New Paper in Entropy: “Minimum and Maximum Entropy…”

The first paper from the Albanna Lab is out in Entropy!

Link to Paper Online

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

Badr F. Albanna, Christopher Hillar, Jascha Sohl-Dickstein and Michael R. DeWeese


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.


Looking for Grad students

If you are a graduate student in neuroscience, physics, or computer science the Albanna Lab is interested in talking to you!  Contact Badr at if you are interested in getting involved.


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The Albanna Lab website is live! I plan on using this site to post news, papers, and code from the Albanna Lab.

Stay tuned!