Learning from human action 1 Running head: LEARNING FROM HUMAN ACTION Learning from others: The consequences of psychological reasoning for human learning

From early childhood, human beings learn not only from collections of facts about the world, but also in social contexts: from observation of other people, from communication, and from explicit teaching. In these contexts, the data are the result of human actions—actions that come about because of people’s goals and intentions. To interpret the implications of others’ actions correctly, learners must understand the people generating the data. Most models of learning, however, assume that data are randomly collected facts about the world, and cannot explain how social contexts influence learning. We provide a Bayesian analysis of learning from knowledgeable others, which formalizes how a learner may reason from a person’s actions and goals to infer the actor’s knowledge about the world. We illustrate this framework using two examples from causal learning and conclude by discussing the implications for cognition, social reasoning, and cognitive development. Learning from human action 3 Learning from others: The consequences of psychological reasoning for human learning Children are often compared to scientists, but even a perfect scientist, using experiments alone, would struggle to rediscover all of human knowledge in the span of one lifetime. How then are children able to acquire a good fraction of this knowledge in just a few years? The answer must be that children do not rediscover everything—they use their ability to reason intuitively about other people to learn what others already know. It is the goal of this paper to sketch a formal analysis of learning from knowledgeable others, by using the tools of Bayesian inference and a careful examination of the kinds of goals that give rise to human actions. We begin by motivating the need of a learner to consider the particular goals of people in their environment. Imagine, while living in Paris, you decide to search for the best cup of coffee in the city. As you wander, you find yourself a good distance away from your neighborhood. You observe three different pieces of evidence: first, a man wearing a baseball cap and an “I heart Paris” t-shirt (obviously a tourist) turns into cafe #1, buys a coffee, and looks down at his cup. Second, Véronique, a woman from your neighborhood, enters cafe #2 to get a coffee, and looks down at her cup. Third, Madeleine, another woman from your neighborhood, goes into cafe #3 and buys a cup. Madeleine sees you, and she nods at the coffee. Which cafe would you think has the best coffee? You know very little about the coffee at cafe #1, because the tourist likely chose the cafe at random. Cafe #2 was visited by a local, but maybe Véronique was just strapped for time and grabbing a cuppa wherever she could. Without knowing her motivations, you can’t tell whether she has gone out of her way to go to this Learning from human action 4 particular cafe (though you may guess at her motivations, and hence guess her beliefs about this cafe). On the other hand, in cafe #3, Madeleine telegraphed her intentions to you: She was there for the coffee, and she congratulated you for figuring out a local secret. Although nothing is certain (for example, Madeleine could have terrible taste), cafe #3 seems likely to have the best coffee, and cafe #2 is likely to have better coffee than #1. In this paper, we propose a formal framework for understanding why reasoning from three different types of actions—randomly chosen, goal-directed, and communicative—lead to qualitative differences in learning from superficially similar observations. Learning from Limited Data Traditional approaches to understanding how people learn about the world so quickly and robustly have focused on the nature of human representations and a priori biases about the physical world, investigating the biases that allow rapid and accurate learning from a limited amount of data. In concept learning, the problem has been characterized as “carving nature at its joints” and the debates have been over the types of representations that support these abilities (Gelman, 1996; Keil, 1989; Mandler, 1992; Medin & Schaffer, 1978; Nosofsky, 1984; Posner & Keele, 1968; Rosch & Mervis, 1975; Rosch, 1978). Similarly, in causal learning, the learning problem has been viewed as one of discovering the laws that govern physical world (Michotte, 1963), and debates have been over the representational and inferential mechanisms that support these abilities (Cheng, 1997; Gopnik, Glymour, Sobel, Schulz, & Danks, 2004; Griffiths & Tenenbaum, 2005; Rescorla & Wagner, 1972). These approaches have been very successful in describing reasoning in contexts where the data are (assumed to be) observed objectively. For example, in logical inference—if A, then B; observing A implies B—the conditions of observation of A are assumed to be irrelevant to the truth of B. A is simply a given. Learning from human action 5 Much of the evidence observed in human learning does not have this character. Often evidence is provided by someone, for some purpose. A potter throwing a pot, a friend fiddling with her iPod, a parent demonstrating how to tie a shoe, and a teacher conveying a mathematical concept are all creating evidence with a particular goal in mind. The goals of the pot thrower and the iPod fiddler have to do with the world—they are trying to get matter or artifacts to conform to their desires. The goals of the parent and teacher have to do with the observer; they want the observer to learn a particular fact, skill, or concept. In each of these cases, it is possible for people to learn a tremendous amount from only a small number of data points. Yet for many traditional formal approaches, learning based on limited data is nearly impossible except in the most circumscribed domains (Gold, 1967; Savage, 1951; Wolpert & Macready, 1997; Zinkevich, 2003). Most famously, Gold (1967) proved that in any formal language that is sufficiently broad to express an infinite range of possible sentences (so that the sentences could not possibly be enumerated one by one), language learning is impossible. Strikingly, this proof suggests that human languages are unlearnable! The conflict between human intuition and formal analysis creates a puzzle. How is human learning so quick and successful when formal learning frameworks suggest that it should be slow and fatally conservative? Social Learning Contexts We believe that the key to this puzzle lies in the assumptions that traditional learning theory makes about the conditions of observation. For instance, Gold’s proof assumes that the datapoints for learning are selected by an adversary. Imagine trying to learn which cafe is good when everyone is deliberately trying to mislead you! When this assumption is relaxed even slightly and data are assumed to be sampled randomly, the language-learning problem studied by Learning from human action 6 Gold is found to be considerably less difficult (Horning, 1969). Nonetheless, even learning from randomly sampled data—as opposed to data from an adversary who wants to “fool” the learner (in Gold’s words)—can still be quite difficult. Paris is a big city. Imagine trying to learn where the best coffee is by randomly sampling cafes. It would take a very long time. Yet most models adopt this sort of random-sampling assumption (Anderson, 1991; Love, Medin, & Gureckis, 2004; Goodman, Tenenbaum, Feldman, & Griffiths, 2008; Kruschke, 1992; Medin & Schaffer, 1978; Nosofsky, 1984; Nosofsky, Palemeri, & McKinley, 1994; Pothos & Chater, 2002). --------------------Insert Figure 1 about here------------------------Research on human learning paints a very different picture of how datapoints are selected. A wide variety of approaches have pointed to people and their intentions, as an important factor in learning, highlighting that data are chosen rather than random (Bruner, 1966; Vygotsky, 1978) and that observed data are often the consequence of goal-directed actions (Bandura, Ross, & Ross, 1961; Gergely & Csibra, 2003; Meltzoff & Moore, 1977) or intentional communication/teaching (Coady, 1992; Csibra & Gergely, 2009; Harris, 2002; Tomasello, 1999; Tomasello, Carpenter, Call, Behne, & Moll, 2005). For instance, Csibra and Gergely (2009) suggest that young children’s interpretation of observed data changes fundamentally based on whether the demonstrator engages the child with ostensive cues—saying the child’s name, using child-direct speech, shifting gaze between the child and the object of the demonstration—prior to the demonstration. According to their account, these cues lead children to assume that the demonstrated data are not randomly sampled instances but purposefully sampled to support broad generalizations. Learning from human action 7