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. 2011 Mar 24;7(3):e1001111. doi: 10.1371/journal.pcbi.1001111

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Fitzgerald et al.

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.

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This cartoon illustrates the consequences of a minimally informative, MNE response function. As knowledge of the correlation structure increases (which amounts to constraining more moments of the conditional output distribution), the least possible amount of information consistent with that knowledge increases along the solid line. Below the MNE limit is a forbidden region where a response function cannot be consistent with the given set of constraints. All models are bounded from above by the response entropy, corresponding to a noiseless system. Any response function above the MNE limit thus involves unknown and unconstrained moments which carry information. The information associated with the MNE response function increases toward the true value as the knowledge of the distribution tends to infinity. For a binary system, the response function is a logistic function (inset) in the transformed input space defined by , cf. Eq. (3).

Inline graphic — This cartoon illustrates the consequences of a minimally informative, MNE response function. As knowledge of the correlation structure increases (which amounts to constraining more moments of the conditional output distribution), the least possible amount of information consistent with that knowledge increases along the solid line. Below the MNE limit is a forbidden region where a response function cannot be consistent with the given set of constraints. All models are bounded from above by the response entropy, corresponding to a noiseless system. Any response function above the MNE limit thus involves unknown and unconstrained moments which carry information. The information associated with the MNE response function increases toward the true value as the knowledge of the distribution tends to infinity. For a binary system, the response function is a logistic function (inset) in the transformed input space defined by , cf. Eq. (3).