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• W3121898976 abstract "Estimating human priors on causal strength Saiwing Yeung (saiwing@berkeley.edu) Thomas L. Griffiths (tom griffiths@berkeley.edu) Department of Psychology, University of California, Berkeley Berkeley, CA. 94720-1650 USA Abstract Bayesian models of human causal induction rely on assump- tions 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 experimen- tal 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 differ- ent priors were then compared against human judgments of strength of causal relationships. The empirical priors estimated via iterated learning resulted in the best predictions. Keywords: Causal learning; Bayesian inference; Probabilistic judgment; Iterated learning Introduction Causal induction involves inferring the relationship between causes and effects. This problem has attracted the attention of cognitive scientists because it is an important skill that peo- ple rely on every day in order to understand the causal rela- tionships in their environment. Traditionally, psychological models of human causal induction have focused on various schemes for comparing the probability of an effect occurring in the presence and absence of a cause (e.g., Ward & Jenk- ins, 1965; Cheng, 1997). However, recent work has explored connections between ideas from Bayesian statistics and hu- man cognition, using causal graphical models to precisely define the problem of causal induction (Griffiths & Tenen- baum, 2005; Lu, Yuille, Liljeholm, Cheng, & Holyoak, 2008) and to formalize the effects of prior knowledge (Griffiths & Tenenbaum, 2009). A key part of these Bayesian models is to precisely specify the prior knowledge that people have about the strength of causal relationships. In previous models of human causal induction, priors on the strength of causal re- lationships were specified in two ways — either as uniform priors by appealing to the principle of indifference (Griffiths & Tenenbaum, 2005), or as generic priors based on assump- tions about the abstract properties of the causal system (Lu et al., 2008). In this paper, we present a new approach to esti- mating human priors on causal strength, using the method of iterated learning (Kalish, Griffiths, & Lewandowsky, 2007; Griffiths, Christian, & Kalish, 2008). Iterated learning was originally proposed as a simple model of the cultural transmission of languages (Kirby, 2001). In this case, we imagine a chain of agents, where each agent observes data generated by the previous agent (such as a set of utterances), forms a hypothesis about the process that generated those data (such as a language), and then gener- ates new data to pass to the next agent. If the agents select hypotheses using Bayesian inference, then as the chain gets longer the probability that an agent selects a particular hy- pothesis converges to the prior probability of that hypothesis (Griffiths & Kalish, 2007). Simulating this process of iterated learning in the laboratory thus provides a way to estimate peo- ple’s priors (Kalish et al., 2007). In fact, there is no need for data to be passed between people — we can just generate the data that people see on one trial based on their responses in a previous trial (Griffiths et al., 2008). The plan for the rest of the paper is as follows. The next section summarizes previous work on modeling human causal induction, focusing on analyses based on causal graph- ical models. We then introduce the basic ideas behind iterated learning and present our experimental investigation of human priors on causal strength. Next we compare the predictions produced by a model using the empirical priors with previous models. Finally we conclude the paper by discussing the im- plications of these results for understanding causal induction. Models of human causal induction The British philosopher David Hume pointed out that people are not “able to comprehend any force or power by which the cause operates, or any connexion between it and its supposed effect” (Hume, 1739/2004, p. 47), suggesting that causal rela- tionships need to be inferred from the observed contingencies of cause and effect. A number of models have been proposed to account for how this inference might be made, with the goal of predicting human judgments about causal relation- ships from contingency data. Models based on cause-effect probabilities The ∆P model (Ward & Jenkins, 1965) proposed that human make inferences about causal strength based on the contrast between P(e + |c + ) and P(e + |c − ), where e and c represent the effect (or outcome) and cause, and superscripts of + and − represent their presence or absence. ∆P is formally expressed as ∆P = P(e + |c + ) - P(e + |c − ). It captures the intuition that a cause is strong if it significantly increases the probability of the outcome occurring relative to its base rate. Cheng (1997) argued that ∆P was just a measure of co- variation and not one of causality. She further proposed the theory of causal power, in which human judgments of causal strength equals the probability of the cause in question pro- duces the effect in the absence of all other causes. For exam- ple, the power model for a generative cause can be expressed ∆P as power = 1−P(e + |c − ) . The causal power model provided bet- ter fit than ∆P for some human data. However, there have been debates about the lack of fit to human data for both mod- els (see Buehner & Cheng, 1997; Lober & Shanks, 2000)." @default.
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• W3121898976 title "Estimating human priors on causal strength" @default.
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