Bayesian brain is a term that is used to refer to the ability of the nervous system to operate in situations of uncertainty in a fashion that is close to the optimal prescribed by Bayesian statistics. This term is used in behavioural sciences and neuroscience and studies associated with this term often strive to explain the brain's cognitive abilities based on statistical principles. It is frequently assumed that the nervous system maintains internal probabilistic models that are updated by neural processing of sensory information using methods approximating those of Bayesian probability.[1],[2] This field of study has its historical roots in numerous disciplines including machine learning, experimental psychology and Bayesian statistics. As early as the 1860s, with the work of Hermann Helmholtz in experimental psychology the brain's ability to extract perceptual information from sensory data was modeled in terms of probabilistic estimation.[3] The basic idea is that the nervous system needs to organize sensory data into an accurate internal model of the outside world. This idea was taken up in research on Unsupervised Learning, in particular the Analysis by Synthesis approach, branches of Machine Learning.[4],[5] In 1983 Geoffrey Hinton and colleagues proposed the brain could be seen as a machine making decisions based on the uncertainties of the outside world.[6] During the 1990s researchers including Peter Dayan, Geoffrey Hinton and Richard Zemel proposed that the brain represents knowledge of the world in terms of probabilities and made specific proposals for tractable neural processes that could manifest such a 'Helmholtz Machine'.[7],[8],[9] Bayesian probability, has been developed by a large field with a wide range of important contributors, e.g. Pierre-Simon Laplace, Thomas Bayes, Harold Jeffreys, Richard Cox and Edwin Jaynes has developed mathematical techniques and procedures for treating probability as the degree of plausibility which should be assigned to a given supposition or hypothesis based on the available evidence.[10] In 1988 E.T. Jaynes presented a framework for using Bayesian Probability to model mental processes.[11] It was thus realized early on that the Bayesian statistical framework holds the potential to lead to insights into the function of the nervous system. A wide range of approaches exist that link Bayesian ideas to the function of the brain. - Psychophysics: Many results about human perceptual or motor behavior are modeled using Bayesian statistics. Examples are the work of Landy, Jacobs, Jordan, Knill, Kording and Wolpert.
- Neural coding: Many theoretical studies ask how the nervous system could implement Bayesian algorithms. Examples are the work of Pouget, Zemel, Deneve, Latham, Hinton and Dayan. A specific flavor of this approach are free energy approaches.
- Electrophysiology: A number of recent electrophysiological studies focus on the representation of probabilities in the nervous system. Examples are the work of Shadlen and Schultz.
[edit] Free energy and the brain During the 1990s some researchers such as Geoffrey Hinton and Karl Friston began examining the concept of 'free energy' as a calculably tractable measure of the discrepancy between actual features of the world and representations of those features captured by neural network models.[12] A synthesis of these researches has recently been attempted by Karl Friston. Using Variational Bayesian methods, he has shown how internal models of the outside world could be updated by sensory information and may be driven to minimize free energy or the discrepancy between the mental model formed and events as they actually occur.[13] According to Friston: "The free-energy considered here represents a bound on the surprise inherent in any exchange with the environment, under expectations encoded by its state or configuration. A system can minimise free-energy by changing its configuration to change the way it samples the environment, or to change its expectations. These changes correspond to action and perception, respectively, and lead to an adaptive exchange with the environment that is characteristic of biological systems. This treatment implies that the system’s state and structure encode an implicit and probabilistic model of the environment."[13] This area of research was summarized in terms understandable by the layperson in a 2008 article in New Scientist that offered an unifying theory of brain function.[14] Karl Friston provides a sense of the potential explanatory power of the theory: "This model of brain function can explain a wide range of anatomical and physiological aspects of brain systems; for example, the hierarchical deployment of cortical areas, recurrent architectures using forward and backward connections and functional asymmetries in these connections. In terms of synaptic physiology, it predicts associative plasticity and, for dynamic models, spike-timing-dependent plasticity. In terms of electrophysiology it accounts for classical and extra-classical receptive field effects and long-latency or endogenous components of evoked cortical responses. It predicts the attenuation of responses encoding prediction error with perceptual learning and explains many phenomena like repetition suppression, mismatch negativity and the P300 in electroencephalography. In psychophysical terms, it accounts for the behavioural correlates of these physiological phenomena, e.g., priming, and global precedence."[13] "It is fairly easy to show that both perceptual inference and learning rest on a minimisation of free energy or suppression of prediction error."[13] [edit] See also Bayesian cognitive science [edit] References - ^ Kenji Doya (Editor), Shin Ishii (Editor), Alexandre Pouget (Editor), Rajesh P. N. Rao (Editor) (2007), Bayesian Brain: Probabilistic Approaches to Neural Coding, The MIT Press; 1 edition (Jan 1 2007)
- ^ Knill David,Pouget Alexandre (2004), The Bayesian brain: the role of uncertainty in neural coding and computation,TRENDS in Neurosciences Vol.27 No.12 December 2004
- ^ Helmholtz, H. (1860/1962). Handbuch der physiologischen optik (Southall, J. P. C. (Ed.), English trans.),Vol. 3. New York: Dover.
- ^ Ghahramani, Z. (2004). Unsupervised learning. In O. Bousquet, G. Raetsch, & U. von Luxburg (Eds.), Advanced lectures on machine learning. Berlin: Springer-Verlag.
- ^ Neisser, U., 1967. Cognitive Psychology. Appleton-Century-Crofts, New York.
- ^ Fahlman, S.E., Hinton, G.E. and Sejnowski, T.J.(1983). Massively parallel architectures for A.I.: Netl, Thistle, and Boltzmann machines. Proceedings of the National Conference on Artificial Intelligence, Washington DC.
- ^ Dayan, P., Hinton, G. E., & Neal, R. M. (1995). The Helmholtz machine. Neural Computation, 7, 889–904.
- ^ Dayan, P. and Hinton, G. E. (1996), Varieties of Helmholtz machines. , Neural Networks, 9 1385-1403.
- ^ Hinton, G. E., Dayan, P., To, A. and Neal R. M. (1995), The Helmholtz machine through time., Fogelman-Soulie and R. Gallinari (editors) ICANN-95, 483-490
- ^ Jaynes, E. T., 1986, `Bayesian Methods: General Background,' in Maximum-Entropy and Bayesian Methods in Applied Statistics, J. H. Justice (ed.), Cambridge Univ. Press, Cambridge
- ^ Jaynes, E. T., 1988, `How Does the Brain Do Plausible Reasoning?', in Maximum-Entropy and Bayesian Methods in Science and Engineering, 1, G. J. Erickson and C. R. Smith (eds.)
- ^ Hinton, G. E. and Zemel, R. S.(1994), Autoencoders, minimum description length, and Helmholtz free energy. Advances in Neural Information Processing Systems 6. J. D. Cowan, G. Tesauro and J. Alspector (Eds.), Morgan Kaufmann: San Mateo, CA.
- ^ a b c d Friston K, Stephan KE., Free energy and the brain, Synthese. 2007. 159:417–458
- ^ Huang Gregory (2008), "Is This a Unified Theory of the Brain?", New Scientist May 23, 2008.
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