Mutual Information of Population Codes and Distance Measures in Probability Space

Details Mutual Information of Population Codes and Distance Measures in Probability Space Mutual Information of Population Codes and Distance Measures in Probability Space

2001-01-11

arxiv.org/abs/cond-mat/0101161v3

Physics

Condensed Matter

Statistical Mechanics

11 pages, 3 figures, accepted to PRL

Scientific paper

10.1103/PhysRevLett.86.4958

We studied the mutual information between a stimulus and a large system consisting of stochastic, statistically independent elements that respond to a stimulus. The Mutual Information (MI) of the system saturates exponentially with system size. A theory of the rate of saturation of the MI is developed. We show that this rate is controlled by a distance function between the response probabilities induced by different stimuli. This function, which we term the {\it Confusion Distance} between two probabilities, is related to the Renyi $\alpha$-Information.

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