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
Flagged first, then by citations
Cited by
Sorted by citations
Items 301–373 of 373
Towards Evaluating Computational Models of Intuitive Decision Making with fMRI Data
Niehaus, J., Romero, V. L., & Pfeffer, A. (2013) · Lecture notes in computer science · doi:10.1007/978-3-642-39454-6_50
Complexity: A Theoretical Analysis with Implications to Self Regulation and Goal PursuitPreprint
Reichman, D. (2012) · SSRN Electronic Journal · doi:10.2139/ssrn.2051980
Attention: A machine learning perspective
Hansen, L. K. (2012) · International Workshop on Cognitive Information Processing (CIP) · doi:10.1109/cip.2012.6232894
Hendrickson, A. (2015) · IUScholarWorks (Indiana University)
Regel-basierte Kategorisierung mit dem Hierarchischen Dirichlet Prozess
Glassen, T., & Nitsch, V. (2016) · DuEPublico (University of Duisburg-Essen) · doi:10.17185/duepublico/40721
Goldreich, O. (2010) · Cambridge University Press eBooks · doi:10.1017/cbo9780511761355.008
Binz, M. (2002) · CRC Press eBooks · doi:10.1201/9780203164587.ch3
Stamps, A., & Frankenhuis, W. E. (2016)
The Role of Empirical Evidence in Modeling Speech Segmentation DISSERTATION
Phillips, L. (2015)
Beam, C. S. (2017) · ResearchWorks at the University of Washington (University of Washington)
Computational Modeling of Word Learning: The Role of Cognitive Processes
Chekoudar, A. N. (2015) · TSpace (University of Toronto)
Local Search and the Explore/Exploit Trade-off in Adult Causal Inferences
Herbst, E. A. (2017) · TSpace (University of Toronto)
Dynamic integration of conceptual information during learningPreprint
Inhoff, M. C., Libby, L. A., Noguchi, T., Love, B. C., & Charan Ranganath, A. (2018) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/280362
Bayesian statistics to test Bayes optimality
Turner, B. M., McClelland, J. L., & Busemeyer, J. R. (2018) · Behavioral and Brain Sciences · doi:10.1017/s0140525x18001334
Categorization in the Wild: Generalizing Cognitive Models to Naturalistic Data across LanguagesPreprint
Frermann, L., & Lapata, M. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1902.08830
A semantics based computational model for word learning
Grover, I. (2018) · DSpace@MIT (Massachusetts Institute of Technology)
A Bayesian model of memory in a multi-context environment.
Kleinschmidt, D., & Hemmer, P. (2019) · eScholarship (California Digital Library)
Impulsivity and risk-seeking as Bayesian inference under dopaminergic controlPreprint
Mikhael, J. G., & Gershman, S. J. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.10.06.327775
Universality in Cultural Transmission
Thompson, B. (2015) · VUBIR (Vrije Universiteit Brussel)
Learning To Learn From Similar Others: Approximate Bayesian Computation Through Babbling
Thompson, B. (2016) · VUBIR (Vrije Universiteit Brussel)
List of Computational Problems
van Rooij, I., Blokpoel, M., Kwisthout, J., & Wareham, T. (2019) · doi:10.1017/9781107358331.019
A Bayesian Account of Memory for TextPreprint
Andrews, M. W. (2019) · doi:10.31234/osf.io/wju3k
Parameterized Complexity Classes
van Rooij, I., Blokpoel, M., Kwisthout, J., & Wareham, T. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107358331.010
Hypothesis generation, the positive test strategy, and sparse categoriesPreprint
Navarro, D., & Perfors, A. (2019) · doi:10.31234/osf.io/rj9kt
Self-citationvan Rooij, I., Blokpoel, M., Kwisthout, J., & Wareham, T. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107358331.013
van Rooij, I., Blokpoel, M., Kwisthout, J., & Wareham, T. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107358331.007
Polynomial versus Exponential Time
van Rooij, I., Blokpoel, M., Kwisthout, J., & Wareham, T. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107358331.005
van Rooij, I., Blokpoel, M., Kwisthout, J., & Wareham, T. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107358331.012
Building Object-based Causal Programs for Human-like GeneralizationPreprint
Zhao, B., Lucas, C. G., & Bramley, N. R. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2111.12560
van Rooij, I., Blokpoel, M., Kwisthout, J., & Wareham, T. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107358331.014
Compendium of Complexity Results
van Rooij, I., Blokpoel, M., Kwisthout, J., & Wareham, T. (2019) · doi:10.1017/9781107358331.020
Communication as Bayesian Inference
van Rooij, I., Blokpoel, M., Kwisthout, J., & Wareham, T. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107358331.017
van Rooij, I., Blokpoel, M., Kwisthout, J., & Wareham, T. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107358331.003
van Rooij, I., Blokpoel, M., Kwisthout, J., & Wareham, T. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107358331.011
Fixed-Parameter Tractable Time
van Rooij, I., Blokpoel, M., Kwisthout, J., & Wareham, T. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107358331.008
van Rooij, I., Blokpoel, M., Kwisthout, J., & Wareham, T. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107358331.006
van Rooij, I., Blokpoel, M., Kwisthout, J., & Wareham, T. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107358331.009
van Rooij, I., Blokpoel, M., Kwisthout, J., & Wareham, T. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107358331.021
van Rooij, I., Blokpoel, M., Kwisthout, J., & Wareham, T. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107358331.016
van Rooij, I., Blokpoel, M., Kwisthout, J., & Wareham, T. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107358331.002
Coherence as Constraint Satisfaction
van Rooij, I., Blokpoel, M., Kwisthout, J., & Wareham, T. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107358331.015
van Rooij, I., Blokpoel, M., Kwisthout, J., & Wareham, T. (2019) · doi:10.1017/9781107358331.001
van Rooij, I., Blokpoel, M., Kwisthout, J., & Wareham, T. (2019) · doi:10.1017/9781107358331.018
Why Bayesian brains perform poorly on explicit probabilistic reasoning problemsPreprint
Smith, R. S., Ramstead, M. J. D., & Kiefer, A. B. (2022) · PsyArXiv (OSF Preprints) · doi:10.31234/osf.io/hne9s
van Rooij, I., Blokpoel, M., Kwisthout, J., & Wareham, T. (2019) · Cambridge University Press eBooks · doi:10.1017/9781107358331.022
Can Bayesian Models of Cognition Show That We Are (Epistemically) Rational?
Levy, A. (2023) · Philosophy of Science · doi:10.1017/psa.2023.37
(2023) · Cambridge University Press eBooks · doi:10.1017/9781108755610.004
Fiedler, K., Juslin, P., & Denrell, J. C. (2023) · Cambridge University Press eBooks · doi:10.1017/9781009002042.025
Fiedler, K., Juslin, P., & Denrell, J. C. (2023) · Cambridge University Press eBooks · doi:10.1017/9781009002042.006
Sampling Data, Beliefs, and Actions
Brockbank, E., Holdaway, C., Acosta‐Kane, D., & Vul, E. (2023) · Cambridge University Press eBooks · doi:10.1017/9781009002042.028 · Cited by 1
Approximating Bayesian Inference through Internal Sampling
Sundh, J., Sanborn, A. N., Zhu, J.-Q., Spicer, J., León-Villagrá, P., & Chater, N. (2023) · Cambridge University Press eBooks · doi:10.1017/9781009002042.027
Self-citationPothos, E. M., & Yearsley, J. M. (2023) · Springer eBooks · doi:10.1007/978-3-031-12986-5_14
Chen, Y. (2023) · SSRN Electronic Journal · doi:10.2139/ssrn.4565502
On the hazards of relating representations and inductive biases
Griffiths, T. L., Kumar, S., & McCoy, R. T. (2023) · Behavioral and Brain Sciences · doi:10.1017/s0140525x23002042
Self-citationThe Delusional Hedge Algorithm as a Model of Human Learning From Diverse Opinions
Chuang, Y., Zhu, X., & Rogers, T. T. (2025) · Topics in Cognitive Science · doi:10.1111/tops.12783
A common algorithm for confidence judgements across visual, auditory and audio-visual decisionsPreprint
West, R. K., Matthews, N. L., Mattingley, J. B., & Sewell, D. K. (2025) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2025.02.12.637846
Information sampling and Bayesian belief formation in statistical judgment
He, L., Wang, H., Bian, Y., Zhang, X., & Bhatia, S. (2025) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2517302122 · Cited by 1
From exchangeability to rational belief: a cognitive interpretation of de Finetti’s theorem
Costa, T. (2025) · Frontiers in Psychology · doi:10.3389/fpsyg.2025.1621552
Zhou, Y., & Khatibi, S. (2025) · International Conference on Artificial Intelligence, Robotics, and Communication (ICAIRC) · doi:10.1109/icairc68035.2025.11385242
Computational learning noise in human decision-making
Findling, C. (2018) · theses.fr (ABES) · doi:10.70675/32e62279zea97z45b1z9326z06a449dae472
Do additional features help or hurt category learning? The curse of dimensionality in human learnersPreprint
Navarro, D., Vong, W. K., Hendrickson, A. T., & Perfors, A. (2019) · OSF Preprints (OSF Preprints)
Self-citationIt Is What It Isn’t: Introducing a Constraint-Based Approach to Structure Learning
Olesen, C., Mikuš, N., Hansen, M., Legrand, N., Waade, P. T., & Mathys, C. D. (2026) · Entropy · doi:10.3390/e28050534
Levels of analysis for large language models
Ku, A. Y., Campbell, D., Bai, X., Geng, J., Liu, R., Marjieh, R., McCoy, R. T., Nam, A., Sucholutsky, I., Zhang, L., et al. (2026) · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rsta.2025.0012 · Cited by 25
Self-citationCategorical Bayes Filtering for Computational Phenotyping in Adaptive LearningPreprint
Chen, J., & Piray, P. (2026) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.64898/2026.05.14.725268
Can Childhood be Used as a Model to Understand the Effects of Psychedelics?
Hurwitz, E. S., Dean, J. G., & Walker, C. M. (2026) · Topics in Cognitive Science · doi:10.1111/tops.70058
Considering Psychological Mechanisms Can Change the Interpretation of Bayesian Models
Bonawitz, E. B., & Griffiths, T. L. (2026) · Topics in Cognitive Science · doi:10.1111/tops.70052
Self-citationPeople use fast and flat simulation to reason about new games
Collins, K. M., Zhang, C. E., Wong, L., da Costa, M. B., Todd, G., Weller, A., Cheyette, S., Griffiths, T. L., & Tenenbaum, J. B. (2026) · Nature · doi:10.1038/s41586-026-10722-1
Self-citationZhi‐Xuan, T., Kang, G., Mansinghka, V. K., & Tenenbaum, J. B. (2026) · Topics in Cognitive Science · doi:10.1111/tops.70075
Brophy, S., Banka, P., Hyland, M., O'Neill, D., & Comiskey, C. (2026) · Vulnerable Children and Youth Studies · doi:10.1080/17450128.2026.2725083
Xu, P., & Zhang, Y. (2026) · Cognition · doi:10.1016/j.cognition.2026.106725
Early impressions count: Category ratings established from small samples
Zhang, C., Kemp, S., & Grace, R. C. (2026) · Attention Perception & Psychophysics · doi:10.3758/s13414-026-03364-y
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
