Nature Neuroscience
- 9, 1432 - 1438 (2006)
Published online: 22 October 2006; | doi:10.1038/nn1790
Bayesian inference with probabilistic population codesWei Ji Ma1, 3, Jeffrey M Beck1, 3, Peter E Latham2 & Alexandre Pouget11
Department of Brain and Cognitive Sciences, Meliora Hall, University of Rochester, Rochester, New York 14627, USA. 2
Gatsby Computational Neuroscience Unit, 17 Queen Square, London WC1N 3AR, UK. 3
These authors contributed equally to this work.
Correspondence should be addressed to Alexandre Pouget alex@bcs.rochester.edu Recent psychophysical experiments indicate that humans perform near-optimal Bayesian inference in a wide variety of tasks, ranging from cue integration to decision making to motor control. This implies that neurons both represent probability distributions and combine those distributions according to a close approximation to Bayes' rule. At first sight, it would seem that the high variability in the responses of cortical neurons would make it difficult to implement such optimal statistical inference in cortical circuits. We argue that, in fact, this variability implies that populations of neurons automatically represent probability distributions over the stimulus, a type of code we call probabilistic population codes. Moreover, we demonstrate that the Poisson-like variability observed in cortex reduces a broad class of Bayesian inference to simple linear combinations of populations of neural activity. These results hold for arbitrary probability distributions over the stimulus, for tuning curves of arbitrary shape and for realistic neuronal variability.
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