The DOI matches its Crossref record; 97 of the 97 references it cites were found in a registry or an index.
Rational approximations to rational models: alternative algorithms for category learning
Open accessPublished version of a preprint
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.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“Bayesian samplers can match behavioral stochasticity in tasks such as perception, categorization, causal reasoning, and decision making [20,21,23,24].”
From Bayesian Brains without Probabilities (2016) · cites this paper as [21]
Citations
Cites
Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2003) · doi:10.1201/9780429258480 · Cited by 27,276
The Elements of Statistical Learning
Hastie, T., Tibshirani, R., & Friedman, J. (2009) · Springer Series in Statistics · doi:10.1007/978-0-387-84858-7 · Cited by 25,970
Judgment under Uncertainty: Heuristics and Biases
Tversky, A., & Kahneman, D. (1975) · Utility, Probability, and Human Decision Making · doi:10.1007/978-94-010-1834-0_8 · Cited by 22,650
Book Review: Pattern Recognition and Machine Learning
Nasrabadi, N. M. (2007) · Journal of Electronic Imaging · doi:10.1117/1.2819119 · Cited by 22,066
Stochastic relaxation, gibbs distributions, and the bayesian restoration of images.
Geman, S., & Geman, D. (1984) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.1984.4767596 · Cited by 17,949
The Elements of Statistical Learning: Data Mining, Inference, and Prediction
Lu, Z. Q. J. (2010) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.1111/j.1467-985x.2010.00646_6.x · Cited by 12,916
Markov Chain Monte Carlo in Practice
Gilks, W. R., Richardson, S. T., & Spiegelhalter, D. J. (1995) · Chapman & Hall/CRC eBooks · doi:10.1201/b14835 · Cited by 7,927
Novel approach to nonlinear/non-Gaussian Bayesian state estimation
Gordon, N., Salmond, D. J., & Smith, A. F. M. (1993) · IEE Proceedings F Radar and Signal Processing · doi:10.1049/ip-f-2.1993.0015 · Cited by 7,711
Sequential Monte Carlo Methods in Practice
Arnaud Doucet, B. (2001) · Springer eBooks · doi:10.1007/978-1-4757-3437-9 · Cited by 7,516
Information theory, inference, and learning algorithms
(2004) · Choice Reviews Online · doi:10.5860/choice.41-5949 · Cited by 6,536
Motwani, R., & Raghavan, P. (1995) · Cambridge University Press eBooks · doi:10.1017/cbo9780511814075 · Cited by 5,098
Information Theory, Inference, and Learning Algorithms
(2004) · Kybernetes · doi:10.1108/03684920410534506 · Cited by 4,937
A Bayesian Analysis of Some Nonparametric Problems
Ferguson, T. S. (1973) · The Annals of Statistics · doi:10.1214/aos/1176342360 · Cited by 4,680
Pattern Recognition and Machine Learning
Neal, R. M. (2007) · Technometrics · doi:10.1198/tech.2007.s518 · Cited by 4,629
Ratcliff, R. (1978) · Psychological Review · doi:10.1037/0033-295x.85.2.59 · Cited by 4,513
Journal of Experimental Psychology: Human Learning and Memory
Bourne, L. E. (1977) · Cited by 4,328
Simple Heuristics That Make Us Smart
Gigerenzer, G., & Todd, P. M. (1999) · Cited by 3,563
Mathematical Statistics and Data Analysis
Rabinowitz, L., & Rice, J. A. (1989) · Technometrics · doi:10.2307/3556160 · Cited by 3,142
Context theory of classification learning
Medin, D. L., & Schaffer, M. M. (1978) · Psychological Review · doi:10.1037/0033-295x.85.3.207 · Cited by 3,061
(2004) · Choice Reviews Online · doi:10.5860/choice.42-1645 · Cited by 2,928
Toward a Universal Law of Generalization for Psychological Science
Shepard, R. N. (1987) · Science · doi:10.1126/science.3629243 · Cited by 2,416
Bayesian Density Estimation and Inference Using Mixtures
Escobar, M. D., & West, M. (1995) · Journal of the American Statistical Association · doi:10.1080/01621459.1995.10476550 · Cited by 2,236
Attention, similarity, and the identification-categorization relationship.
Nosofsky, R. M. (1986) · Journal of Experimental Psychology General · doi:10.1037//0096-3445.115.1.39 · Cited by 2,207
Markov Chain Sampling Methods for Dirichlet Process Mixture Models
Neal, R. M. (2000) · Journal of Computational and Graphical Statistics · doi:10.1080/10618600.2000.10474879 · Cited by 2,204
The Adaptive Character of Thought
Massaro, D. W., Friedman, D., & Anderson, J. R. (1991) · The American Journal of Psychology · doi:10.2307/1423253 · Cited by 2,174
Attention, similarity, and the identification–categorization relationship.
Nosofsky, R. M. (1986) · Journal of Experimental Psychology General · doi:10.1037/0096-3445.115.1.39 · Cited by 2,136
Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric Problems
Antoniak, C. E. (1974) · The Annals of Statistics · doi:10.1214/aos/1176342871 · Cited by 1,976
Wallas, G. (1926) · Medical Entomology and Zoology · Cited by 1,973
Markov Chain Monte Carlo in Practice
Gasparini, M., Gilks, W. R., Richardson, S. T., & Spiegelhalter, D. J. (1997) · Technometrics · doi:10.2307/1271145 · Cited by 1,881
Homo Heuristicus: Why Biased Minds Make Better Inferences
Gigerenzer, G., & Brighton, H. (2009) · Topics in Cognitive Science · doi:10.1111/j.1756-8765.2008.01006.x · Cited by 1,801
Proceedings of the 29th Annual Conference of the Cognitive Science Society
Rohde, H., Kehler, A., & Elman, J. L. (2007) · Cognitive Science · Cited by 1,782
The serial position effect of free recall.
Murdock, B. B. (1962) · Journal of Experimental Psychology · doi:10.1037/h0045106 · Cited by 1,717
A Constructive Definition of Dirichlet Priors
Sethuraman, J. (1991) · doi:10.21236/ada238689 · Cited by 1,605
Exchangeability and related topics
Aldous, D. (1985) · Lecture notes in mathematics · doi:10.1007/bfb0099421 · Cited by 1,348
Ferguson Distributions Via Polya Urn Schemes
Blackwell, D., & MacQueen, J. B. (1973) · The Annals of Statistics · doi:10.1214/aos/1176342372 · Cited by 1,343
The adaptive nature of human categorization.
Anderson, J. R. (1991) · Psychological Review · doi:10.1037/0033-295x.98.3.409 · Cited by 1,069
A rational analysis of the selection task as optimal data selection.
Oaksford, M., & Chater, N. (1994) · Psychological Review · doi:10.1037/0033-295x.101.4.608 · Cited by 1,065
Psychology and neurobiology of simple decisions
Smith, P. L., & Ratcliff, R. (2004) · Trends in Neurosciences · doi:10.1016/j.tins.2004.01.006 · Cited by 1,051
Probabilistic Inference Using Markov Chain Monte Carlo Methods
Neal, R. M. (2011) · Cited by 1,047
Pattern recognition and categorization
Reed, S. K. (1972) · Cognitive Psychology · doi:10.1016/0010-0285(72)90014-x · Cited by 1,002
The Infinite Gaussian Mixture Model
Rasmussen, C. E. (1999) · Cited by 985
A model for recognition memory: REM—retrieving effectively from memory
Shiffrin, R. M., & Steyvers, M. (1997) · Psychonomic Bulletin & Review · doi:10.3758/bf03209391 · Cited by 956
Generalization, similarity, and Bayesian inference
Tenenbaum, J. B., & Griffiths, T. L. (2001) · Behavioral and Brain Sciences · doi:10.1017/s0140525x01000061 · Cited by 878
Self-citationLearning and memorization of classifications.
Shepard, R. N., Hovland, C. I., & Jenkins, H. M. (1961) · The Psychological Monographs · doi:10.1037/h0093825 · Cited by 844
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
Geman, S., & Geman, D. (1987) · Elsevier eBooks · doi:10.1016/b978-0-08-051581-6.50057-x · Cited by 784
Judgment under Uncertainty: Heuristics and Biases
Tversky, A., & Kahneman, D. J. (1973) · doi:10.21236/ad0767426 · Cited by 781
Stewart, N., Chater, N., & Brown, G. D. A. (2006) · Cognitive Psychology · doi:10.1016/j.cogpsych.2005.10.003 · Cited by 737
Why are some problems hard? Evidence from Tower of Hanoi
Kotovsky, K., Hayes, J. R., & Simon, H. A. (1985) · Cognitive Psychology · doi:10.1016/0010-0285(85)90009-x · Cited by 722
Structure and strength in causal induction☆
Griffiths, T. L., & Tenenbaum, J. B. (2005) · Cognitive Psychology · doi:10.1016/j.cogpsych.2005.05.004 · Cited by 626
Self-citationThe theory of learning by doing.
Anzai, Y., & Simon, H. A. (1979) · PubMed · Cited by 605
Decision Processes in Visual Perception
(1979) · Elsevier eBooks · doi:10.1016/c2013-0-11654-6 · Cited by 513
Markov Chain Sampling Methods for Dirichlet Process Mixture Models
Neal, R. M. (2000) · Journal of Computational and Graphical Statistics · doi:10.2307/1390653 · Cited by 507
Prototypes in the mist: The early epochs of category learning.
Smith, J. D., & Minda, J. P. (1998) · Journal of Experimental Psychology Learning Memory and Cognition · doi:10.1037/0278-7393.24.6.1411 · Cited by 491
Information Sampling and Adaptive Cognition
(2005) · Cambridge University Press eBooks · doi:10.1017/cbo9780511614576 · Cited by 399
Ferguson, T. S. (1983) · Elsevier eBooks · doi:10.1016/b978-0-12-589320-6.50018-6 · Cited by 388
Proceedings of the 23rd annual conference of the cognitive science society
O’Toole, M., Oberlander, J., & Shillcock, R. C. (2001) · Cited by 343
Mathematical Statistics and Data Analysis.
Aa, & Rice, J. A. (1995) · Journal of the American Statistical Association · doi:10.2307/2291188 · Cited by 339
Vul, E., & Pashler, H. (2008) · Psychological Science · doi:10.1111/j.1467-9280.2008.02136.x · Cited by 333
Nosofsky, R. M., Gluck, M. A., Palmeri, T. J., McKinley, S. C., & Glauthier, P. (1994) · Memory & Cognition · doi:10.3758/bf03200862 · Cited by 292
Gobet, F. R. (2000) · Swiss Journal of Psychology · doi:10.1024//1421-0185.59.3.211b · Cited by 288
Ten years of the rational analysis of cognition
Chater, N., & Oaksford, M. (1999) · Trends in Cognitive Sciences · doi:10.1016/s1364-6613(98)01273-x · Cited by 280
Evidence accumulation in decision making: Unifying the “take the best” and the “rational” models
Lee, M. D., & Cummins, T. D. R. (2004) · Psychonomic Bulletin & Review · doi:10.3758/bf03196581 · Cited by 277
An Exemplar-Based Random Walk Model of Speeded Classification
Nosofsky, R., & Palmeri, T. (1997) · Psychological Review · doi:10.1037/0033-295x.104.2.266 · Cited by 271
Chater, N., & Oaksford, M. (2005) · Wiley eBooks · doi:10.1002/0470018860.s00603 · Cited by 252
Linear separability in classification learning.
Medin, D. L., & Schwanenflugel, P. J. (1981) · Journal of Experimental Psychology Human Learning & Memory · doi:10.1037/0278-7393.7.5.355 · Cited by 251
École d'Été de Probabilités de Saint-Flour XIII — 1983
Aldous, D., Ibragimov, I. A., & Jacod, J. (1985) · Lecture notes in mathematics · doi:10.1007/bfb0099420 · Cited by 245
Similarity, frequency, and category representations.
Nosofsky, R. (1988) · Journal of Experimental Psychology Learning Memory and Cognition · doi:10.1037/0278-7393.14.1.54 · Cited by 243
Categorization as Probability Density Estimation
Ashby, F. G., & Alfonso-Reese, L. A. (1995) · Journal of Mathematical Psychology · doi:10.1006/jmps.1995.1021 · Cited by 217
Proceedings of the 31st Annual Conference of the Cognitive Science Society
Taatgen, N. A., & van Rijn, H. (2009) · Max Planck Institute for Plasma Physics · Cited by 213
Nosofsky, R. M., & Zaki, S. R. (2002) · Journal of Experimental Psychology Learning Memory and Cognition · doi:10.1037/0278-7393.28.5.924 · Cited by 211
Smith, S. M., & Blankenship, S. E. (1989) · Bulletin of the Psychonomic Society · doi:10.3758/bf03334612 · Cited by 204
Proceedings of the 30th Annual Conference of the Cognitive Science Society.
Love, B. C., McRae, K., & Sloutsky, V. M. (2008) · Cited by 173
Exemplar models as a mechanism for performing Bayesian inference
Shi, L., Griffiths, T. L., Feldman, N. H., & Sanborn, A. N. (2010) · Psychonomic Bulletin & Review · doi:10.3758/pbr.17.4.443 · Cited by 168
Self-citationJaeger, D., & Jung, R. (2015) · Encyclopedia of Computational Neuroscience · doi:10.1007/978-1-4614-6675-8_100494 · Cited by 168
Modeling individual differences using Dirichlet processes
Navarro, D., Griffiths, T. L., Mark Steyvers, B., & Lee, M. D. (2006) · Journal of Mathematical Psychology · doi:10.1016/j.jmp.2005.11.006 · Cited by 150
Self-citationDetecting and predicting changes
Brown, S. D., & Mark Steyvers, B. (2008) · Cognitive Psychology · doi:10.1016/j.cogpsych.2008.09.002 · Cited by 129
A more rational model of categorization
Sanborn, A. N., Griffiths, T. L., & Navarro, D. (2006) · Warwick Research Archive Portal (University of Warwick) · Cited by 109
Self-citationParticle filters for mixture models with an unknown number of components
Fearnhead, P. (2003) · Statistics and Computing · doi:10.1023/b:stco.0000009418.04621.cd · Cited by 107
Locally Bayesian learning with applications to retrospective revaluation and highlighting.
Kruschke, J. K. (2006) · Psychological Review · doi:10.1037/0033-295x.113.4.677 · Cited by 105
In search of abstraction: The varying abstraction model of categorization
Vanpaemel, W., & Storms, G. (2008) · Psychonomic Bulletin & Review · doi:10.3758/pbr.15.4.732 · Cited by 102
Mixture Models of Categorization
Rosseel, Y. (2002) · Journal of Mathematical Psychology · doi:10.1006/jmps.2001.1379 · Cited by 100
Optimal Predictions in Everyday Cognition: The Wisdom of Individuals or Crowds?
Mozer, M. C., Pashler, H., & Homaei, H. (2008) · Cognitive Science · doi:10.1080/03640210802353016 · Cited by 90
Modeling the effects of memory on human online sentence processing with particle filters
Lévy, R., Reali, F., & Griffiths, T. L. (2008) · neural information processing systems · Cited by 79
Self-citationDaw, N. D., & Courville, A. C. (2007) · neural information processing systems · Cited by 77
Unifying rational models of categorization via the hierarchical Dirichlet processPreprint
Griffiths, T. L., Canini, K. R., Sanborn, A. N., & Navarro, D. (2019) · doi:10.31234/osf.io/ketw3 · Cited by 76
Self-citationPresentation order and recognition of categorically related examples
Medin, D. L., & Bettger, J. G. (1994) · Psychonomic Bulletin & Review · doi:10.3758/bf03200776 · Cited by 62
Categorization as nonparametric Bayesian density estimation
Griffiths, T. L., Sanborn, A. N., Canini, K. R., & Navarro, D. (2008) · doi:10.1093/acprof:oso/9780199216093.003.0014 · Cited by 42
Self-citationLinear separability in classification learning.
Medin, D. L., & Schwanenflugel, P. J. (1981) · Journal of Experimental Psychology Human Learning & Memory · doi:10.1037//0278-7393.7.5.355 · Cited by 35
Performing Bayesian Inference with Exemplar Models
Shi, L., Feldman, N. H., & Griffiths, T. L. (2008) · eScholarship (California Digital Library) · Cited by 33
Self-citationA crossed random effects diffusion model for speeded semantic categorization decisions
Vandekerckhove, J., Verheyen, S., & Tuerlinckx, F. (2009) · Acta Psychologica · doi:10.1016/j.actpsy.2009.10.009 · Cited by 29
On the interaction between exemplar-based concepts and a response scaling process
Navarro, D. (2007) · Journal of Mathematical Psychology · doi:10.1016/j.jmp.2006.11.003 · Cited by 28
Self-citationNonparametric Bayesian models of categorization
Griffiths, T. L., Sanborn, A. N., Canini, K. R., Navarro, D., & Tenenbaum, J. B. (2011) · Cambridge University Press eBooks · doi:10.1017/cbo9780511921322.008 · Cited by 17
Self-citationModeling individual differences using Dirichlet processesPreprint
Navarro, D., Griffiths, T. L., Steyvers, M., et al. (2019) · doi:10.31234/osf.io/bc3ya · Cited by 14
Self-citationKruschke, J. K. (2006) · eScholarship (California Digital Library) · Cited by 11
Optimal performance and exemplar models of classification
Nosofsky, R. M. (2000) · doi:10.1093/oso/9780198524151.003.0011 · Cited by 10
Confirmation bias is rational when hypotheses are sparse
Perfors, A., & Navarro, D. (2009) · eScholarship (California Digital Library) · Cited by 7
Self-citationModeling Human Performance in Restless Bandits with Particle Filters (Preprint)
Yi, S. K. M., Steyvers, M., & Lee, M. (2009) · Cited by 1
Cited by
Sorted by citations
Lieder, F., & Griffiths, T. L. (2020) · Behavioral and Brain Sciences · doi:10.1017/s0140525x1900061x · Cited by 892
Self-citationComputational rationality: A converging paradigm for intelligence in brains, minds, and machines
Gershman, S. J., Horvitz, E., & Tenenbaum, J. B. (2015) · Science · doi:10.1126/science.aac6076 · Cited by 722
Robust speech perception: Recognize the familiar, generalize to the similar, and adapt to the novel.
Kleinschmidt, D., & Jaeger, T. F. (2015) · Psychological Review · doi:10.1037/a0038695 · Cited by 684
A tutorial on Bayesian nonparametric models
Gershman, S. J., & Blei, D. M. (2011) · Journal of Mathematical Psychology · doi:10.1016/j.jmp.2011.08.004 · Cited by 626
Jones, M., & Love, B. C. (2011) · Behavioral and Brain Sciences · doi:10.1017/s0140525x10003134 · Cited by 533
Metadata
- Authors
- Sanborn, A. N., Griffiths, T. L., & Navarro, D. J.
- Affiliations
- Gatsby Computational Neuroscience Unit (GB)
- University of California System (US)
- Venue
- Psychological Review
- Published
- 2010
- Volume
- 117
- Issue
- 4
- Pages
- 1144-1167
- ISSN
- 0033-295X (ISSN-L)
- 1939-1471
- OpenAlex
- W2038407704
- Semantic Scholar
- bf244633a58d0ca27f2b383ed225f3c42481eed9
- Cited by
- 369
- References
- 94
- Citations by year
- 2026: 10 · 2025: 15 · 2024: 9 · 2023: 28 · 2022: 12 · 2021: 15 · 2020: 26 · 2019: 48 · 2018: 24 · 2017: 28 · 2016: 22 · 2015: 34 · 2014: 17 · 2013: 26 · 2012: 29
- FWCI
- 34.33
- Type
- journal article
- Language
- en
- Open access
- green
- doi.org
- Licence
- cc-by
- Locations
- Psychological Review (publishedVersion)
- PubMed (publishedVersion)
- Warwick Research Archive Portal (University of Warwick) (acceptedVersion)
- Adelaide Research & Scholarship (AR&S) (University of Adelaide) (submittedVersion)
- UCL Discovery (University College London) (submittedVersion)
- PsyArXiv (OSF Preprints) (submittedVersion, cc-by)
- PsyArXiv (OSF Preprints) (submittedVersion)
- Funders
- National Science Foundation (IIS-0845410)
- Royal Society
- Air Force Office of Scientific Research (FA9550-07-1-0351)
- Australian Research Council (DP0773794)
- Topics
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Categorization, perception, and language
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
- Life Sciences › Neuroscience › Cognitive Neuroscience › Cognitive Science and Education Research
- Keywords
- category learning, categorization, approximation algorithms, Monte Carlo methods, Gibbs sampling, particle filter, approximate inference, sequential inference, human inference
- MeSH terms
- Algorithms, Cognition, Discrimination, Psychological, Humans, Learning, Models, Psychological, Monte Carlo Method, Probability, Models, Statistical
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
