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• W2622545963 abstract "Revealing Priors on Category Structures Through Iterated Learning Thomas L. Griffiths (Thomas Griffiths@brown.edu) Brian R. Christian (Brian Christian@brown.edu) Department of Cognitive and Linguistic Sciences, Brown University, Providence, RI 02912 Michael L. Kalish (kalish@louisiana.edu) Institute of Cognitive Science, University of Louisiana at Lafayette, Lafayette, LA 70504 Abstract 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’ re- sponses on one trial to generate the stimuli they see on the next. A theoretical analysis of this “iterated learn- ing” 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 be- ings can be framed as inductive problems, in which ob- served data are used to evaluate underdetermined hy- potheses. 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 struc- tures and the data are the observed members of a cate- gory. Analyses of inductive problems in both philosophy (Goodman, 1955) and learning theory (Geman, Bienen- stock, & Doursat, 1992; Kearns & Vazirani, 1994; Vap- nik, 1995) stress the importance of combining the evi- dence 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 in- ductive 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 con- strain their inferences. However, identifying these biases can be a challenge. Inductive biases can result from bi- ological constraints on learning, general-purpose prin- ciples 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 avail- able 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 “iter- ated learning”, due to its close correspondence to a class of models that have been used to study language evolu- tion (Kirby, 2001). Our use of iterated learning is mo- tivated by a theoretical analysis that shows that, in the case where the learners are Bayesian agents, the proba- bility that a learner chooses a particular hypothesis will ultimately be determined by their inductive biases, as ex- pressed in a prior probability distribution over hypothe- ses (Griffiths and Kalish, 2005). We tested this predic- tion in two experiments with stimuli for which people’s inductive biases are well understood, examining whether the outcome of iterated learning is consistent with previ- ous 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 iter- ated 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 lan- guages. 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 repre- sents, 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" @default.
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• W2622545963 title "Revealing Priors on Category Structures Through Iterated Learning - eScholarship" @default.
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