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Bayesian inference with probabilistic population codes


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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Figure 1: Certainty and gain.
Figure 2: Inference with probabilistic population codes for Gaussian probability distributions and Poisson variability.
Figure 3: Inference with non–translation invariant Gaussian and sigmoidal tuning curves.
Figure 4: Near-optimal inference with a two-layer network of integrate-and-fire neurons similar in spirit to the network shown in Figure 2.


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W.J.M. was supported by a grant from the Schmitt foundation, J.B. by grants from the US National Institutes of Health (NEI 5 T32 MH019942) and the National Institute of Mental Health (T32 MH19942), P.E.L. by the Gatsby Charitable Foundation and National Institute of Mental Health (grant R01 MH62447) and A.P. by the National Science Foundation (grants BCS0346785 and BCS0446730) and by a research grant from the James S. McDonnell Foundation.

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Correspondence to Alexandre Pouget.

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Ma, W., Beck, J., Latham, P. et al. Bayesian inference with probabilistic population codes. Nat Neurosci 9, 1432–1438 (2006).

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