Cause and Intent: Social Reasoning in Causal Learning Noah D. Goodman, Chris L. Baker, Joshua B. Tenenbaum {ndg, clbaker, jbt}@mit.edu MIT, Dept. of Brain and Cognitive Sciences Abstract the structure of the world as background knowledge avail- able to all agents. We combine these modeling approaches by The acquisition of causal knowledge is a primary goal of child- hood; yet most of this knowledge is known already to adults. constructing a model of intuitive psychology in which beliefs We argue that causal learning which leverages social reason- about the causal structure of the world are represented and ing is a rapid and important route to knowledge. We present used for action selection, and showing how such an intuitive a computational model integrating knowledge about causality with knowledge about intentional agency, but using a domain- theory of causal-agency can explain the source of interven- general mechanism for reasoning. Inference in this model pre- tions and speed causal learning. dicts qualitatively different learning than an equivalent model We test this model experimentally by studying adult intu- based on causality alone or a hybrid causal-encoding model. We test these predictions experimentally with adult partici- itions in a set of scenarios that provide both social and causal pants, and discuss the relation of these results to the devel- information. These scenarios are chosen to distinguish be- opmental phenomenon of over-imitation. tween the combined social-causal model and two alternatives: Keywords: Causal learning, social cognition, Bayesian mod- a similar causal-only model, and a hybrid gated-inference eling, imitation. model. We then use these results to explain a puzzling phe- nomenon of imitation-based learning in children. Introduction How do children acquire conceptual knowledge? One answer Computational modeling is that children are adept at rational inference from direct Our goal is to construct a formal model which simultaneously experience with the world—children as scientists (Gopnik, represents knowledge about causality and knowledge about Meltzoff, & Kuhl, 1999). Human culture suggests another an- intentional agency, and to explore how Bayesian inference swer: the quickest route to conceptual knowledge may be by over the combination differs from inference over each piece learning what others already know (Tomasello, 1999; Gergely in isolation. Knowledge can be represented as probabilis- & Csibra, 2006). Indeed, a vast majority of the knowledge tic generative models; Bayesian inference then “inverts” this that a child will acquire is already known by adults in their generative knowledge, specifying appropriate beliefs about society. This suggests that children come equipped with so- latent states given observed evidence. We begin by recalling cial learning mechanisms to encode the knowledge of adults standard generative models capturing (aspects of) causality (Lyons, Young, & Keil, 2007). We suggest a middle ground and intentional agency, then describe how they may be inte- between these two views: that an understanding of intentional grated, and finally describe predictions of the resulting model. agency makes it possible to use social context as a source of Causality A causal Bayes net (CBN) model describes the evidence to enable rapid learning without requiring dedicated probability P(E|A,S) of observing a set of events E, given psychological mechanisms. the causal structure S, and the interventions, or exogenous Among the most profound achievements of human knowl- actions, A (Fig. 1a). More formally, a CBN consists of a di- edge is an understanding of causal structure in the world; not rected acyclic graph on a set of variables, together with a coincidentally, causality has been a major area of research specification of the probabilistic dependence of each variable into children’s ability to learn from evidence (Gopnik et al., on its parents in the graph. The variables represent events 2004). In this paper we therefore focus on the acquisition or states, and the edges represent the fact of a causal depen- of causal knowledge in a social, but non-linguistic, setting. dence. For some variables there is an intervention: an ex- To explore the hypothesis that social learning emerges from ogenous event that forces the variable to a particular value, the interaction, under domain-general inference processes, irrespective of the values of its parents. We will assume that of existing conceptual structures, we construct a computa- the dependencies between variables are described by noisy- tional model integrating social and causal representations. or functions (each parent is a sufficient cause) or noisy-and Recent modeling of human causal reasoning has focused on functions (parents are jointly sufficient and individually nec- the causal Bayes nets approach (Pearl, 2000; Gopnik et al., essary); the causal strength of these dependencies, ε, is a fixed 2004). This view helps explain how causal learning can suc- parameter. (See Pearl (2000) for more about the formalism ceed based on observed co-occurance between events and and uses of causal Bayes nets.) well-chosen interventions. The interventions, however, are treated as unexplained actions on a system. In contrast, recent Agency Bayesian decision theory (Berger, 1985) describes models of intuitive psychology have focused on the selec- the choices made by a rational agent facing a stochastic de- tion of actions by agents given their goals and beliefs (Baker, cision problem (SDP) (Fig. 1b). A SDP consists of a set of Tenenbaum, & Saxe, 2007; Goodman et al., 2006), but treated possible actions the agent may take, a utility function U(E), Desired Causal Belief about = outcome structure causal structure (events, costs) Causal Bayes net: Stochastic decision process: Causal Actions Beliefs Desires Actions structure Events Actions Events (a) (b) (c) Figure 1: Schematic representations of generative models for causality (a), intentional agency (b), and the social-causal combination (c). Equality between the true causal structure and an agent’s belief about causal structure embodies the knowledgeable agent assumption. capturing the agent’s desires (reward for each possible out- represents a combined model in which the interventions of come E), and a belief function PB(E|A), capturing the agent’s the CBN have been identified with the actions of the SDP. beliefs about how the world works (the likely outcomes of an We will simplify by making the knowledgeable agent as- action A). Bayesian decision theory specifies that the agent sumption: the beliefs of the observed agent about the causal should choose an action to maximize her expected utility: structure of the world reflect the true (but unknown to the EPB(E|A)U(E). If we assume that agents are only approx- observing agent) causal structure of the world. While this imately rational, and hence only softly maximize expected is clearly not always the case, people, and especially chil- utility: dren, are often in situations where they can observe the ac- β·EP (E|A)U(E) P(A|U,PB) ∝ e B , (1) tions of an expert on a novel-to-the-observer causal system. In Fig. 1c this is represented with the equality between the where the parameter β determines the amount of decision true causal structure of the world and the observed agent’s noise. beliefs about the causal structure. (It is possible to relax this Eq. 1 can be used to model the intuitive theory of inten- assumption, leading to a model which incorporates explicit tional agency of a person who makes the rational agent as- reasoning about belief formation and update; see Goodman sumption (Baker et al., 2007). et al. (2006) for a related model.) Integration In order to capture reasoning about an inten- Given this setup, Bayesian inference can be used to in- tional agent choosing actions based on their causal knowl- fer a causal structure from observation of events and actions edge, we construct a model which integrates the above ap- in two ways: assuming only causal knowledge (causal-only proaches to causality and agency. We first assume that the inference), and assuming both causal and social knowledge observed agent represents the world in terms of causal Bayes (social-causal inference). For causal-only inference, the pos- net S: the set of outcomes is the set of all possible events terior over causal structures is given by: (variable values), the set of actions is all combinations of in- terventions, and the belief function is described by the CBN Pc(S|A,E) ∝ P(E|A,S)P(S), (2) dependency: PB(E|A)=P(E|A,S). Further, we assume that the utility function of the agent splits into a cost, C, for each where P(S) is the prior probability over causal structures— intervention made, and a reward, R , for each desired event we take this to be given by an independent prior probability 1 achieved. P(vi→v j) that each potential edge is in S. This CBN-based stochastic decision problem describes a For social-causal inference the joint posterior over causal simple theory of mind for reasoning about a causal agent— structure, S, and the (unknown) utility function, U, of the the intuitive theory one person has about another person’s agent performing the actions is given by: causal knowledge, desires, and actions. Note that a per- son might represent the causal structure of the world via a Ps-c(S,U|A,E) ∝ P(A,E|S,U)P(S)P(U) (3) CBN, and represent another agent’s beliefs via a second CBN ∝ P(E|A,S)P(A|S,U)P(S)P(U), (wrapped inside a SDP). When the interventions that enter the person’s own causal reasoning are the actions of the other where P(A|S,U) is given by Eq. 1. (Note that the same causal agent, they need not be treated as unexplained events. Fig. 1c structure, S, enters both the CBN term and the SDP term of Eq.