Decisions to intervene on causal systems are adaptively selected

Decisions to intervene on causal systems are adaptively selected Anna Coenen, Bob Rehder, and Todd Gureckis Department of Psychology, NYU, 6 Washington Place, New York, NY 10003 USA {anna.coenen, bob.rehder, todd.gureckis}@nyu.edu Abstract Furthermore, we show that this strategy mixture is not fixed but that people can change their strategies in response to the payoff structure in a given environment. On the basis of these findings we argue that people have a flexible and adaptive repertoire for causal structure learning, rather than relying on a single strategy. The structure of this paper is as follows. First, we will define two computational models of interven- tion selection. We then report an experiment aimed at distin- guishing the models. Based on the results, we present a sec- ond study in which we manipulate the expected payoff from each strategy to investigate the impact on people’s interven- tion decisions. How do people choose interventions to learn about a causal system? Here, we tested two possibilities: an optimal infor- mation sampling strategy which aims to discriminate between multiple hypotheses, and a second strategy that aims to confirm individual hypotheses. We show in Experiment 1 that individ- ual behavior is best fit using a mixture of these two options. In a second experiment, we find that people are able to adaptively alter the strategies they use in response to their expected payoff in a particular task environment. Keywords: causal learning; information sampling; interven- tions. Introduction Interventions are an important instrument for learning about causal structures. By manipulating causal variables we can better discover the relationships between them. This ability is crucial in many areas of human inquiry including empirical science, medical reasoning, or simply when learning how a new mechanism, like a smartphone, works. In this paper we ask how people decide which variables to manipulate when they want to test specific hypotheses about a causal system. Previous work has most often sought a single strategy or model that describes how people search for information when learning. In particular, two competing perspectives have emerged. One set of models assumes that people se- lect information to optimally discriminate between different hypotheses. Such rational sampling norms have been used to model information search in many different domains (for an overview see Nelson, 2005), including learning of causal structures. For example, Steyvers and colleagues (2003) ar- gue that participants use an Information Gain strategy (IG) when choosing causal interventions. This strategy aims to minimize a learner’s uncertainty about which out of a num- ber of graph descriptions (hypotheses) underly a particular causal system. On the other hand, research on hypothesis testing in other domains, particularly in rule-learning tasks, has often argued that people use confirmatory strategies to search for informa- tion (Nickerson, 1998). For example, they might use the pos- itive testing strategy (PTS) which makes search queries that they expect to be true under one hypothesis, irrespective of whether it helps to discriminate between different hypothe- ses (Klayman & Ha, 1989; Wason, 1960). Although PTS can be optimal under certain circumstances (Navarro & Perfors, 2011; Oaksford & Chater, 1994), it often runs counter to op- timal sampling norms such as IG. This paper challenges the view that people use a single strategy to test causal hypotheses via interventions, and in- stead finds that people simultaneously use both discrimina- tory and confirmatory reasoning when making interventions. Two models of intervention-based causal learning Information Gain The IG model predicts that learners should choose interventions that they expect to maximally re- duce their current uncertainty, H(G), about a set of causal hy- potheses or graphs, G (Murphy, 2001; Tong & Koller, 2001). The expected Information Gain of an intervention a can be calculated as: EIG(a) = H(G) − ∑ P(y|a)H(G|a, y) y∈Y where P(y|a) is the probability of outcome y ∈ Y , given ac- tion a. Calculating EIG requires knowing the new uncertainty after making intervention a and observing outcome y: H(G|a, y) = ∑ P(g|a, y)log P(g|a, y) g∈G where P(g|a, y) is the probability of graph g given in- tervention a and resulting outcome y. To calculate P(g|a, y), Bayes’ rule can be applied, yielding P(g|a, y) = P(y|g, a)P(g)/P(y|a). Finally, P(y|a) can be computed by marginalizing over all possible graphs and their likelihood of producing outcome y given intervention a, P(y|g, a). Positive testing There is no existing definition of positive testing as a causal intervention strategy in the literature. PTS has mainly been articulated in rule learning tasks, where it constitutes a preference for search queries that lead to pos- itive outcomes (i.e. “yes” rather than “no”) under a given hypothesis (Klayman & Ha, 1989; Wason, 1960). We propose that such a preference for positive outcomes might translate into a preference for creating positive effects in the causal learning scenario. Consequently, PTS could manifest as a preference for nodes that have high causal centrality in a hypothesis that is currently under evaluation (Sloman, Love, & Ahn, 1998; Ahn, Kim, Lassaline, & Den- nis, 2000), where centrality is measured by the number of di-