Rational approximations to rational models: alternative algorithms for category learning
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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.
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Bayesian samplers can match behavioral stochasticity in tasks such as perception, categorization, causal reasoning, and decision making.
“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]
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Structuring Memory Through Inference‐Based Event Segmentation
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Learning the Structure of Social Influence
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Holistic Reinforcement Learning: The Role of Structure and Attention
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A rational model of function learning
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Where do hypotheses come from?
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Selectionist and Evolutionary Approaches to Brain Function: A Critical Appraisal
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The Algorithmic Level Is the Bridge Between Computation and Brain
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A Cognitive Modeling Approach to Strategy Formation in Dynamic Decision Making
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Asking the right questions about the psychology of human inquiry: Nine open challenges
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A tutorial on particle filters
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Burn-in, bias, and the rationality of anchoring
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Self-citationTea With Milk? A Hierarchical Generative Framework of Sequential Event Comprehension
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On the adequacy of current empirical evaluations of formal models of categorization.
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Infant-directed speech is consistent with teaching.
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Finding New Facts; Thinking New Thoughts
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Children’s use of interventions to learn causal structure
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Probabilistic Biases Meet the Bayesian Brain
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Charles Bonnet Syndrome: Evidence for a Generative Model in the Cortex?
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Approach-Induced Biases in Human Information Sampling
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Categorization=decision making+generalization
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The Bayesian boom: good thing or bad?
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Inferring action structure and causal relationships in continuous sequences of human action.
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Intentional Communication: Computationally Easy or Difficult?
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- 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.
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