Random versus maximum entropy models of neural population activity

Ulisse Ferrari, Tomoyuki Obuchi, and Thierry Mora
Phys. Rev. E 95, 042321 – Published 27 April 2017

Abstract

The principle of maximum entropy provides a useful method for inferring statistical mechanics models from observations in correlated systems, and is widely used in a variety of fields where accurate data are available. While the assumptions underlying maximum entropy are intuitive and appealing, its adequacy for describing complex empirical data has been little studied in comparison to alternative approaches. Here, data from the collective spiking activity of retinal neurons is reanalyzed. The accuracy of the maximum entropy distribution constrained by mean firing rates and pairwise correlations is compared to a random ensemble of distributions constrained by the same observables. For most of the tested networks, maximum entropy approximates the true distribution better than the typical or mean distribution from that ensemble. This advantage improves with population size, with groups as small as eight being almost always better described by maximum entropy. Failure of maximum entropy to outperform random models is found to be associated with strong correlations in the population.

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  • Received 9 December 2016

DOI:https://doi.org/10.1103/PhysRevE.95.042321

©2017 American Physical Society

Physics Subject Headings (PhySH)

Physics of Living SystemsNetworksStatistical Physics & Thermodynamics

Authors & Affiliations

Ulisse Ferrari1, Tomoyuki Obuchi2, and Thierry Mora3,*

  • 1Institut de la Vision, INSERM and UMPC, 75012 Paris, France
  • 2Department of Mathematical and Computing Science, Tokyo Institute of Technology, Yokohama 226-8502, Japan
  • 3Laboratoire de physique statistique, École normale supérieure, CNRS and UPMC, 75005 Paris, France

  • *Corresponding author: tmora@lps.ens.fr

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Vol. 95, Iss. 4 — April 2017

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