Revealing Priors on Category Structures Through Iterated Learning

We present a novel experimental method for identifying the inductive biases of human learners. The key idea behind this method is simple: we use participants’ responses on one trial to generate the stimuli they see on the next. A theoretical analysis of this “iterated learning” procedure, based on the assumption that learners are Bayesian agents, predicts that it should reveal the inductive biases of the learners, as expressed in a prior probability distribution. We test this prediction through two experiments in iterated category learning. Many of the cognitive challenges faced by human beings can be framed as inductive problems, in which observed data are used to evaluate underdetermined hypotheses. To take two common examples, in language acquisition the hypotheses are languages and the data are the utterances to which the learner is exposed, while in category learning the hypotheses are category structures and the data are the observed members of a category. Analyses of inductive problems in both philosophy (Goodman, 1955) and learning theory (Geman, Bienenstock, & Doursat, 1992; Kearns & Vazirani, 1994; Vapnik, 1995) stress the importance of combining the evidence provided by the data with a priori biases about the plausibility of hypotheses. These biases prevent learners from jumping to outlandish conclusions that might be consistent with the data, and can produce successful inductive inferences so long as they approximately capture the nature of the learner’s environment. If we want to understand how people solve inductive problems, we need to understand the biases that constrain their inferences. However, identifying these biases can be a challenge. Inductive biases can result from biological constraints on learning, general-purpose principles such as a preference for simplicity, or previous domain-specific experience, and in many cases will be a mixture of all three. Not all of these factors are available to introspection, and as a consequence assessment of the biases of learners has tended to be indirect. In the past, people’s inductive biases have been evaluated using experiments that examine whether, for example, certain category structures are easier or harder to learn (e.g., Shepard, Hovland, & Jenkins, 1961), or by assessing how well models that embody particular biases correspond to human judgments (e.g., Tenenbaum, 1999). In this paper, we explore a novel experimental method that makes it possible to directly determine the biases of learners. The basic idea behind this method is simple: having people solve a series of inductive problems where the hypothesis selected on one trial is used to generate the data observed on the next. We call this method “iterated learning”, due to its close correspondence to a class of models that have been used to study language evolution (Kirby, 2001). Our use of iterated learning is motivated by a theoretical analysis that shows that, in the case where the learners are Bayesian agents, the probability that a learner chooses a particular hypothesis will ultimately be determined by their inductive biases, as expressed in a prior probability distribution over hypotheses (Griffiths and Kalish, 2005). We tested this prediction in two experiments with stimuli for which people’s inductive biases are well understood, examining whether the outcome of iterated learning is consistent with previous work on the difficulty of learning different category structures (Shepard et al., 1961; Feldman, 2000). The plan of the paper is as follows. First, we outline the theoretical background behind our approach, laying out the formal framework that justifies the use of iterated learning as a method for determining the biases of learners. We then provide a more detailed analysis of the specific case of inferring category structures from observed members, presenting a Bayesian model of this task. The predictions of this model, and of our more general theoretical framework, are tested through two experiments. We close by discussing the implications of these experiments for iterated learning as a method for revealing inductive biases, and some future directions. Iterated learning reveals inductive biases Iterated learning has been discussed most extensively in the context of language evolution, where it is seen as a potential explanation for the structure of human languages. Language, like many other aspects of human culture, can only be learned from other people, who were once learners themselves. The consequences of this fact have been studied using what Kirby (2001) termed the iterated learning model, in which several generations of one or more learners each learn from data produced by the previous generation. For example, with one learner per generation, the first learner is exposed to some initial data, forms a hypothesis about the language it represents, and generates new data from that language. This new data are passed to the second learner, who infers a hypothesis and generates data from it that are provided to the third learner, and so forth. Through simulations, Kirby and his colleagues have shown that languages with properties similar to those of human languages can emerge from iterated learning with simple learning algorithms (Kirby, 2001; Smith, Kirby, & Brighton, 2003). Griffiths and Kalish (2005) provided a formal analysis of the consequences of iterated learning for the case where learners are Bayesian agents. Assume that a learner has a set of hypotheses, H, and that their biases are encoded through a prior probability distribution, P (h), specifying the probability a learner assigns to the truth of each hypothesis h ∈ H before seeing some data d. Bayesian agents evaluate hypotheses using a principle of probability theory called Bayes’ rule. This principle states that the posterior probability P (h|d) that should be assigned to each hypothesis h after seeing d is P (h|d) = P (d|h)P (h)