Cited by 45Bayesian Modeling and Causal InferenceCognitive Science and Education ResearchDecision-Making and Behavioral Economics

Types of approximation for probabilistic cognition: Sampling and variational.

Open access
Sanborn, Adam N.·2017·Brain and Cognition

Abstract

A basic challenge for probabilistic models of cognition is explaining how probabilistically correct solutions are approximated by the limited brain, and how to explain mismatches with human behavior. An emerging approach to solving this problem is to use the same approximation algorithms that were been developed in computer science and statistics for working with complex probabilistic models. Two types of approximation algorithms have been used for this purpose: sampling algorithms, such as importance sampling and Markov chain Monte Carlo, and variational algorithms, such as mean-field approximations and assumed density filtering. Here I briefly review this work, outlining how the algorithms work, how they can explain behavioral biases, and how they might be implemented in the brain. There are characteristic differences between how these two types of approximation are applied in brain and behavior, which points to how they could be combined in future research.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1016/j.bandc.2015.06.008

Cites

4 of 4 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

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?

  • It is possible to cast many approximate inference schemes as resource-rational algorithms.

    “It is possible to cast many approximate inference schemes as resource-rational algorithms (A. N. Sanborn, 2017).”

    From Meta-learned models of cognition (2024) · cites this paper as A. N. Sanborn, 2017

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

Flagged first, then by citations

Research works printed but not linked: 31

  1. Abbott, J. T., & Griffiths, T. L. (2011). Exploring the influence of particle filter parameters on order effects in causal learning. In Proceedings of the 33rd annual conference of the cognitive science society.
  2. Anderson, J. R. (1991). The adaptive nature of human categorization. Psychological Review, 98(3), 409-429.
  3. Beck, J., Pouget, A., & Heller, K. A. (2012). Complex inference in neural circuits with probabilistic population codes and topic models. In F. Pereira, C. Burges, L. Bottou, & K. Weinberger (Eds.). Advances in neural information processing systems (Vol. 25, pp. 3059-3067).
  4. Bishop, C. M. (2006). Pattern recognition and machine learning. New York, NY: Springer.
  5. Buesing, L., Bill, J., Nessler, B., & Maass, W. (2011). Neural dynamics as sampling: A model for stochastic computation in recurrent networks of spiking neurons. PLoS Computational Biology, 7(11), e1002211.
  6. 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.
  7. Daw, N. D., Courville, A. C., & Dayan, P. (2008). Semi-rational models of conditioning: The case of trial order. In N. Chater & M. Oaksford (Eds.), The probabilistic mind (pp. 431-452). Oxford, UK: Oxford University Press.
  8. Doucet, A., de Freitas, N., & Gordon, N. (2001). Sequential Monte Carlo methods in practice. New York: Springer.
  9. Griffiths, T. L., Steyvers, M., & Tenenbaum, J. B. (2007). Topics in semantic representation. Psychological Review, 114(2), 211.
  10. Hennequin, G., Aitchison, L., & Lengyel, M. (2014). Fast sampling-based inference in balanced neuronal networks. In Z. Ghahramani, M. Welling, C. Cortes, N. Lawrence, & K. Weinberger (Eds.). Advances in neural information processing systems (Vol. 27, pp. 2240-2248).
  11. Hinton, G. E., & Van Camp, D. (1993). Keeping the neural networks simple by minimizing the description length of the weights. In Proceedings of the sixth annual conference on computational learning theory (pp. 5-13).
  12. Huang, Y., & Rao, R. P. (2014). Neurons as Monte Carlo samplers: Bayesian inference and learning in spiking networks. In Z. Ghahramani, M. Welling, C. Cortes, N. Lawrence, & K. Weinberger (Eds.). Advances in neural information processing systems (Vol. 27, pp. 1943-1951).
  13. Kemp, C., & Tenenbaum, J. B. (2008). The discovery of structural form. Proceedings of the National Academy of Sciences, 105(31), 10687-10692.
  14. Kruschke, J. K. (1996). Base rates in category learning. Journal of Experimental Psychology: Learning, Memory, and Cognition, 22, 3-26.
  15. Kruschke, J. K. (2006a). Locally Bayesian learning. In R. Sun (Ed.), Proceedings of the 28th annual meeting of the cognitive science society (pp. 453-458). Erlbaum.
  16. Kruschke, J. K. (2006b). Locally Bayesian learning with applications to retrospective revaluation and highlighting. Psychological Review, 113, 677-699.
  17. Legenstein, R., & Maass, W. (2014). Ensembles of spiking neurons with noise support optimal probabilistic inference in a dynamically changing environment. PLoS Computational Biology, 10(10), e1003859.
  18. 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).
  19. Lieder, F., Griffiths, T., & Goodman, N. (2012). Burn-in, bias, and the rationality of anchoring. In Advances in neural information processing systems (pp. 2690-2798).
  20. Medin, D. L., & Edelson, S. M. (1988). Problem structure and the use of base-rate information from experience. Journal of Experimental Psychology: General, 117, 68-85.
  21. Minka, T. (2001). A family of algorithms for approximate Bayesian inference. Unpublished doctoral dissertation. MIT, Boston.
  22. Moreno-Bote, R., Knill, D. C., & Pouget, A. (2011). Bayesian sampling in visual perception. Proceedings of the National Academy of Sciences, 108(30), 12491-12496.
  23. Sanborn, A. N., Griffiths, T. L., & Navarro, D. J. (2010). Rational approximations to the rational model of categorization. Psychological Review, 117, 1144-1167.
  24. Sanborn, A. N., & Silva, R. (2013). Constraining bridges between levels of analysis: A computational justification for locally Bayesian learning. Journal of Mathematical Psychology.
  25. Shanks, D. R. (1985). Forward and backward blocking in human contingency judgment. Quarterly Journal of Experimental Psychology, 97B, 1-21.
  26. Shi, L., & Griffiths, T. L. (2009). Neural implementation of hierarchical Bayesian inference by importance sampling. In Advances in neural information processing systems (pp. 1669-1677).
  27. 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.
  28. Simon, H. A. (1955). A behavioral model of rational choice. The Quarterly Journal of Economics, 69(1), 99-118.
  29. Tassinari, H., Hudson, T. E., & Landy, M. S. (2006). Combining priors and noisy visual cues in a rapid pointing task. The Journal of Neuroscience, 26(40), 10154-10163.
  30. Van Rooij, I. (2008). The tractable cognition thesis. Cognitive Science, 32(6), 939-984.
  31. Wainwright, M. J., & Jordan, M. I. (2008). Graphical models, exponential families, and variational inference. Foundations and Trends Ò in Machine Learning, 1(1-2), 1-305.

Cited by

Sorted by citations

Authors
Sanborn, A. N.
Affiliations
University of Warwick (GB)
Corresponding author
Sanborn, Adam N.
Venue
Brain and Cognition
Publisher
Elsevier BV
Published
2017-03
Volume
112
Pages
98-101
ISSN
0278-2626 (ISSN-L)
OpenAlex
W1813828162
Cited by
45
References
4
Citations by year
2026: 1 · 2025: 4 · 2024: 5 · 2023: 9 · 2022: 4 · 2021: 4 · 2020: 4 · 2019: 5 · 2018: 2 · 2017: 5 · 2016: 2
FWCI
2.94
Type
journal article
Language
en
Open access
Locations
  • Brain and Cognition (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • Warwick Research Archive Portal (University of Warwick) (acceptedVersion)
Funders
Economic and Social Research Council (ES/K004948/1)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Cognitive Science and Education Research
  • Social Sciences › Decision Sciences › General Decision Sciences › Decision-Making and Behavioral Economics
Keywords
approximation algorithms, sampling algorithms, variational algorithms, importance sampling, Markov chain Monte Carlo, mean-field approximation, behavioral biases, cognitive modeling
MeSH terms
Algorithms, Brain, Cognition, Computer Simulation, Humans, 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