TY - JOUR

T1 - Rational Approximations to Rational Models

T2 - Alternative Algorithms for Category Learning

AU - Sanborn, Adam N.

AU - Griffiths, Thomas L.

AU - Navarro, Daniel J.

N1 - Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2010/10

Y1 - 2010/10

N2 - 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.

AB - 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.

KW - Categorization

KW - Rational approximations

KW - Rational models

UR - http://www.scopus.com/inward/record.url?scp=78249247078&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78249247078&partnerID=8YFLogxK

U2 - 10.1037/a0020511

DO - 10.1037/a0020511

M3 - Article

C2 - 21038975

AN - SCOPUS:78249247078

VL - 117

SP - 1144

EP - 1167

JO - Psychological Review

JF - Psychological Review

SN - 0033-295X

IS - 4

ER -