期刊
ENTROPY
卷 19, 期 8, 页码 -出版社
MDPI
DOI: 10.3390/e19080427
关键词
information theory; minimum entropy; maximum entropy; statistical mechanics; Ising model; pairwise correlations; compressed sensing; neural networks
资金
- Hellman Foundation
- McDonnell Foundation
- McKnight Foundation
- Mary Elizabeth Rennie Endowment for Epilepsy Research
- National Science Foundation [IIS-1219199]
- NSF All-Institutes Postdoctoral Fellowship
- Mathematical Sciences Research Institute through its core grant [DMS-0441170]
- U.S. Army Research Laboratory
- U.S. Army Research Office [W911NF-13-1-0390]
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.
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