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Rational Approximations to Rational Models: Alternative Algorithms for Category Learning

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Title: Rational Approximations to Rational Models: Alternative Algorithms for Category Learning
Language: English
Authors: Sanborn, Adam N., Griffiths, Thomas L., Navarro, Daniel J.
Source: Psychological Review. Oct 2010 117(4):1144-1167.
Availability: American Psychological Association. Journals Department, 750 First Street NE, Washington, DC 20002-4242. Tel: 800-374-2721; Tel: 202-336-5510; Fax: 202-336-5502; e-mail: order@apa.org; Web site: http://www.apa.org/publications
Peer Reviewed: Y
Physical Description: PDF
Page Count: 24
Publication Date: 2010
Document Type: Journal Articles
Reports - Evaluative
Descriptors: Models, Cognitive Processes, Psychology, Monte Carlo Methods, Computer Science, Bayesian Statistics, Inferences, Classification, Learning, Computation, Mathematics, Sampling
DOI: 10.1037/a0020511
ISSN: 0033-295X
Abstract: Rational models of cognition typically consider the abstract computational problems posed by the environment, assuming that people are capable of optimally solving those problems. This differs from more traditional formal models of cognition, which focus on the psychological processes responsible for behavior. A basic challenge for rational models is thus explaining how optimal solutions can be approximated by psychological processes. We outline a general strategy for answering this question, namely to explore the psychological plausibility of approximation algorithms developed in computer science and statistics. In particular, we argue that Monte Carlo methods provide a source of "rational process models" that connect optimal solutions to psychological processes. We support this argument through a detailed example, applying this approach to Anderson's (1990, 1991) rational model of categorization (RMC), which involves a particularly challenging computational problem. Drawing on a connection between the RMC and ideas from nonparametric Bayesian statistics, we propose 2 alternative algorithms for approximate inference in this model. The algorithms we consider include Gibbs sampling, a procedure appropriate when all stimuli are presented simultaneously, and particle filters, which sequentially approximate the posterior distribution with a small number of samples that are updated as new data become available. Applying these algorithms to several existing datasets shows that a particle filter with a single particle provides a good description of human inferences. (Contains 11 figures, 3 tables and 2 footnotes.)
Abstractor: As Provided
Number of References: 82
Entry Date: 2010
Accession Number: EJ903778
Database: ERIC
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  Data: Rational models of cognition typically consider the abstract computational problems posed by the environment, assuming that people are capable of optimally solving those problems. This differs from more traditional formal models of cognition, which focus on the psychological processes responsible for behavior. A basic challenge for rational models is thus explaining how optimal solutions can be approximated by psychological processes. We outline a general strategy for answering this question, namely to explore the psychological plausibility of approximation algorithms developed in computer science and statistics. In particular, we argue that Monte Carlo methods provide a source of "rational process models" that connect optimal solutions to psychological processes. We support this argument through a detailed example, applying this approach to Anderson's (1990, 1991) rational model of categorization (RMC), which involves a particularly challenging computational problem. Drawing on a connection between the RMC and ideas from nonparametric Bayesian statistics, we propose 2 alternative algorithms for approximate inference in this model. The algorithms we consider include Gibbs sampling, a procedure appropriate when all stimuli are presented simultaneously, and particle filters, which sequentially approximate the posterior distribution with a small number of samples that are updated as new data become available. Applying these algorithms to several existing datasets shows that a particle filter with a single particle provides a good description of human inferences. (Contains 11 figures, 3 tables and 2 footnotes.)
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