The order of things: Inferring causal structure from temporal patterns

The order of things: Inferring causal structure from temporal patterns Neil R. Bramley 1 (neil.bramley.10@ucl.ac.uk) , Tobias Gerstenberg 2 (tger@mit.edu) , David A. Lagnado 1 (d.lagnado@ucl.ac.uk) 1 Department of Cognitive Perceptual & Brain Sciences, UCL, 26 Bedford Way, London, WC1H 0DS, UK 2 Brain and Cognitive Sciences, MIT, Cambridge, MA 02139, USA Abstract These findings suggest that causal inference and event tim- ing are tightly coupled (Lagnado & Sloman, 2006; Rottman & Keil, 2012; Sloman, 2005), with causal inference from temporal information appearing to be more automatic (Mi- chotte, 1946) and more developmentally basic (McCormack, Frosch, et al., under review) than other modes of causal learn- ing. However, to date there has been little work on the role of temporal order 1 . The timing and order in which a set of events occur strongly in- fluences whether people judge them to be causally related. But what do people think particular temporal patterns of events tell them about causal structure? And how do they integrate multi- ple pieces of temporal evidence? We present a behavioral ex- periment that explores human causal structure induction from multiple temporal patterns of observations. We compare two simple Bayesian models that make no assumptions about de- lay lengths, assume that causes must precede their effects but differ in whether they assume simultaneous events can also be causally connected. We find that participants’ judgments are in line with the model that rules out simultaneous causation. Variants of this model that assume people update their beliefs conservatively provide a close fit to participants’ judgments. We discuss possible psychological bases for this conservative belief updating and how we plan to further explore how people learn about causal structure from time. Keywords: causal learning; sequential learning; structure; Bayesian modeling; conservatism; time; memory; belief up- dating The learning problem Here we explore the general problem of how people induce causal structure from temporal patterns of activation. We investigate whether people make a default assumption that causes must precede their effects, or merely a weaker assump- tion that causes either precede or happen at the same time as their effects. We focus on identification of the causal struc- ture of a simple system with two candidate cause components A and B, and a single effect component E (Figure 2). To keep the problem space manageable, we restrict the systems to binary (active/inactive) components with causal relation- ships that are generative and deterministic and where there are no spontaneous component activations. However, delays between causes and their effects are variable, such that the same causal structure can generate more than a single type of temporal activation pattern. We also restrict the evidence to temporal patterns in which all components activate. This means that people cannot rely on contingency information and have to base their causal judgments on temporal order information only (Figure 3 a). Introduction Hume’s (1748/1975) claim that people infer causal connec- tions when they find temporal precedence, contiguity and constant conjunction has largely been embraced by psy- chology. Associative learning theories predict that, ceteris paribus, the closer in time two events occurred, the more likely people are to believe that they are causally related (Shanks & Dickinson, 1987). However, much recent work has shown that for many real world scenarios, people’s causal judgments are influenced by their expectations about delay length (Buehner & May, 2004; Schlottmann, 1999), and de- lay variability (Greville & Buehner, 2010) such that shorter- than-expected delays can also reduce causal judgments. On the other hand, a related line of work suggests that consis- tency of temporal order with a causal structure (over and above specific delay length), may be an even more important factor in how people induce causal structure (Lagnado & Slo- man, 2002, 2004; Rottman & Keil, 2012). People appear to draw causal conclusions based on temporal order even when the mechanisms underlying the causal system are completely unknown, or when temporal order contradicts other sources of information such as covariation and the outcomes of inter- ventions (Lagnado & Sloman, 2006). Several recent studies also suggest that people are reluctant to endorse causal con- nections between events which appear to occur at the same time (Burns & McCormack, 2009), even when the causal mechanism is plausibly instantaneous (Lagnado & Sloman, 2006; McCormack, Bramley, Frosch, Patrick, & Lagnado, under review; McCormack, Frosch, Patrick, & Lagnado, un- der review). Baseline models In order to formalize the idea that people expect causes to pre- cede their effects in a Bayesian framework, we created likeli- hood functions for the seven causal structures in the problem space. We assumed that the probability of seeing a particu- lar temporal pattern of activations given a causal structure is 1/N, where N is the number of distinct temporal orderings consistent with that structure (Figure 3 a). For example, pat- tern 4 in which component A activates before component E and B, is consistent with structure IV (B ← A → E) but in- consistent with structure V (A ← B → E) because it is impos- sible in this common cause structure for A to activate before B. This approach is simple because it makes no assumptions about the exact length of the time delays between causes and effects but only considers the qualitative ordering in which 1 An exception is Pacer and Griffiths (2012), but their work fo- cused on induction of connections between continuously varying variables, while we will focus here on sequences of point events.