Types of approximation for probabilistic cognition: Sampling and variational.
Open accessAbstract
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.
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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).”
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Hierarchical Bayesian inference in the visual cortex
Lee, T. S., & Mumford, D. (2003) · Journal of the Optical Society of America A · doi:10.1364/josaa.20.001434 · Cited by 1,473 · cited 2× · see citing works
“This idea is an expansion of Lee and Mumford (2003), who proposed local regions used particle filters and messages were passed between regions using a message passing scheme called loopy belief propagation, which results from an expectation propagation approximation similar to the variational…”
Hierarchical Models in the Brain
Friston, K. (2008) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000211 · Cited by 952 · cited 3× · see citing works
“A common choice is to find the Gaussian distribution that is closest to a true distribution because then only the means and variances need to be encoded (Friston, 2008; Hinton & Van Camp, 1993).”
Rational approximations to rational models: alternative algorithms for category learning
Sanborn, A. N., Griffiths, T. L., & Navarro, D. J. (2010) · Psychological Review · doi:10.1037/a0020511 · Cited by 369 · see citing works
Self-citationMultistability and perceptual inference
Gershman, S. J., Vul, E., & Tenenbaum, J. B. (2012) · Neural Computation · doi:10.1162/neco_a_00226 · Cited by 140 · see citing works
Flagged first, then by citations
Research works printed but not linked: 31
- 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.
- Anderson, J. R. (1991). The adaptive nature of human categorization. Psychological Review, 98(3), 409-429.
- 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).
- Bishop, C. M. (2006). Pattern recognition and machine learning. New York, NY: Springer.
- 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.
- 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.
- 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.
- Doucet, A., de Freitas, N., & Gordon, N. (2001). Sequential Monte Carlo methods in practice. New York: Springer.
- Griffiths, T. L., Steyvers, M., & Tenenbaum, J. B. (2007). Topics in semantic representation. Psychological Review, 114(2), 211.
- 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).
- 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).
- 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).
- Kemp, C., & Tenenbaum, J. B. (2008). The discovery of structural form. Proceedings of the National Academy of Sciences, 105(31), 10687-10692.
- Kruschke, J. K. (1996). Base rates in category learning. Journal of Experimental Psychology: Learning, Memory, and Cognition, 22, 3-26.
- 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.
- Kruschke, J. K. (2006b). Locally Bayesian learning with applications to retrospective revaluation and highlighting. Psychological Review, 113, 677-699.
- 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.
- 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).
- 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).
- 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.
- Minka, T. (2001). A family of algorithms for approximate Bayesian inference. Unpublished doctoral dissertation. MIT, Boston.
- 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.
- Sanborn, A. N., Griffiths, T. L., & Navarro, D. J. (2010). Rational approximations to the rational model of categorization. Psychological Review, 117, 1144-1167.
- Sanborn, A. N., & Silva, R. (2013). Constraining bridges between levels of analysis: A computational justification for locally Bayesian learning. Journal of Mathematical Psychology.
- Shanks, D. R. (1985). Forward and backward blocking in human contingency judgment. Quarterly Journal of Experimental Psychology, 97B, 1-21.
- 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).
- 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.
- Simon, H. A. (1955). A behavioral model of rational choice. The Quarterly Journal of Economics, 69(1), 99-118.
- 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.
- Van Rooij, I. (2008). The tractable cognition thesis. Cognitive Science, 32(6), 939-984.
- 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.
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“tion, etc); they have also been put forth as candidate cognitive algorithms [96, 72].”
Background
- Authors
- Sanborn, A. N.
- Affiliations
- University of Warwick (GB)
- Corresponding author
- Sanborn, Adam N.
- ORCID
- 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
- hybrid
- doi.org
- Licence
- 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
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