Doing After Seeing

Doing After Seeing Bjorn Meder (bmeder@uni-goettingen.de) York Hagmayer (york.hagmayer@bio.uni-goettingen.de) Michael R. Waldmann (michael.waldmann@bio.uni-goettingen.de) Department of Psychology, University of Gottingen, Gosslerstr. 14, 37073 Gottingen, Germany causal learning are sensitive to covariations but do not distinguish between causal and spurious relations. It is true that these theories distinguish between observational (classical conditioning) and interventional learning (instrumental conditioning), but, as the barometer example shows, they fail when predictions for instrumental actions have to be derived from observational learning. Causal Bayes nets (Pearl, 2000; Spirtes, Glymour, & Scheines, 1993; Woodward, 2003) provide a formal account of causal representations and inference that allows it to derive precise predictions for hypothetical interventions from observational knowledge. The goal of the present experiments is to investigate whether people who have observed individual trials presenting the states of a complex causal model can later access their causal knowledge to derive observational and interventional predictions in a fashion anticipated by causal Bayes nets. To test the robustness of this competency we manipulated the temporal cues in the learning data (predictive learning from causes to effects vs. diagnostic learning from effects to causes). Abstract Causal knowledge serves two functions: it allows us to predict future events on the basis of observations and to plan actions. Although associative learning theories traditionally differentiate between learning based on observations (classical conditioning) and learning based on the outcomes of actions (instrumental conditioning), they fail to express the common basis of these two modes of accessing causal knowledge. In contrast, the theory of causal Bayes nets captures the distinction between observations (seeing) and interventions (doing), and provides mechanisms for predicting the outcomes of hypothetical interventions from observational data. In two experiments, in which participants acquired observational knowledge in a trial-by-trial learning procedure, the adequacy of causal Bayes nets as models of human learning was examined. To test the robustness of learners’ competency, the experiments varied the temporal order in which the causal events were presented (predictive vs. diagnostic). The results support the theory of causal Bayes nets but also show that conflicting temporal information can impair performance. Introduction The ability of acquiring and using causal knowledge is a central competency necessary for explaining past events, predicting future events, and planning actions. But how do people infer the consequences of their actions when planning interventions in causal systems? In some cases they might have tried out the interventions on previous occasions so that they already know the potential outcomes of their actions. But what if only knowledge about observational relations between causal events is available? A tempting solution would be to equate observational knowledge with instrumental knowledge and proceed from there. Unfortunately this strategy will often lead to ineffective actions. For example, the status of a barometer is statistically related to the upcoming weather, but manipulating the barometer does not affect the weather. Barometer readings and weather are spuriously related due to their common cause, atmospheric pressure. As a consequence, observational predictions can capitalize on the spurious statistical relation, whereas instrumental predictions cannot. Effects do not change their causes; thus, manipulating the barometer does not affect its cause atmospheric pressure, and therefore has no causal influence on the weather. The difference between observing (seeing) and intervening (doing) is compelling in the barometer example. Nevertheless, most theories of causal cognition do not distinguish between different modes of accessing identical causal knowledge. For example, associative theories of Seeing vs. Doing in Causal Bayes Nets The formal framework of causal Bayes nets uses directed acyclic graphs (DAGs) to represent causal relations between variables, and parameters to express the strength of these relations (e.g., conditional probabilities). A complete causal model therefore combines qualitative assumptions about the structure of the causal model with quantitative knowledge about the size of the parameters associated with these causal relations (e.g., base rates, causal strength, integration rules). An example is given in Figure 1. This causal model consists of four (binary) variables A, B, C, and D, in which A can cause D either via B or via C. In the causal Bayes nets framework, the joint probability distribution of this model can be factored into: p(A.B.C.D)=p(A) · p(B|A) · p(C|A) · p(D|B.C) This decomposition follows from applying the causal Markov condition (Spirtes et al., 1993; Pearl, 2000) to the causal model. The causal Markov condition (informally) states that the state of any variable X j in the system is independent of all other variables (except for its causal descendants) conditional on the set of its direct causes, pa x . For example, the causal Markov condition implies for the causal model shown in Figure 1 that variable D is independent of A conditional on its direct causes B and C. Relations of conditional dependence and independence are critical for deriving observational and interventional inferences.