Connecting Causal Events: Learning Causal Structures Through Repeated Interventions Over Time

Connecting Causal Events: Learning Causal Structures Through Repeated Interventions Over Time Benjamin M. Rottman (benjamin.rottman@yale.edu) Department of Psychology, Yale U. , 2 Hillhouse Ave New Haven, CT 06520 Frank C. Keil (frank.keil@yale.edu) Department of Psychology, Yale U. , 2 Hillhouse Ave New Haven, CT 06520 Abstract the temporal strategy may be common if not a default for learning causal structures. In formal statistics we have developed specialized procedures for independent cases (e.g., between-subjects) and dependent cases (e.g., repeated-measures, time-series). Analogously, do people use different learning strategies for the two scenarios? In the following sections we detail the different inferences people might make. How do we learn causal structures? All current approaches use scenarios in which trials are temporally independent; however, people often learn about scenarios unfolding over time. In such cases, people may assume that other variables don’t change at the same instant as an intervention. In Experiment 1, participants were much more successful at learning causal structures when this assumption was upheld than violated. In Experiment 2, participants were less influenced by such temporal information when they believed the trials to be temporally independent, but still used the temporal strategy to some extent. People seem to be inclined to learn causal structures by connecting events over time. Interventions with Independent Trials Consider first one prominent account of how people learn causal structures from interventions when trials are independent (e.g., Gopnik et al., 2004; Pearl, 2000; Steyvers et al., 2003). According to this model, when you intervene upon a variable such that you control its state, that variable is assumed to be independent from its other causes, but its effects are still dependent on that variable. Consider again the example of learning the causal relationships between employment (E), GPD (G), and consumption (C). Pretend that a priori it is possible that any of these factors could influence or be influenced by any of the other factors. To learn the causal structure, one could intervene on each of the three variables to determine which other variables are influenced by (dependent upon) the intervention. Suppose that the true causal structure is a chain; E influences G, which influences C; E→G→C. If we could institute jobs-creation programs in 10 countries, we would expect them to have high G and C. If, hypothetically, we instituted a mass lay-off of government employees, we would expect comparatively low G and low C. These opposite interventions demonstrate how G and C are dependent on E. If we somehow selectively boosted G for10 new countries, they would have high C, but the same E as if we decreased G for 10 other countries; C is dependent on G but E is not. And if we gave 10 countries a boost in C, and another 10 countries a decrease in C, the two countries should have the same E and G; neither is dependent upon C. If instead the true causal structure is a common cause such that E influences both G and C, G←E→C, we would expect a different pattern of (in)dependence. If we increase or decrease G, the respective countries would have the same levels of E and C because they are independent of G. This strategy can identify the precise causal structure because each causal structure has a different pattern of (in)dependence when the variables are intervened upon. Keywords: causal reasoning; causal structures; time Introduction How do our concepts of event units influence how we learn causal structures? Despite the surge of research on causal structure learning, there has been little attention to how learners “connect” streams of information over time. Existing theories of how people learn causal structures have focused on cases with events considered to be independent. For example, suppose we are trying to learn the causal relationships between three economic variables: employment, GDP, and consumption. Existing psychological theories suggest that one looks at the relationships among the variables across many separate countries to determine the causal structure. We call this strategy the independent events strategy because the countries are assumed to be independent. An alternative approach is to pick one country and follow the three variables over time. We could track whether GDP goes up when employment goes up, etc. We call this strategy the dependent events or temporal strategy because the state of each variable is dependent on its prior state. Psychologically, the temporal strategy may be pervasive and perhaps a default. As temporal beings we often perform or witness sequences of actions on one entity. For example, a car mechanic or computer technician can repair different components until the problem is solved. A psychotherapist can attempt to change one person's beliefs, emotions, and behaviors systematically over time. A physician can intervene on heart rate, breathing, and blood pressure to stabilize a patient. In many real-world situations we do interact with causal systems repeatedly over time, and thus