Sanborn, Adam N., Griffiths, Thomas L. and Navarro, Daniel J. (2010) Rational approximations to rational models : alternative algorithms for category learning. Psychological Review, Vol.117 (No.4). pp. 1144-67. ISSN 1939-1471

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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.

Item Type:	Journal Article
Subjects:	B Philosophy. Psychology. Religion > BF Psychology R Medicine > RC Internal medicine > RC0321 Neuroscience. Biological psychiatry. Neuropsychiatry
Divisions:	Faculty of Science > Psychology
Library of Congress Subject Headings (LCSH):	Categorization (Psychology), Cognition, Monte Carlo method
Journal or Publication Title:	Psychological Review
Publisher:	American Psychological Association
ISSN:	1939-1471
Date:	2010
Volume:	Vol.117
Number:	No.4
Page Range:	pp. 1144-67
Identification Number:	10.1037/a0020511
Status:	Peer Reviewed
Funder:	National Science Foundation (U.S.), United States. Air Force. Office of Scientific Research
Grant number:	IIS-0845410 (NSF), FA9550-07-1-0351 (AFOSR)
References:	Aldous, D. (1985). Exchangeability and related topics. In P. L. Hennequin (Ed.), E´ cole d’e´te´ de probabilite´s de Saint-Flour, XIII—1983 (pp. 1–198). Berlin, Germany: Springer. Anderson, J. R. (1990). The adaptive character of thought. Hillsdale, NJ: Erlbaum. Anderson, J. R. (1991). The adaptive nature of human categorization. Psychological Review, 98, 409–429. Antoniak, C. (1974). Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. The Annals of Statistics, 2, 1152– 1174. Anzai, Y., & Simon, H. A. (1979). The theory of learning by doing. Psychological Review, 86, 124–140. Ashby, F. G., & Alfonso-Reese, L. A. (1995). Categorization as probability density estimation. Journal of Mathematical Psychology, 39, 216–233. Bishop, C. M. (2006). Pattern recognition and machine learning. New York, NY: Springer. Blackwell, D., & MacQueen, J. (1973). Ferguson distributions via Polya urn schemes. The Annals of Statistics, 1, 353–355. Brown, S. D., & Steyvers, M. (2009). Detecting and predicting changes. Cognitive Psychology, 58, 49–67. Chater, N., & Oaksford, M. (1999). Ten years of the rational analysis of cognition. Trends in Cognitive Sciences, 3, 57–65. Daw, N. D., & Courville, A. C. (2008). The pigeon as particle filter. In J. Platt, D. Koller, Y. Singer, & S. Roweis (Eds.), Advances in neural information processing systems (Vol. 20, pp. 369–376). Cambridge, MA: MIT Press. Doucet, A., de Freitas, N., & Gordon, N. (2001). Sequential Monte Carlo methods in practice. New York, NY: Springer. Escobar, M. D., & West, M. (1995). Bayesian density estimation and inference using mixtures. Journal of the American Statistical Association, 90, 577–588. Fearnhead, P. (2004). Particle filters for mixture models with an unknown number of components. Statistics and Computing, 14, 11–21. Ferguson, T. S. (1973). A Bayesian analysis of some nonparametric problems. The Annals of Statistics, 1, 209–230. Ferguson, T. S. (1983). Bayesian density estimation by mixtures of normal distributions. In M. Rizvi, J. Rustagi, & D. Siegmund (Eds.), Recent advances in statistics (pp. 287–302). New York, NY: Academic Press. Fiedler, K., & Juslin, P. (Eds.). (2006). Information sampling and adaptive cognition. Cambridge, England: Cambridge University Press. Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2004). Bayesian data analysis. Boca Raton, FL: Chapman and Hall/CRC. Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721–741. Gigerenzer, G., & Brighton, H. (2009). Homo heuristicus: Why biased minds make better inferences. Topics in Cognitive Science, 1, 107–143. Gigerenzer, G., & Todd, P. M. (1999). Simple heuristics that make us smart. Oxford, England: Oxford University Press. Gilks, W. R., Richardson, S., & Spiegelhalter, D. J. (Eds.). (1996). Markov chain Monte Carlo in practice. Suffolk, England: Chapman and Hall. Gordon, N. J., Salmond, D. J., & Smith, A. F. M. (1993). Novel approach to non-linear/non-Gaussian Bayesian state estimation. IEE Proceedings-F, 140, 107–113. Griffiths, T. L., Canini, K. R., Sanborn, A. N., & Navarro, D. (2007). Unifying rational models of categorization via the hierarchical Dirichlet process. In D. S. McNamara & J. G. Trafton (Eds.), Proceedings of the 29th annual conference of the Cognitive Science Society (pp. 323–328). Hillsdale, NJ: Erlbaum. Griffiths, T., Sanborn, A., Canini, K., & Navarro, D. (2008). Categorization as nonparametric Bayesian density estimation. In Oaksford, M. & Chater, N. (Eds.), Probabalistic mind: Prospects for rational models of cognition (pp. 303–328). Oxford, England: Oxford University Press. Griffiths, T., Sanborn, A., Canini, K., Navarro, D., & Tenenbaum, J. (in press). Nonparametric Bayesian models of categorization. In E. M. Pothos & A. J. Wills, Formal approaches in cognition. New York, NY: Cambridge University Press. Griffiths, T. L., & Tenenbaum, J. B. (2005). Structure and strength in causal induction. Cognitive Psychology, 51, 354–384. Hastie, T., Tibshirani, R., & Friedman, J. (2001). The elements of statistical learning: Data mining, inference, and prediction. New York, NY: Springer. Hubert, L., & Arabie, P. (1985). Comparing partitions. Journal of Classification, 2, 193–218. Kotovsky, K., Hayes, J. R., & Simon, H. A. (1985). Why are some problems hard? Evidence from the Tower of Hanoi. Cognitive Psychology, 17, 248–294. Kruschke, J. K. (2006a). Locally Bayesian learning. In R. Sun & N. Miyake, Proceedings of the 28th annual meeting of the Cognitive Science Society (pp. 453–458). Hillsdale, NJ: Erlbaum. Kruschke, J. K. (2006b). Locally Bayesian learning with applications to retrospective revaluation and highlighting. Psychological Review, 113, 677–699. Lee, M. D., & Cummins, T. D. R. (2004). Evidence accumulation in decision making: Unifying the “take the best” and “rational” models. Psychonomic Bulletin & Review, 11, 343–352. Levy, R., Reali, F., & Griffiths, T. L. (2009). Modeling the effects of memory on human online sentence processing with particle filters. In D. Koller, D. Schuurmans, Y. Bengio, & L. Bottou (Eds.), Advances in neural information processing systems (Vol. 21, pp. 937–944). Mackay, D. J. C. (2003). Information theory, inference, and learning algorithms. Cambridge, England: Cambridge University Press. Marr, D. (1982). Vision. San Francisco, CA: Freeman. Medin, D. L., & Bettger, J. G. (1994). Presentation order and recognition of categorically related examples. Psychonomic Bulletin & Review, 1, 250–254. Medin, D. L., & Schaffer, M. M. (1978). Context theory of classification learning. Psychological Review, 85, 207–238. Medin, D. L., & Schwanenflugel, P. J. (1981). Linear separability in classification learning. Journal of Experimental Psychology: Human Learning and Memory, 7, 355–368. Motwani, R., & Raghavan, P. (1996). Randomized algorithms. ACM Computing Surveys, 28, 33–37. Mozer, M., Pashler, H., & Homaei, H. (2008). Optimal predictions in everyday cognition: The wisdom of individuals or crowds? Cognitive Science, 32, 1133–1147. Murdock, B. B. (1962). The serial position effect of free recall. Journal of Experimental Psychology, 64, 482–488. Navarro, D. J. (2007). On the interaction between exemplar-based concepts and a response scaling process. Journal of Mathematical Psychology, 51, 85–98. 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. Neal, R. M. (1993). Probabilistic inference using Markov Chain Monte Carlo methods (Technical Report No. CRG-TR-93–1). Toronto, Ontario, Canada: Department of Computer Science, University of Toronto. Neal, R. M. (1998). Markov chain sampling methods for Dirichlet process mixture models (Technical Report No. 9815). Toronto, Ontario, Canada: Department of Statistics, University of Toronto. Nosofsky, R. M. (1986). Attention, similarity, and the identificationcategorization relationship. Journal of Experimental Psychology: General, 115, 39–57. RATIONAL APPROXIMATIONS TO CATEGORY LEARNING 1163 Nosofsky, R. M. (1988). Similarity, frequency, and category representations. Journal of Experimental Psychology: Learning, Memory, and Cognition, 14, 54–65. Nosofsky, R. M. (1998). Optimal performance and exemplar models of classification. In M. Oaksford & N. Chater (Eds.), Rational models of cognition (pp. 218–247). Oxford, England: Oxford University Press. Nosofsky, R. M., Gluck, M., Palmeri, T. J., McKinley, S. C., & Glauthier, P. (1994). Comparing models of rule-based classification learning: A replication and extension of Shepard, Hovland, and Jenkins (1961). Memory & Cognition, 22, 352–369. Nosofsky, R. M., & Palmeri, T. J. (1997). An exemplar-based random walk model of speeded classification. Psychological Review, 104, 266–300. Nosofsky, R. M., & Zaki, S. R. (2002). Exemplar and prototype models revisited: Response strategies, selective attention, and stimulus generalization. Journal of Experimental Psychology: Learning, Memory, and Cognition, 28, 924–940. Oaksford, M., & Chater, N. (1994). A rational analysis of the selection task as optimal data selection. Psychological Review, 101, 608–631. Oaksford, M., & Chater, N. (Eds.). (1998). Rational models of cognition. Oxford, England: Oxford University Press. Perfors, A. F., & Navarro, D. J. (2009). Confirmation bias is rational when hypotheses are sparse. In N. Taatgen, H. van Rijn, L. Schomaker, & J. Nerbonne (Eds.), Proceedings of the 31st annual conference of the Cognitive Science Society (pp. 2471–2476). Austin, TX: Cognitive Science Society. Rasmussen, C. (2000). The infinite Gaussian mixture model. In S. A. Solla, T. K. Leen, & K. R. Mu¨ller, Advances in neural information processing systems (Vol. 12, pp. 554–560). Cambridge, MA: MIT Press. Ratcliff, R. (1978). A theory of memory retrieval. Psychological Review, 85, 59–108. Reed, S. K. (1972). Pattern recognition and categorization. Cognitive Psychology, 3, 393–407. Rice, J. A. (1995). Mathematical statistics and data analysis (2nd ed.). Belmont, CA: Duxbury. Rosseel, Y. (2002). Mixture models of categorization. Journal of Mathematical Psychology, 46, 178–210. Sanborn, A. N., Griffiths, T. L., & Navarro, D. J. (2006). A more rational model of categorization In R. Sun & N. Miyake, Proceedings of the 28th annual meeting of the Cognitive Science Society (pp. 726–731). Hillsdale, NJ: Erlbaum. Sethuraman, J. (1994). A constructive definition of Dirichlet priors. Statistica Sinica, 4, 639–650. Shepard, R. N. (1987). Toward a universal law of generalization for psychological science. Science, 237, 1317–1323. Shepard, R. N., Hovland, C. I., & Jenkins, H. M. (1961). Learning and memorization of classifications. Psychological Monographs, 75, (13, Whole No. 517). Shi, L., Feldman, N., & Griffiths, T. L. (2008). Performing Bayesian inference with exemplar models. In V. Sloutsky, B. Love, & K. McRae, Proceedings of the 30th annual conference of the Cognitive Science Society (pp. 745–750). Austin, TX: Cognitive Science Society. Shi, L., Griffiths, T. L., Feldman, N. H., & Sanborn, A. N. (2010). Exemplar models as a mechanism for performing Bayesian inference. Psychological Bulletin and Review, 17, 443–464. Shiffrin, R. M., & Steyvers, M. (1997). A model for recognition memory: REM: Retrieving effectively from memory. Psychonomic Bulletin & Review, 4, 145–166. Silverman, B. W. (1986). Density estimation. London, England: Chapman and Hall. Smith, J. D., & Minda, J. P. (1998). Prototypes in the mist: The early epochs of category learning. Journal of Experimental Psychology: Learning, Memory, and Cognition, 24, 1411–1436. Smith, P. L., & Ratcliff, R. (2004). Psychology and neurobiology of simple decisions. Trends in Neurosciences, 27, 161–168. Smith, S. M., & Blankenship, S. E. (1989). Incubation effects. Bulletin of the Psycholonomic Society, 27, 311–314. Stewart, N., Chater, N., & Brown, G. D. A. (2006). Decision by sampling. Cognitive Psychology, 53, 1–26. Surowiecki, J. (2004). The wisdom of crowds: Why the many are smarter than the few and how collective wisdom shapes business, economics, societies, and nations. New York, NY: Doubleday. Tenenbaum, J. B., & Griffiths, T. L. (2001a). Generalization, similarity, and Bayesian inference. Behavioral and Brain Sciences, 24, 629–641. Tenenbaum, J. B., & Griffiths, T. (2001b). The rational basis of representativeness. In J. Moore & K. Stenning (Eds.), Proceedings of the 23rd annual conference of the Cognitive Science Society (pp. 1064–1069). Hillsdale, NJ: Erlbaum. Tversky, A., & Kahneman, D. (1974, September). Judgment under uncertainty: Heuristics and biases. Science, 185, 1124–1131. Vandekerckhove, J., Verheyen, S., & Tuerlinckx, F. (2010). A crossed random effects diffusion model for speeded semantic categorization decisions. Acta Psychologica, 133, 269–282. Vanpaemel, W., & Storms, G. (2008). In search of abstraction: The varying abstraction model of categorization. Psychonomic Bulletin & Review, 15, 732–749. Vickers, D. (1979). Decision processes in visual perception. London, England: Academic Press. Vul, E., & Pashler, H. (2008). Measuring the crowd within: Probabilistic representations within individuals. Psychological Science, 19, 645–647. Wallas, G. (1926). The art of thought. New York, NY: Harcourt. Yi, S., Steyvers, M., & Lee, M. (2010). Modeling human performance in restless bandits using particle filters. Journal of Problem Solving.
URI:	http://wrap.warwick.ac.uk/id/eprint/36000

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