nips nips2007 nips2007-125 nips2007-125-reference knowledge-graph by maker-knowledge-mining

125 nips-2007-Markov Chain Monte Carlo with People


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Author: Adam Sanborn, Thomas L. Griffiths

Abstract: Many formal models of cognition implicitly use subjective probability distributions to capture the assumptions of human learners. Most applications of these models determine these distributions indirectly. We propose a method for directly determining the assumptions of human learners by sampling from subjective probability distributions. Using a correspondence between a model of human choice and Markov chain Monte Carlo (MCMC), we describe a method for sampling from the distributions over objects that people associate with different categories. In our task, subjects choose whether to accept or reject a proposed change to an object. The task is constructed so that these decisions follow an MCMC acceptance rule, defining a Markov chain for which the stationary distribution is the category distribution. We test this procedure for both artificial categories acquired in the laboratory, and natural categories acquired from experience. 1


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[1] M. Oaksford and N. Chater, editors. Rational models of cognition. Oxford University Press, 1998.

[2] N. Chater, J. B. Tenenbaum, and A. Yuille. Special issue on “Probabilistic models of cognition”. Trends in Cognitive Sciences, 10(7), 2006.

[3] J. R. Anderson. The adaptive character of thought. Erlbaum, Hillsdale, NJ, 1990.

[4] F. G. Ashby and L. A. Alfonso-Reese. Categorization as probability density estimation. Journal of Mathematical Psychology, 39:216–233, 1995.

[5] W.R. Gilks, S. Richardson, and D. J. Spiegelhalter, editors. Markov Chain Monte Carlo in Practice. Chapman and Hall, Suffolk, 1996.

[6] A. W. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller. Equations of state calculations by fast computing machines. Journal of Chemical Physics, 21:1087–1092, 1953.

[7] W. K. Hastings. Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57:97–109, 1970.

[8] A. A. Barker. Monte Carlo calculations of the radial distribution functions for a proton-electron plasma. Australian Journal of Physics, 18:119–133, 1965.

[9] S. K. Reed. Pattern recognition and categorization. Cognitive Psychology, 3:393–407, 1972.

[10] D. L. Medin and M. M. Schaffer. Context theory of classification learning. Psychological Review, 85:207– 238, 1978.

[11] R. M. Nosofsky. Attention, similarity, and the identification-categorization relationship. Journal of Experimental Psychology: General, 115:39–57, 1986.

[12] R. D. Luce. Detection and recognition. In R. D. Luce, R. R. Bush, and E. Galanter, editors, Handbook of Mathematical Psychology, Volume 1, pages 103–190. John Wiley and Sons, Inc., New York and London, 1963.

[13] R. N. Shepard. Stimulus and response generalization: A stochastic model relating generalization to distance in psychological space. Psychometrika, 22:325–345, 1957.

[14] R. A. Bradley. Incomplete block rank analysis: On the appropriateness of the model of a method of paired comparisons. Biometrics, 10:375–390, 1954.

[15] F. R. Clarke. Constant-ratio rule for confusion matrices in speech communication. The Journal of the Acoustical Society of America, 29:715–720, 1957.

[16] J. W. Hopkins. Incomplete block rank analysis: Some taste test results. Biometrics, 10:391–399, 1954.

[17] N. Vulkan. An economist’s perspective on probability matching. Journal of Economic Surveys, 14:101– 118, 2000.

[18] F. G. Ashby. Multidimensional models of perception and cognition. Erlbaum, Hillsdale, NJ, 1992.

[19] R. M. Nosofsky. Attention and learning processes in the identification and categorization of integral stimuli. Journal of Experimental Psychology: Learning, Memory, and Cognition, 13:87–108, 1987.

[20] G. C. Oden and D. W. Massaro. Integration of featural information in speech perception. Psychological Review, 85:172–191, 1978.

[21] J. L. McClelland and J. L. Elman. The TRACE model of speech perception. Cognitive Psychology, 18:1–86, 1986.

[22] F. G. Ashby and W. T. Maddox. Relations between prototype, exemplar, and decision bound models of categorization. Journal of Mathematical Psychology, 37:372–400, 1993.

[23] D. H. Brainard. The psychophysics toolbox. Spatial Vision, 10:433–436, 1997.

[24] D. G. Pelli. The VideoToolbox software for visual psychophysics: Transforming numbers into movies. Spatial Vision, 10:437–442, 1997.

[25] J. Huttenlocher, L. V. Hedges, and J. L. Vevea. Why do categories affect stimulus judgment? Journal of Experimental Psychology: General, 129:220–241, 2000.

[26] C. Olman and D. Kersten. Classification objects, ideal observers, and generative models. Cognitive Science, 28:227–239, 2004.

[27] A. J. Ahumada and J. Lovell. Stimulus features in signal detection. Journal of the Acoustical Society of America, 49:1751–1756, 1971. 8