دورية أكاديمية
Minimum and Maximum Entropy Distributions for Binary Systems with Known Means and Pairwise Correlations
| العنوان: | Minimum and Maximum Entropy Distributions for Binary Systems with Known Means and Pairwise Correlations |
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| المؤلفون: | Badr F. Albanna, Christopher Hillar, Jascha Sohl-Dickstein, Michael R. DeWeese |
| المصدر: | Entropy, Vol 19, Iss 8, p 427 (2017) |
| بيانات النشر: | MDPI AG, 2017. |
| سنة النشر: | 2017 |
| المجموعة: | LCC:Science LCC:Astrophysics LCC:Physics |
| مصطلحات موضوعية: | information theory, minimum entropy, maximum entropy, statistical mechanics, Ising model, pairwise correlations, compressed sensing, neural networks, Science, Astrophysics, QB460-466, Physics, QC1-999 |
| الوصف: | 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. |
| نوع الوثيقة: | article |
| وصف الملف: | electronic resource |
| اللغة: | English |
| تدمد: | 1099-4300 |
| Relation: | https://www.mdpi.com/1099-4300/19/8/427; https://doaj.org/toc/1099-4300 |
| DOI: | 10.3390/e19080427 |
| URL الوصول: | https://doaj.org/article/3d5eac55f9df4ddc8feee04cb32452e0 |
| رقم الأكسشن: | edsdoj.3d5eac55f9df4ddc8feee04cb32452e0 |
| قاعدة البيانات: | Directory of Open Access Journals |
Full Text Finder | تدمد: | 10994300 |
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| DOI: | 10.3390/e19080427 |