There is strong behavioral and physiological evidence that the brain both represents probability distributions and performs probabilistic inference. Computational neuroscientists have started to shed light on how these probabilistic representations and computations might be implemented in neural circuits. One particularly appealing aspect of these theories is their generality: they can be used to model a wide range of tasks, from sensory processing to high-level cognition. To date, however, these theories have only been applied to very simple tasks. Here we discuss the challenges that will emerge as researchers start focusing their efforts on real-life computations, with a focus on probabilistic learning, structural learning and approximate inference.
This is a preview of subscription content, access via your institution
Open Access articles citing this article.
Nature Communications Open Access 04 November 2023
A quantitative model reveals a frequency ordering of prediction and prediction-error signals in the human brain
Communications Biology Open Access 10 October 2022
Fractional neural sampling as a theory of spatiotemporal probabilistic computations in neural circuits
Nature Communications Open Access 05 August 2022
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Rent or buy this article
Prices vary by article type
Prices may be subject to local taxes which are calculated during checkout
Van Horn, K.S. Constructing a logic of plausible inference: a guide to Cox's theorem. Int. J. Approx. Reason. 34, 3–24 (2003).
De Finetti, B., Machi, A. & Smith, A. Theory of Probability: a Critical Introductory Treatment (Wiley, New York, 1993).
Bayes, T. An essay towards solving a problem in the doctrine of chances. Philos. Trans. R. Soc. Lond. 53, 370–418 (1763).
Laplace, P.S. Theorie Analytique des Probabilites (Ve Courcier, Paris, 1812).
Stigler, S.M. Stigler's law of eponymy. Trans. N. Y. Acad. Sci. 39, 147–158 (1980).
Mach, E. Contributions to the Analysis of the Sensations (Open Court Pub., 1897).
Helmholtz, H.v. Versuch einer erweiterten Anwendung des Fechnerschen Gesetzes im Farbensystem. Z. Psychol. Physiol. Sinnesorgane 2, 1–30 (1891).
Knill, D.C. & Richards, W. Perception as Bayesian Inference (Cambridge University Press, New York, 1996).
van Beers, R.J., Sittig, A.C. & Gon, J.J. Integration of proprioceptive and visual position-information: an experimentally supported model. J. Neurophysiol. 81, 1355–1364 (1999).
Knill, D.C. Surface orientation from texture: ideal observers, generic observers and the information content of texture cues. Vision Res. 38, 1655–1682 (1998).
Ernst, M.O. & Banks, M.S. Humans integrate visual and haptic information in a statistically optimal fashion. Nature 415, 429–433 (2002).
Jacobs, R.A. Optimal integration of texture and motion cues to depth. Vision Res. 117, 3621–3629 (1999).
Wolpert, D.M., Ghahramani, Z. & Jordan, M. An internal model for sensorimotor integration. Science 269, 1880–1882 (1995).
Todorov, E. Optimality principles in sensorimotor control. Nat. Neurosci. 7, 907–915 (2004).
Körding, K.P. & Wolpert, D.M. Bayesian integration in sensorimotor learning. Nature 427, 244–247 (2004).
Chater, N., Tenenbaum, J.B. & Yuille, A. Probabilistic models of cognition: conceptual foundations. Trends Cogn. Sci. 10, 287–291 (2006).
Gopnik, A. et al. A theory of causal learning in children: causal maps and Bayes nets. Psychol. Rev. 111, 3–32 (2004).
Tenenbaum, J.B., Griffiths, T.L. & Kemp, C. Theory-based Bayesian models of inductive learning and reasoning. Trends Cogn. Sci. 10, 309–318 (2006).
Tenenbaum, J.B. & Griffiths, T.L. Theory-based causal inference. in Advances in Neural Information Processing Systems (eds. Becker, S., Thrun, S. & Obermayer, K.) 35–42 (MIT Press, 2003).
Steyvers, M., Griffiths, T.L. & Dennis, S. Probabilistic inference in human semantic memory. Trends Cogn. Sci. 10, 327–334 (2006).
Jurafsky, D. A probabilistic model of lexical and syntactic access and disambiguation. Cogn. Sci. 20, 137–194 (1996).
Levy, R. & Jaeger, T.F. Speakers optimize information density through syntactic reduction. in Advances in Neural Information Processing Systems (eds. Schlökopf, B., Platt, J.C. & Hofmann, T.) 849–856 (MIT Press, 2007).
Tenenbaum, J.B., Kemp, C., Griffiths, T.L. & Goodman, N.D. How to grow a mind: statistics, structure and abstraction. Science 331, 1279–1285 (2011).
van Beers, R.J., Sittig, A.C. & Denier van der Gon, J.J. How humans combine simultaneous proprioceptive and visual position information. Exp. Brain Res. 111, 253–261 (1996).
Alais, D. & Burr, D. The ventriloquist effect results from near-optimal bimodal integration. Curr. Biol. 14, 257–262 (2004).
Ratcliff, R. & Rouder, J.N. Modeling response times for two-choice decisions. Psychol. Sci. 9, 347–356 (1998).
Mazurek, M.E., Roitman, J.D., Ditterich, J. & Shadlen, M.N. A role for neural integrators in perceptual decision making. Cereb. Cortex 13, 1257–1269 (2003).
Krajbich, I., Armel, C. & Rangel, A. Visual fixations and the computation and comparison of value in simple choice. Nat. Neurosci. 13, 1292–1298 (2010).
Kappen, H.J., Gómez, V. & Opper, M. Optimal control as a graphical model inference problem. Mach. Learn. 87, 159–182 (2012).
Todorov, E. General duality between optimal control and estimation. in 47th IEEE Conference on Decision and Control 4286–4292 (2008).
Barlow, H.B. Pattern recognition and the responses of sensory neurons. Ann. NY Acad. Sci. 156, 872–881 (1969).
Koechlin, E., Anton, J.L. & Burnod, Y. Bayesian inference in populations of cortical neurons: a model of motion integration and segmentation in area MT. Biol. Cybern. 80, 25–44 (1999).
Anastasio, T.J., Patton, P.E. & Belkacem-Boussaid, K. Using Bayes' rule to model multisensory enhancement in the superior colliculus. Neural Comput. 12, 1165–1187 (2000).
Hoyer, P.O. & Hyvarinen, A. Interpreting neural response variability as Monte Carlo sampling of the posterior. in Neural Informatoin Processing Systems (eds. Becker, S., Thrun, S. & Obermayer, K.) 293–300 (MIT Press, 2003).
Paulin, M.G. Evolution of the cerebellum as a neuronal machine for Bayesian state estimation. J. Neural Eng. 2, S219–S234 (2005).
Lee, T.S. & Mumford, D. Hierarchical Bayesian inference in the visual cortex. J. Opt. Soc. Am. A Opt. Image Sci. Vis. 20, 1434–1448 (2003).
Achler, T. & Amir, E. Input feedback networks: classification and inference based on network structure. Proc. Artificial General Intelligence 1, 15–26 (2008).
Rao, R.P. Bayesian computation in recurrent neural circuits. Neural Comput. 16, 1–38 (2004).
Jazayeri, M. & Movshon, J.A. Optimal representation of sensory information by neural populations. Nat. Neurosci. 9, 690–696 (2006).
Denève, S., Duhamel, J.R. & Pouget, A. Optimal sensorimotor integration in recurrent cortical networks: a neural implementation of Kalman filters. J. Neurosci. 27, 5744–5756 (2007).
Beck, J.M. & Pouget, A. Exact inferences in a neural implementation of a hidden Markov model. Neural Comput. 19, 1344–1361 (2007).
Bogacz, R. & Gurney, K. The basal ganglia and cortex implement optimal decision making between alternative actions. Neural Comput. 19, 442–477 (2007).
Gold, J.I. & Shadlen, M.N. Neural computations that underlie decisions about sensory stimuli. Trends Cogn. Sci. 5, 10–16 (2001).
Anderson, C. Neurobiological computational systems. in Computational Intelligence: Imitating Life (eds. Marks, R.J., Zurada, J.M. & Robinson, C.J.) 213–222 (IEEE Press, New York, 1994).
Zemel, R.S., Dayan, P. & Pouget, A. Probabilistic interpretation of population code. Neural Comput. 10, 403–430 (1998).
Poggio, T. A theory of how the brain might work. Cold Spring Harb. Symp. Quant. Biol. 55, 899–910 (1990).
Ma, W.J., Beck, J.M., Latham, P.E. & Pouget, A. Bayesian inference with probabilistic population codes. Nat. Neurosci. 9, 1432–1438 (2006).
Huys, Q.J., Zemel, R.S., Natarajan, R. & Dayan, P. Fast population coding. Neural Comput. 19, 404–441 (2007).
Sanger, T.D. Probability density estimation for the interpretation of neural population codes. J. Neurophysiol. 76, 2790–2793 (1996).
Foldiak, P. The 'ideal homunculus': statistical inference from neural population responses. in Computation and Neural Systems (eds. Eeckman, F. & Bower, J.) 55–60 (Kluwer Academic Publishers, Norwell, Massachusetts, USA, 1993).
Graf, A.B., Kohn, A., Jazayeri, M. & Movshon, J.A. Decoding the activity of neuronal populations in macaque primary visual cortex. Nat. Neurosci. 14, 239–245 (2011).
Berens, P. et al. A fast and simple population code for orientation in primate V1. J. Neurosci. 32, 10618–10626 (2012).
Fiser, J., Berkes, P., Orban, G. & Lengyel, M. Statistically optimal perception and learning: from behavior to neural representations. Trends Cogn. Sci. 14, 119–130 (2010).
Moreno-Bote, R., Knill, D.C. & Pouget, A. Bayesian sampling in visual perception. Proc. Natl. Acad. Sci. USA 108, 12491–12496 (2011).
Fetsch, C.R., Pouget, A., Deangelis, G.C. & Angelaki, D.E. Neural correlates of reliability-based cue weighting during multisensory integration. Nat. Neurosci. 15, 146–154 (2012).
Beck, J.M. et al. Bayesian decision making with probabilistic population codes. Neuron 60, 1142–1152 (2008).
Churchland, A.K. et al. Variance as a signature of neural computations during decision making. Neuron 69, 818–831 (2011).
Beck, J.M., Latham, P.E. & Pouget, A. Marginalization in neural circuits with divisive normalization. J. Neurosci. 31, 15310–15319 (2011).
Ma, W.J., Navalpakkam, V., Beck, J.M., Berg, R. & Pouget, A. Behavior and neural basis of near-optimal visual search. Nat. Neurosci. 14, 783–790 (2011).
Beck, J., Heller, K. & Pouget, A. Complex inference in neural circuits with probabilistic population codes and topic models. in Advances in Neural Information Processing Systems (ed. Bartlett, P.) 3068–3076 (MIT Press, 2012).
Deneve, S., Latham, P.E. & Pouget, A. Reading population codes: a neural implementation of ideal observers. Nat. Neurosci. 2, 740–745 (1999).
Deneve, S., Latham, P.E. & Pouget, A. Efficient computation and cue integration with noisy population codes. Nat. Neurosci. 4, 826–831 (2001).
Eliasmith, C. & Anderson, C.H. Neural Engineering: Computation, Representation and Dynamics in Neurobiological Systems (MIT Press, 2003).
Barber, M.J., Clark, J.W. & Anderson, C.H. Neural representation of probabilistic information. Neural Comput. 15, 1843–1864 (2003).
Anderson, J.S., Lampl, I., Gillespie, D.C. & Ferster, D. The contribution of noise to contrast invariance of orientation tuning in cat visual cortex. Science 290, 1968–1972 (2000).
MacKay, D.J.C. Bayesian Interpolation. Neural Comput. 4, 415–447 (1992).
Toyoizumi, T., Pfister, J.P., Aihara, K. & Gerstner, W. Generalized Bienenstock-Cooper-Munro rule for spiking neurons that maximizes information transmission. Proc. Natl. Acad. Sci. USA 102, 5239–5244 (2005).
Bohte, S.M. & Mozer, M.C. Reducing the variability of neural responses: a computational theory of spike timing–dependent plasticity. Neural Comput. 19, 371–403 (2007).
Parra, L.C., Beck, J.M. & Bell, A.J. On the maximization of information flow between spiking neurons. Neural Comput. 21, 2991–3009 (2009).
Bishop, C.M. Pattern Recognition and Machine Learning (Springer, 2006).
MacKay, D.J.C. A practical Bayesian framework for backpropagation networks. Neural Comput. 4, 448–472 (1992).
Collins, A. & Koechlin, E. Reasoning, learning and creativity: frontal lobe function and human decision-making. PLoS Biol. 10, e1001293 (2012).
Braun, D.A., Mehring, C. & Wolpert, D.M. Structure learning in action. Behav. Brain Res. 206, 157–165 (2010).
Kemp, C. & Tenenbaum, J.B. The discovery of structural form. Proc. Natl. Acad. Sci. USA 105, 10687–10692 (2008).
Quartz, S.R. & Sejnowski, T.J. The neural basis of cognitive development: a constructivist manifesto. Behav. Brain Sci. 20, 537–556, discussion 556–596 (1997).
Holtmaat, A., Wilbrecht, L., Knott, G.W., Welker, E. & Svoboda, K. Experience-dependent and cell type–specific spine growth in the neocortex. Nature 441, 979–983 (2006).
Isope, P. & Barbour, B. Properties of unitary granule cell→Purkinje cell synapses in adult rat cerebellar slices. J. Neurosci. 22, 9668–9678 (2002).
Ballard, D.H., Hayhoe, M.M., Pook, P.K. & Rao, R.P. Deictic codes for the embodiment of cognition. Behav. Brain Sci. 20, 723–742, discussion 743–767 (1997).
Gallistel, C.R. & King, A.P. Memory and the Computational Brain: Why Cognitive Science Will Transform Neuroscience (Wiley/Blackwell, New York, 2009).
Smolensky, P. Tensor product variable binding and the representation of symbolic structures in connectionist systems. Artif. Intell. 46, 159–217 (1990).
Plate, T. Holographic Reduced Representations (CSLI Publication, Stanford, California, 2003).
Stewart, T. & Eliasmith, C. Compositionality and biologically plausible models. in Oxford Handbook of Compositionality (eds. Hinzen, W., Machery, E. & Werning, M.) (2011).
Gigerenzer, G.T. & Todd, P.M. Simple Heuristics that Make Us Smart (Oxford University Press, New York, 1999).
Fajen, B.R. & Warren, W.H. Behavioral dynamics of intercepting a moving target. Exp. Brain Res. 180, 303–319 (2007).
Bowers, J.S. & Davis, C.J. Bayesian just-so stories in psychology and neuroscience. Psychol. Bull. 138, 389–414 (2012).
Griffiths, T.L., Chater, N., Norris, D. & Pouget, A. How the Bayesians got their beliefs (and what those beliefs actually are): comment on Bowers and Davis (2012). Psychol. Bull. 138, 415–422 (2012).
Knill, D.C. & Pouget, A. The Bayesian brain: the role of uncertainty in neural coding and computation. Trends Neurosci. 27, 712–719 (2004).
Chomsky, N. Aspects of the Theory of Syntax (MIT Press, 1965).
Hsu, A.S., Chater, N. & Vitanyi, P.M. The probabilistic analysis of language acquisition: theoretical, computational and experimental analysis. Cognition 120, 380–390 (2011).
Simard, P.Y., LeCun, Y., Denke, J.S. & Victorri, B. Transformation invariance in pattern recognition–tangent distance and tangent propagation. in Neural Networks: Tricks of the Trade (eds. Montavon, G., Orr, G.B. & Müller, K.-R.) 235–269 (2012).
Poggio, T. & Edelman, S. A network that learns to recognize three-dimensional objects. Nature 343, 263–266 (1990).
Beck, J.M., Ma, W.J., Pitkow, X., Latham, P.E. & Pouget, A. Not noisy, just wrong: the role of suboptimal inference in behavioral variability. Neuron 74, 30–39 (2012).
MacKay, D. Information Theory, Inference and Learning Algorithms (Cambridge University Press, 2003).
P.E.L. is supported by the Gatsby Charitable Foundation, W.J.M. by National Eye Institute grant R01EY020958-01, National Science Foundation grant IIS-1132009 (Collaborative Research in Computational Neuroscience), and Army Research Office grant W911NF-12-1-0262, and A.P. by National Science Foundation grant #BCS0446730, Multi-University Research Initiative grant #N00014-07-1-0937, National Institute on Drug Abuse grants #BCS0346785, the Swiss National Fund (31003A 143707) and a research grant from the James S. McDonnell Foundation.
The authors declare no competing financial interests.
About this article
Cite this article
Pouget, A., Beck, J., Ma, W. et al. Probabilistic brains: knowns and unknowns. Nat Neurosci 16, 1170–1178 (2013). https://doi.org/10.1038/nn.3495
This article is cited by
Nature Human Behaviour (2023)
Nature Communications (2023)
A narrative review of immersive virtual reality’s ergonomics and risks at the workplace: cybersickness, visual fatigue, muscular fatigue, acute stress, and mental overload
Virtual Reality (2023)
Scientific Reports (2022)
Fractional neural sampling as a theory of spatiotemporal probabilistic computations in neural circuits
Nature Communications (2022)