A Rational Model of Function Learning

Overview

Journal Psychon Bull Rev

Specialty Psychology

Date 2015 Mar 4

PMID 25732094

Citations 17

Authors

Christopher G Lucas

Thomas L Griffiths

Joseph J Williams

Michael L Kalish

Affiliations

Soon will be listed here.

Abstract

Theories of how people learn relationships between continuous variables have tended to focus on two possibilities: one, that people are estimating explicit functions, or two that they are performing associative learning supported by similarity. We provide a rational analysis of function learning, drawing on work on regression in machine learning and statistics. Using the equivalence of Bayesian linear regression and Gaussian processes, which provide a probabilistic basis for similarity-based function learning, we show that learning explicit rules and using similarity can be seen as two views of one solution to this problem. We use this insight to define a rational model of human function learning that combines the strengths of both approaches and accounts for a wide variety of experimental results.

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References

McDaniel M, Busemeyer J . The conceptual basis of function learning and extrapolation: comparison of rule-based and associative-based models. Psychon Bull Rev. 2005; 12(1):24-42. DOI: 10.3758/bf03196347. View

Koh K, Meyer D . Function learning: induction of continuous stimulus-response relations. J Exp Psychol Learn Mem Cogn. 1991; 17(5):811-36. DOI: 10.1037//0278-7393.17.5.811. View

Kaush M, Griffiths T, Lewandowsky S . Iterated learning: intergenerational knowledge transmission reveals inductive biases. Psychon Bull Rev. 2007; 14(2):288-94. DOI: 10.3758/bf03194066. View

DeLosh E, Busemeyer J, McDaniel M . Extrapolation: the sine qua non for abstraction in function learning. J Exp Psychol Learn Mem Cogn. 1997; 23(4):968-86. DOI: 10.1037//0278-7393.23.4.968. View

Kalish M, Lewandowsky S, Kruschke J . Population of linear experts: knowledge partitioning and function learning. Psychol Rev. 2004; 111(4):1072-99. DOI: 10.1037/0033-295X.111.4.1072. View

Chater N, Vitanyi P . Simplicity: a unifying principle in cognitive science?. Trends Cogn Sci. 2003; 7(1):19-22. DOI: 10.1016/s1364-6613(02)00005-0. View

Shepard R . Toward a universal law of generalization for psychological science. Science. 1987; 237(4820):1317-23. DOI: 10.1126/science.3629243. View

Lewandowsky S, Kalish M, Ngang S . Simplified learning in complex situations: knowledge partitioning in function learning. J Exp Psychol Gen. 2002; 131(2):163-93. DOI: 10.1037//0096-3445.131.2.163. View

Erickson M, Kruschke J . Rules and exemplars in category learning. J Exp Psychol Gen. 1998; 127(2):107-40. DOI: 10.1037//0096-3445.127.2.107. View

10.

Sanborn A, Griffiths T, Navarro D . Rational approximations to rational models: alternative algorithms for category learning. Psychol Rev. 2010; 117(4):1144-67. DOI: 10.1037/a0020511. View

11.

Speekenbrink M, Shanks D . Learning in a changing environment. J Exp Psychol Gen. 2010; 139(2):266-98. DOI: 10.1037/a0018620. View

12.

Hemmer P, Tauber S, Steyvers M . Moving beyond qualitative evaluations of Bayesian models of cognition. Psychon Bull Rev. 2014; 22(3):614-28. DOI: 10.3758/s13423-014-0725-z. View

13.

Kwantes P, Neal A . Why people underestimate y when extrapolating in linear functions. J Exp Psychol Learn Mem Cogn. 2006; 32(5):1019-30. DOI: 10.1037/0278-7393.32.5.1019. View

14.

Kalish M . Learning and extrapolating a periodic function. Mem Cognit. 2013; 41(6):886-96. DOI: 10.3758/s13421-013-0306-9. View

15.

Bott L, Heit E . Nonmonotonic extrapolation in function learning. J Exp Psychol Learn Mem Cogn. 2004; 30(1):38-50. DOI: 10.1037/0278-7393.30.1.38. View

16.

McDaniel M, Dimperio E, Griego J, Busemeyer J . Predicting transfer performance: a comparison of competing function learning models. J Exp Psychol Learn Mem Cogn. 2009; 35(1):173-95. DOI: 10.1037/a0013982. View

17.

Tenenbaum J, Griffiths T, Kemp C . Theory-based Bayesian models of inductive learning and reasoning. Trends Cogn Sci. 2006; 10(7):309-18. DOI: 10.1016/j.tics.2006.05.009. View