Accession Number : AD1053652


Title :   Minimum and Maximum Entropy Distributions for Binary Systems with Known Means and Pairwise Correlations


Descriptive Note : Journal Article - Open Access


Corporate Author : Department of Natural Sciences, Fordham University New York United States


Personal Author(s) : Albanna, Badr F ; Hillar,Christopher ; Sohl-Dickstein,Jascha ; DeWeese,Michael R


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/1053652.pdf


Report Date : 21 Aug 2017


Pagination or Media Count : 33


Abstract : Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured mean neural activities and pairwise correlations, but the full space of probability distributions consistent with these constraints has not been explored. We provide upper and lower bounds on the entropy for the minimum entropy distribution over arbitrarily large collections of binary units with any fixed set of mean values and pairwise correlations. We also construct specific low-entropy distributions for several relevant cases. Surprisingly, the minimum entropy solution has entropy scaling logarithmically with system size for any set of first- and second-order statistics consistent with arbitrarily large systems. We further demonstrate that some sets of these low-order statistics can only be realized by small systems. Our results show how only small amounts of randomness are needed to mimic low-order statistical properties of highly entropic distributions, and we discuss some applications for engineered and biological information transmission systems.


Descriptors :   statistical mechanics , compressed sensing , entropy , channel capacity , complex systems , information processing , algorithms , order statistics , probability distributions , random variables


Subject Categories : Statistics and Probability


Distribution Statement : APPROVED FOR PUBLIC RELEASE