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Mutual Information of Population Codes and Distance Measures in Probability Space

Kukjin Kang·Haim Sompolinsky
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Abstract

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 $α$-Information.

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Kukjin Kang, Haim Sompolinsky. 2001-03-19. Mutual Information of Population Codes and Distance Measures in Probability Space. https://doi.org/10.1103/physrevlett.86.4958

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