A rational model of function learning

Psychonomic Bulletin and Review

Volumn 22, Issue 5, 2015, Pages 1193-1215

  Lucas, Christopher G ^a   Griffiths, Thomas L ^b   Williams, Joseph J ^c   Kalish, Michael L ^d  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c HARVARD UNIVERSITY   (United States)

^d SYRACUSE UNIVERSITY   (United States)

Author keywords

Bayesian modeling; Function learning

Indexed keywords

BAYES THEOREM; CONCEPT FORMATION; HUMAN; LEARNING; MACHINE LEARNING; NORMAL DISTRIBUTION; PROBLEM SOLVING; PSYCHOLOGICAL MODEL; STATISTICAL MODEL;

ASSOCIATION LEARNING; BAYES THEOREM; CONCEPT FORMATION; HUMANS; LINEAR MODELS; MACHINE LEARNING; MODELS, PSYCHOLOGICAL; NORMAL DISTRIBUTION; PROBLEM SOLVING; TRANSFER (PSYCHOLOGY);

EID: 84942371597     PISSN: 10699384     EISSN: 15315320     Source Type: Journal    
DOI: 10.3758/s13423-015-0808-5     Document Type: Review

References (53)

1. Aldous, D. (1985). Exchangeability and related topics, In École d’été de probabilités de Saint-Flour, XIII—1983. (pp. 1–198). Berlin: Springer.
2. Anderson, J.R. (1990). The adaptive character of thought. NJ: Erlbaum Hillsdale.
3. Anderson, J.R. (1991). The adaptive nature of human categorization. Psychological Review, 98(3), 409–429.
4. Ashby, F.G., & Alfonso-Reese, L.A. (1995). Categorization as probability density estimation. Journal of Mathematical Psychology, 39, 216–233.
5. Bernardo, J.M., & Smith, A.F.M. (1994). Bayesian theory. New York: Wiley.
6. Borji, A., & Itti, L. (2013). Bayesian optimization explains human active search. In Burges, C., Bottou, L., Welling, M., Ghahramani, Z., Weinberger, K. (Eds.), Advances in Neural Information Processing Systems 26. (pp. 55–63): Curran Associates, Inc.
7. Bott, L., & Heit, E. (2004). Nonmonotonic extrapolation in function learning. Journal of Experimental Psychology: Learning Memory, and Cognition, 30(1).
8. Brehmer, B. (1971). Subjects’ ability to use functional rules. Psychonomic Science, 24, 259–260.
9. Brehmer, B. (1974). Hypotheses about relations between scaled variables in the learning of probabilistic inference tasks. Organizational Behavior and Human Decision Processes, 11, 1– 27.
10. Brehmer, B. (1976). Subjects’ ability to find the parameters of functional rules in probabilistic inference tasks. Organizational Behavior and Human Performance, 17(2), 388–397.
11. Brehmer, B., Alm, H., Warg, L. (1985). Learning and hypothesis testing in probabilistic inference tasks. Scandinavian Journal of Psychology, 26(1), 305–313.
12. Busemeyer, J.R., Byun, E., DeLosh, E.L., McDaniel, M.A. (1997). Learning functional relations based on experience with input-output pairs by humans and artificial neural networks. In Lamberts, K., & Shanks, D. (Eds.), Concepts and Categories. (pp. 405–437). Cambridge: MIT Press.
13. Byun, E. (1995). Interaction between prior knowledge and type of nonlinear relationship on function learning. Purdue University: Unpublished doctoral dissertation.
14. Carroll, J. (1963). Functional learning: The learning of continuous functional mappings relating stimulus and response continua. NJ: Educational Testing Service Princeton.
15. Chater, N., & Vitanyi, P. (2003). Simplicity: a unifying principle in cognitive science. Trends in Cognitive Science, 7, 19–22.
16. DeLosh, E.L., Busemeyer, J.R., McDaniel, M.A. (1997). Extrapolation: The sine qua non of abstraction in function learning. Journal of Experimental Psychology: Learning Memory, and Cognition, 23, 968–986.
17. Duvenaud, D., Lloyd, J.R., Grosse, R., Tenenbaum, J.B., Ghahramani, Z. (2013). Structure discovery in nonparametric regression through compositional kernel search. arXiv preprint. arXiv:1302.4922.
18. Erickson, M., & Kruschke, J. (1998). Rules and exemplars in category learning. Journal of Experimental Psychology: General, 127(2), 107.
19. Gelman, A., Carlin, J., Stern, H., Rubin, D (2004). Bayesian data analysis. CRC Press.
20. Gilks, W., Richardson, S., Spiegelhalter, D.J. (Eds.) (1996). Markov Chain Monte Carlo in Practice. UK: Chapman and Hall Suffolk.
21. Griffiths, T.L., Lucas, C.G., Williams, J.J., Kalish, M.L. (2009). Modeling human function learning with Gaussian processes. Advances in Neural Information Processing Systems, 21.
22. Griffiths, T.L., Vul, E., Sanborn, A. (2012). Bridging levels of analysis for probabilistic models of cognition. Current Directions in Psychological Science, 21(4), 263–268.
23. Hemmer, P., Tauber, S., Steyvers, M. (2014). Moving beyond qualitative evaluations of Bayesian models of cognition. Psychonomic Bulletin & Review, 1–15.
24. Hensman, J., Fusi, N., Lawrence, N.D. (2013). arXiv:1309.6835.
25. Jacobs, R., Jordan, M., Nowlan, S., Hinton, G. (1991). Adaptive mixtures of local experts. Neural Computation, 3(1), 79–87.
26. Kalish, M.L. (2013). Learning and extrapolating a periodic function. Memory & Cognition, 41(6), 886–896.
27. Kalish, M.L., Griffiths, T.L., Lewandowsky, S. (2007). Iterated learning intergenerational knowledge transmission reveals inductive biases Psychonomic Bulletin and Review.
28. Kalish, M.L., Lewandowsky, S., Kruschke, J. (2004). Population of linear experts: Knowledge partitioning and function learning. Psychological Review, 111, 1072–1099.
29. Kirby, S. (2001). Spontaneous evolution of linguistic structure: An iterated learning model of the emergence of regularity and irregularity. IEEE Journal of Evolutionary Computation, 5, 102–110.
30. Koh, K., & Meyer, D. (1991). Function learning: Induction of continuous stimulus-response relations. Journal of Experimental Psychology: Learning Memory, and Cognition, 17(5), 811–836.
31. Kwantes, P., & Neal, A. (2006). Why people underestimate y when extrapolating in linear functions. Journal of Experimental Psychology: Learning Memory, and Cognition, 32(5), 1019.
32. Lewandowsky, S.L., Kalish, M.L., Ngang, S.K. (2002). Simplified learning in complex situations: Knowledge partitioning in human learning. Journal of Experimental Psychology: General, 131, 163–193.
33. Lindsey, R.V., Mozer, M.C., Huggins, W.J., Pashler, H. (2013). Optimizing instructional policies. In Burges, C., Bottou, L., Welling, M., Ghahramani, Z., Weinberger, K. (Eds.), Advances in Neural Information Processing Systems 26. (pp. 2778–2786): Curran Associates, Inc.
34. Little, D.R., & Shiffrin, R.M. (2009). Simplicity bias in the estimation of causal functions. In Proceedings of the Thirty-First Annual Conference of the Cognitive Science Society.
35. Lucas, C.G., Sterling, D.J., Kemp, C. (2012). Superspace extrapolation reveals inductive biases in function learning, In: Miyake, N., Peebles, D., and Cooper, R. P., editors, Proceedings of the 34th Annual Conference of the Cognitive Science Society. Cognitive Science Society.
36. MacKay, D. (1995). Probable networks and plausible predictions—a review of practical Bayesian methods for supervised neural networks. Network: Computation in Neural Systems, 6, 469–505.
37. Marr, D., & Vision. W.H. (1982). San Francisco CA: Freeman.
38. McDaniel, M., & Busemeyer, J. (2005). The conceptual basis of function learning and extrapolation: Comparison of rule-based and associative-based models. Psychonomic Bulletin & Review, 12(1), 24.
39. McDaniel, M., Dimperio, E., Griego, J., Busemeyer, J. (2009). Predicting transfer performance: A comparison of competing function learning models. Journal of Experimental Psychology: Learning Memory, and Cognition, 35(1), 173.
40. Meeds, E., & Osindero, S. (2006). Advances in Neural Information Processing Systems 18. In Weiss, Y., Schölkopf, B., Platt, J. (Eds.) (pp. 883–890). Cambridge, MA: MIT Press.
41. Minh, H., Niyogi, P., Yao, Y. (2006). Mercer?s theorem, feature maps, and smoothing Learning theory.
42. Mitchell, T.M. (1997). Machine learning. New York: McGraw Hill.
43. Navarro, D.J., Griffiths, T.L., Steyvers, M., Lee, M.D. (2006). Modeling individual differences using Dirichlet processes. Journal of Mathematical Psychology, 50, 101–122.
44. Neal, R.M. (1994). Priors for infinite networks technical report, Technical Report CRG-TR-94-1 Department of Computer Science University of Toronto.
45. Neal, R.M. (1998). Markov chain sampling methods for Dirichlet process mixture models Technical Report 9815. University of Toronto: Department of Statistics.
46. Rasmussen, C.E., & Ghahramani, Z. (2002). Infinite mixtures of Gaussian process experts In: Dietterich, T., Becker, S., and Ghahramani, Z., editors, Advances in Neural Information Processing Systems 14, pages 881–888. MIT Press.
47. Rasmussen, C.E., & Williams, C.K.I. (2006). Gaussian processes for machine learning. MIT Press.
48. Sanborn, A.N., Griffiths, T.L., Navarro, D.J. (2010). Rational approximations to rational models: alternative algorithms for category learning. Psychological Review, 117(4), 1144.
49. Shepard, R.N. (1987). Towards a universal law of generalization for psychological science. Science, 237, 1317–1323.
50. Speekenbrink, M., & Shanks, D.R. (2010). Learning in a changing environment. Journal of Experimental Psychology: General, 139(2), 266.
51. Tenenbaum, J.B., Griffiths, T.L., Kemp, C. (2006). Theory-based Bayesian models of inductive learning and reasoning. Trends in Cognitive Science, 10, 309–318.
52. Williams, C.K.I. (1998). Prediction with Gaussian processes: From linear regression to linear prediction and beyond. In Jordan, M. I. (Ed.), Learning in Graphical Models. (pp. 599–621). Cambridge MA.: MIT Press.
53. Wilson, A.G., & Adams, R.P. (2013). Gaussian process covariance kernels for pattern discovery and extrapolation arXiv preprint. arXiv:1302.4245.