Bayesian Generic Priors for Causal LearningHongjing Lu, Alan L. Yuille, Mimi Liljeholm, Patricia W. Cheng, and Keith J. HolyoakUniversity of California, Los AngelesThe article presents a Bayesian model of causal learning that incorporates generic priors—systematicassumptions about abstract properties of a system of cause–effect relations. The proposed generic priorsfor causal learning favor sparse and strong (SS) causes—causes that are few in number and high in theirindividual powers to produce or prevent effects. The SS power model couples these generic priors witha causal generating function based on the assumption that unobservable causal influences on an effectoperate independently (P. W. Cheng, 1997). The authors tested this and other Bayesian models, as wellas leading nonnormative models, by fitting multiple data sets in which several parameters were variedparametrically across multiple types of judgments. The SS power model accounted for data concerningjudgments of both causal strength and causal structure (whether a causal link exists). The model explainswhy human judgments of causal structure (relative to a Bayesian model lacking these generic priors) areinfluenced more by causal power and the base rate of the effect and less by sample size. Broaderimplications of the Bayesian framework for human learning are discussed.Keywords: causal learning, Bayesian models, strength judgments, structure judgments, generic priorsFrom a very young age, humans display a remarkable ability toacquire knowledge of the causal structure of the world (e.g.,Bullock, Gelman, & Baillargeon, 1982), often learning cause–effect relations from just a handful of observations (e.g., Gopnik,Sobel, Schulz, & Glymour, 2001; Sobel & Kirkham, 2007). Causalknowledge is particularly valuable in guiding intelligent behavior,making it possible to make predictions, diagnose faults, planinterventions, and form explanations (see Buehner & Cheng,2005). Rather than expending their limited cognitive resources ina vain effort to learn all possible covariations among events,humans appear to focus on the more tractable (but still daunting)task of learning which types of events produce (or prevent) other typesof events. A basic question remains: How can people (and possiblyother animals) acquire causal knowledge from limited observations?The philosopher Charles Peirce (1931–1958) argued that humaninduction must be guided by “special aptitudes for guessing right”(Vol. 2, p. 476). One possible guide to guessing right is simplicity orparsimony. The admonition often called Occam’s razor was suc-cinctly stated by Isaac Newton (1729/1968) as the first of his “Rulesof Reasoning in Philosophy”: “We are to admit no more causes ofnatural things, than such as are both true and sufficient to explain theirappearances” (p. 3). The concept of simplicity poses thorny philo-sophical problems (Sober, 2002, 2006), both in defining simplicityand in justifying its use as a guide to induction. Yet the concept haslongstanding appeal and recently has been proposed as a unifyingprinciple for cognitive science (Chater & Vita´nyi, 2003). Applyingthe simplicity principle to causal reasoning, Lombrozo (2007) showedthat when assessing causal explanations of individual events, peopleprefer explanations based on fewer causes (also Lagnado, 1994).As Lombrozo (2007) noted, individual events are explained bycausal tokens, that is, specific events that are instances of causalregularities. Our central aim in the present article is to formalizeand test the possible role of simplicity in the acquisition of causalregularities that hold between types of events (see Sosa & Tooley,1993). Working within a Bayesian framework for causal learning(Griffiths & Tenenbaum, 2005), we model simplicity using ge-neric priors—systematic assumptions that human learners holdabout abstract properties of a system of cause–effect relations.These generic priors, which function to constrain causal learning,provide a middle ground between complete absence of domainknowledge and dependence on highly specific prior knowledge.Even when the domain is unfamiliar, if the environment providesdata consistent with the learner’s generic priors, then causal learn-ing can be rapid—on the human scale.To explain how causal knowledge may be acquired and used,recent theoretical work on causal learning has made extensive useof formalisms based on directed causal graphs, simple examples ofwhich are shown in Figure 1. Within a causal graph, each directedarrow connects a node representing a cause to one of its effects,Hongjing Lu, Mimi Liljeholm, Patricia W. Cheng, and Keith J. Holyoak,Department of Psychology, University of California, Los Angeles(UCLA); Alan L. Yuille, Department of Statistics, Psychology, and Com-puter Science, UCLA.Preparation of this article was supported by UCLA (Hongjing Lu), theW. H. Keck Foundation (Alan L. Yuille), the National Institutes of Health(Grant MH64810 to Patricia W. Cheng), and the Office of Naval Research(Grant N000140810186 to Keith J. Holyoak). Experiment 3 was part of adoctoral thesis completed in the UCLA Department of Psychology byMimi Liljeholm under the direction of Patricia W. Cheng. Preliminaryreports of part of this research were presented at the 28th (Vancouver,British Columbia, Canada, July 2006) and 29th (Nashville, TN, August2007) Annual Conferences of the Cognitive Science Society. We thankDavid Danks, David Lagnado, and Michael Waldmann for helpful com-ments on earlier drafts. Matlab code for the models presented here isavailable from the Web site of the UCLA Computational Vision andLearning Lab (http://cvl.psych.ucla.edu).Correspondence concerning this article should be addressed to HongjingLu, Department of Psychology, University of California, Los Angeles, 405Hilgard Avenue, Los Angeles, CA 90095-1563. E-mail: [email protected] Review Copyright 2008 by the American Psychological Association2008, Vol. 115, No. 4, 955–984 0033-295X/08/$12.00 DOI: 10.1037/a0013256955where it is understood that the cause does not follow its effect(typically preceding it) and has the power to generate or prevent it.(For the set of assumptions defining causal graphs, see Gopnik etal., 2004; Pearl, 1988, 2000; Spirtes, Glymour, & Scheines, 2000.)Causal powers can be interpreted as being probabilistic (i.e., acause may yield its effect with a probability ⬍ 1). Such graphicalrepresentations, often termed causal models,