or statistical inference, or their interaction. These algorithms use tests of statisti- cal independence to establish constraints that must be satisﬁed by causal structures consistent with the observed data. No knowledge of how causal mech- anisms operate, or the functional form of relation- ships between cause and eﬀect, enters into the in- ference process. As we argue below, such knowledge is necessary to explain how people are able to in- fer causal structure from very small samples, and to infer hidden causes from purely observational data. Constraint-based methods are also unable to explain people’s graded sensitivity to the strength of evi- dence for a causal structure, because they reason de- ductively from constraints to consistent structures. We will present a rational account of human in- ference, Theory-Based Causal Induction, which em- phasizes the interaction between causal knowledge and statistical learning. Causal knowledge appears in the form of causal theories, specifying the princi- ples by which causal relationships operate in a given domain. These theories are used to generate hy- pothesis spaces of causal models – some with hid- den causes, some without – that can be evaluated by domain-general statistical inference. We will use this framework to develop models of people’s infer- ences about hidden causes in two physical systems: a mechanical system called the stick-ball machine (Kushnir et al., 2003), and a dynamical system in- volving an explosive compound called Nitro X.  We argue that human judgments about hidden causal structure can be explained as the operation of domain-general statistical inference over causal models constructed using domain knowledge. We present Bayesian models of causal induction in two previous experiments and a new study. Hypothet- ical causal models are generated by theories ex- pressing two essential aspects of abstract knowledge about causal mechanisms: which causal relations are plausible, and what functional form they take. Everyday reasoning draws on notions that go far beyond the observable world, just as modern sci- ence draws upon theoretical constructs beyond the limits of measurement. The richness of our naive theories is a direct result of our ability to postu- late hidden causal structure. This capacity to rea- son about unobserved causes forms an essential part of cognition from early in life, whether we are rea- soning about the forces involved in physical systems (e.g., Shultz, 1982), the mental states of others (e.g., Perner, 1991), or the essential properties of natural kinds (e.g., Gelman & Wellman, 1991). The central role of hidden causes in naive theories makes the question of how people infer hidden causal structure fundamental to understanding human rea- soning. Psychological research has shown that peo- ple can infer the existence of hidden causes from oth- erwise unexplained events (Ahn & Luhmann, 2003), and determine hidden causal structure from very lit- tle data (Kushnir, Gopnik, Schulz, & Danks, 2003). This work has parallels in computer science, where the development of a formalism for reasoning about causality – causal graphical models – has led to algo- rithms that use patterns of dependency to identify causal relationships (Pearl, 2000; Spirtes, Glymour, & Scheines, 1993). It has recently been proposed, chieﬂy by Gopnik, Glymour, and their colleagues (Glymour, 2001; Gopnik, Glymour, Sobel, Schulz, Kushnir, & Danks, 2004), that these algorithms may also explain how people infer causal structure. A fundamental issue in explaining how people in- fer causal relationships is accounting for the interac- tion between abstract causal knowledge and statisti- cal inference. The classic debate between approaches that emphasize cause-eﬀect covariation and those that emphasize mechanism knowledge (e.g., New- Theory-based causal induction Our account of causal induction builds on causal graphical models, extending the formalism to incor- porate the abstract knowledge about causal mecha- nism that plays an essential role in human inferences. We will brieﬂy introduce causal graphical models, consider how prior knowledge inﬂuences causal in- duction, and describe how we formalize the contri- bution of causal theories.