Sampling Assumptions in Inductive Generalization

Cognitive Science

Volumn 36, Issue 2, 2012, Pages 187-223

  Navarro, Daniel J ^a   Dry, Matthew J ^a   Lee, Michael D ^b  

^a UNIVERSITY OF ADELAIDE   (Australia)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Bayesian modeling; Generalization; Inductive inference

Indexed keywords

ARTICLE; BAYES THEOREM; CONCEPT FORMATION; HUMAN; LEARNING; PSYCHOLOGICAL MODEL;

BAYES THEOREM; CONCEPT FORMATION; GENERALIZATION (PSYCHOLOGY); HUMANS; MODELS, PSYCHOLOGICAL;

EID: 84863275363     PISSN: 03640213     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1551-6709.2011.01212.x     Document Type: Article

References (56)

1. Anderson, J. R. (1991). The adaptive nature of human categorization. Psychological Review, 98(3), 409-429.
2. Anderson, J. R., & Milson, R. (1989). Human memory: An adaptive perspective. Psychological Review, 96, 703-719.
3. Anderson, J. R., & Schooler, L. J. (1991). Reflections of the environment in memory. Psychological Science, 2, 396-408.
4. Ennis, D. M. (1988). Confusable and discriminable stimuli: Comment on Nosofsky (1986) and Shepard (1986). Journal of Experimental Psychology: General, 117, 408-411.
5. Estes, W. K. (1956). The problem of inference from curves based on group data. Psychological Bulletin, 53, 134-140.
6. Gigerenzer, G., & Brighton, H. (2009). Homo heuristicus: Why biased minds make better inferences. Topics in Cognitive Science, 1, 107-143.
7. Gigerenzer, G., & Goldstein, D. G. (1996). Reasoning the fast and frugal way: Models of bounded rationality. Psychological Review, 103, 650-669.
8. Gilks, W., Richardson, S., & Spiegelhalter, D. J. (Eds.). (1996). Markov chain Monte Carlo in practice. Suffolk, England: Chapman and Hall.
9. Gold, E. M. (1967). Language identification in the limit. Information and Control, 10, 447-474.
10. Goldwater, S., Griffiths, T. L., & Johnson, M. (2006). Interpolating between types and tokens by estimating power-law generators. In Y. Weiss, B. Schölkopf, & J. Platt (Eds.), Advances in neural information processing systems (Vol. 18, pp. 459-466). Cambridge, MA: MIT Press.
11. Goodman, N. (1955). Fact, fiction, and forecast. Cambridge, MA: Harvard University Press.
12. Hastie, T., Tibshirani, R., & Friedman, J. (2001). The elements of statistical learning. New York: Springer.
13. Hausser, J., & Strimmer, K. (2009). Entropy inference and the James-Stein estimator, with application to nonlinear gene association networks. Journal of Machine Learning Research, 10, 1469-1484.
14. Heit, E. (1998). A Bayesian analysis of some forms of inductive reasoning. In M. Oaksford & N. Chater (Eds.), Rational models of cognition (pp. 248-274). Oxford, England: Oxford University Press.
15. Hinton, G. E., McClelland, J. L., & Rumelhart, D. E. (1986). Distributed representations. In D. E. Rumelhart & J. L. McClelland (Eds.), Parallel distributed processing: Explorations in the microstructure of cognition. vol. 1: Foundations (pp. 75-109). Cambridge, MA: MIT Press.
16. Huber, P. J. (1981). Robust statistics. New York: Wiley.
17. James, W., & Stein, C. (1961). Estimation with quadratic loss. In J. Neyman (Ed.), Proceedings of the fourth berkeley symposium on mathematical statistics and probability, vol 1 (pp. 361-379). Berkeley: University of California Press.
18. Kemp, C., & Tenenbaum, J. B. (2008). The discovery of structural form. Proceedings of the National Academy of Sciences, 105, 10687-10692.
19. Kemp, C., & Tenenbaum, J. B. (2009). Structured statistical models of inductive reasoning. Psychological Review, 116, 20-58.
20. Kruschke, J. K. (1992). Alcove: An exemplar-based connectionist model of category learning. Psychological Review, 99(1), 22-44.
21. Lee, M. D., & Webb, M. R. (2005). Modeling individual differences in cognition. Psychonomic Bulletin & Review, 12, 605-621.
22. Lee, M. D., Chandrasena, L., & Navarro, D. J. (2002). Using cognitive decision models to prioritize E-mails. In W. D. Gray & C. D. Schunn (Eds.), Proceedings of the 24th Annual Conference of the Cognitive Science Society (pp. 478-483). Mahwah, NJ: Lawrence Erlbaum.
23. Love, B. C., Medin, D. L., & Gureckis, T. M. (2004). SUSTAIN: A network model of category learning. Psychological Review, 11, 309-332.
24. Marr, D. (1982). Vision. San Francisco, CA: W. H. Freeman.
25. Muggleton, S. (1997). Learning from positive data. In S. Muggleton (Ed.), Selected papers from the 6th international workshop on inductive logic programming (pp. 358-376). Berlin, Germany: Springer-Verlag.
26. Myung, I. J. (2000). The importance of complexity in model selection. Journal of Mathematical Psychology, 44, 190-204.
27. Myung, J. I., Navarro, D. J., & Pitt, M. A. (2006). Model selection by normalized maximum likelihood. Journal of Mathematical Psychology, 50, 167-179.
28. Navarro, D. J. (2006). From natural kinds to complex categories. In R. Sun & N. Miyake (Eds.), Proceedings of the 28th Annual Conference of the Cognitive Science Society (pp. 621-626). Mahwah, NJ: Lawrence Erlbaum.
29. Navarro, D. J., & Perfors, A. F. (2010). Similarity, feature discovery, and the size principle. Acta Psychologica, 133, 256-268.
30. 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.
31. Navon, D. (1978). The importance of being conservative: Some reflections on human Bayesian behavior. British Journal of Mathematical and Statistical Psychology, 31, 33-48.
32. Nosofsky, R. M. (1984). Choice, similarity and the context theory of classification. Journal of Experimental Psychology, Learning, Memory and Cognition, 10(1), 104-114.
33. Osherson, D. N., Smith, E. E., Wilkie, O., Lopez, A., & Shafir, E. (1990). Category-based induction. Psychological Review, 97(2), 185-200.
34. Pavlov, I. P. (1927). Conditioned reflexes. London, UK: Oxford University Press.
35. Perfors, A. F., Tenenbaum, J. B., & Regier, T. (2006). Poverty of the stimulus? A rational approach. In Proceedings of the 28th Annual Conference of the Cognitive Science Society. Mahwah, NJ: Lawrence Erlbaum.
36. Perfors, A. F., Tenenbaum, J. B., & Regier, T. (2011). The learnability of abstract syntactic principles. Cognition, 118(3), 306-338.
37. Phillips, L. D., & Edwards, W. (1966). Conservatism in a simple probability inference task. Journal of Experimental Psychology, 72, 346-357.
38. Pitt, M. A., Myung, I. J., & Zhang, S. (2002). Toward a method of selecting among computational models of cognition. Psychological Review, 109(3), 472-491.
39. Popper, K. R. (1935/1990). The logic of scientific discovery. Boston: Unwin Hyman.
40. Ratcliff, R., & Tuerlinckx, F. (2002). Estimating parameters of the diffusion model: Approaches to dealing with contaminant reaction times and parameter variability. Psychonomic Bulletin and Review, 9, 438-481.
41. Russell, S. J. (1986). A quantitative analysis of analogy by similarity. In T. Kehler & S. Rosenschein (Eds.), Proceedings of the national conference on artificial intelligence (pp. 284-288). Los Altos, CA: Morgan Kaufmann.
42. Sanjana, N. E., & Tenenbaum, J. B. (2003). Bayesian models of inductive generalization. In S. Becker, S. Thrun, & K. Obermayer (Eds.), Advances in neural information processing systems (Vol. 15, pp. 51-58). Cambridge, MA: MIT Press.
43. Schäfer, J., & Strimmer, K. (2005). A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Statistical Applications in Genetics and Molecular Biology, 4.
44. Shepard, R. N. (1987). Toward a universal law of generalization for psychological science. Science, 237, 1317-1323.
45. Sloman, S. (1993). Feature-based induction. Cognitive Psychology, 25, 231-280.
46. Solomonoff, R. J. (1964). A formal theory of inductive inference. Part I. Information and Control, 7, 1-22.
47. Stein, C. (1956). Inadmissibility of the usual estimator for the mean of a multivariate distribution. In J. Neyman (Ed.), Proceedings of the third berkeley symposium on mathematical statistics and probability, vol 1 (pp. 197-206). Berkeley: University of California Press.
48. Tenenbaum, J. B. (1999). A Bayesian framework for concept learning. Unpublished doctoral dissertation, Massachussets Institute of Technology, Cambridge, MA.
49. Tenenbaum, J. B., & Griffiths, T. L. (2001a). Generalization, similarity, and Bayesian inference. Behavioral and Brain Sciences, 24, 629-641.
50. Tenenbaum, J. B., & Griffiths, T. L. (2001b). Some specifics about generalization. Behavioral and Brain Sciences, 24, 762-778.
51. Tversky, A. (1977). Features of similarity. Psychological Review, 84(4), 327-352.
52. Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185, 1124-1131.
53. Welsh, M. B., & Navarro, D. J. (2007). Seeing is believing: Priors, trust and base rate neglect. In D. S. McNamara & J. G. Trafton (Eds.), Proceedings of the 29th Annual Conference of the Cognitive Science Society (pp. 701-705). Austin, TX: Cognitive Science Society.
54. Xu, F., & Tenenbaum, J. B. (2007a). Sensitivity to sampling in Bayesian word learning. Developmental Science, 10, 288-297.
55. Xu, F., & Tenenbaum, J. B. (2007b). Word learning as Bayesian inference. Psychological Review, 114, 245-272.
56. Zeigenfuse, M. D., & Lee, M. D. (2010). A general latent-assignment approach for modeling psychological contaminants. Journal of Mathematical Psychology, 54, 354-362.