Learning Causal Structure through Local Prediction-error Learning.

Learning Causal Structure through Local Prediction-error Learning Sarah Wellen (swellen@andrew.cmu.edu) Department of Philosophy, Baker Hall 135 Pittsburgh, PA 15213 USA David Danks (ddanks@cmu.edu) Department of Philosophy, Baker Hall 135 Pittsburgh, PA 15213 USA; and Institute for Human & Machine Cognition, 40 S. Alcaniz St. Pensacola, FL 32502 USA Abstract and are connected by a pair of assumptions (Markov and Faithfulness) that capture the ways in which causal structure manifests in observed data. Sloman (2005) and Spirtes, Glymour, & Scheines (1993) provide useful expositions of the causal Bayes net framework. Research on human causal learning has largely focused on strength learning, or on computational-level theories; there are few formal algorithmic models of how people learn causal structure from covariations. We introduce a model that learns causal structure in a local manner via prediction-error learning. This local learning is then integrated dynamically into a unified representation of causal structure. The model uses computationally plausible approximations of (locally) rational learning, and so represents a hybrid between the associationist and rational paradigms in causal learning research. We conclude by showing that the model provides a good fit to data from a previous experiment. Figure 1: Prototypical 3-variable causal Bayes nets Keywords: Causal learning; causal Bayes nets; prediction-error learning; algorithmic level Introduction From a young age, we spontaneously, and often effortlessly, come to understand the causal structure of the world, and then use that knowledge to both predict what might happen in the future and also design actions that will achieve our goals (e.g., Gopnik, et al., 2004; Sloman, 2005). Our focus here is causal learning from covariational data: how do people learn the causal structure of the world from a sequence of observations or interventions of that world? Causal learning can usefully be separated into the related- but-distinct problems of representation and dynamics—what is learned and how is it learned. In this paper, we develop a novel account of causal learning that, at a high level, uses quasi-associationist processes to learn directed graph-like causal representations. It is thus a hybrid of the standard rationalist vs. associationist approaches to causal learning. Representations of Causal Structure The development of causal Bayesian networks prompted a major advance in our understanding of causal knowledge. A causal Bayes net has two components: (i) a directed acyclic graph (DAG) whose nodes represent variables and directed edges represent direct causal relations (see Figure 1); and (ii) a probability distribution that encodes how causes influence their effects. These two elements represent qualitative and quantitative causal structure, respectively, There is substantial evidence that the type of structural knowledge captured by a causal Bayes net—or at least, the directed graphical model part—is necessary to account for many causal reasoning abilities. One hallmark of causal reasoning, rather than correlational, is that cases involving observations vs. interventions are treated differently (Sloman & Lagnado, 2005; Waldmann & Hagmayer, 2005). For example, one can infer, from an observation of a professor’s gray hair, that she likely has many publications. No such inference follows if she instead intervened to dye her hair gray. Causal Bayes nets can straightforwardly account for this difference, as interventions are represented by ‘graph surgery,’ where a variable that is intervened upon is separated from its typical causes (Spirtes, et al., 1993). This surgery changes the informational relations, and so one’s inferences can be different in the two situations. Some aspects of causal knowledge are not easily represented by this formalism (e.g. the spatiotemporal relations between causes and effects), but it seems to provide a good account of people’s representations of causal structure. Thus, we aim to develop a theory of causal learning in which people learn a directed graph (perhaps acyclic, though we will allow for cyclic structures). Dynamics of Causal Structure Learning Theories about how people use covariation to learn directed graph representations can be divided roughly into rational and heuristic accounts of causal learning. Rational accounts