Skip to main content

Pairwise Ising Model Analysis of Human Cortical Neuron Recordings

Part of the Lecture Notes in Computer Science book series (LNIP,volume 10589)


During wakefulness and deep sleep brain states, cortical neural networks show a different behavior, with the second characterized by transients of high network activity. To investigate their impact on neuronal behavior, we apply a pairwise Ising model analysis by inferring the maximum entropy model that reproduces single and pairwise moments of the neuron’s spiking activity. In this work we first review the inference algorithm introduced in Ferrari, Phys. Rev. E (2016) [1]. We then succeed in applying the algorithm to infer the model from a large ensemble of neurons recorded by multi-electrode array in human temporal cortex. We compare the Ising model performance in capturing the statistical properties of the network activity during wakefulness and deep sleep. For the latter, the pairwise model misses relevant transients of high network activity, suggesting that additional constraints are necessary to accurately model the data.


  • Ising model
  • Maximum entropy principle
  • Natural gradient
  • Human temporal cortex
  • Multielectrode array recording
  • Brain states

This is a preview of subscription content, access via your institution.

Buying options

USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-68445-1_30
  • Chapter length: 8 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
USD   109.00
Price excludes VAT (USA)
  • ISBN: 978-3-319-68445-1
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   139.99
Price excludes VAT (USA)
Fig. 1.
Fig. 2.
Fig. 3.


  1. 1.

    The results of this section are grounded on the repeated use of central limit theorem. See [1] for more detail.


  1. Ferrari, U.: Learning maximum entropy models from finite-size data sets: a fast data-driven algorithm allows sampling from the posterior distribution. Phys. Rev. E 94, 023301 (2016)

    CrossRef  Google Scholar 

  2. Stevenson, I.H., Kording, K.P.: How advances in neural recording affect data analysis. Nat. Neurosci. 14(2), 139–142 (2011)

    CrossRef  Google Scholar 

  3. Schneidman, E., Berry, M., Segev, R., Bialek, W.: Weak pairwise correlations imply strongly correlated network states in a population. Nature 440, 1007 (2006)

    CrossRef  Google Scholar 

  4. Peyrache, A., Dehghani, N., Eskandar, E.N., Madsen, J.R., Anderson, W.S., Donoghue, J.A., Hochberg, L.R., Halgren, E., Cash, S.S., Destexhe, A.: Spatiotemporal dynamics of neocortical excitation and inhibition during human sleep. Proc. Nat. Acad. Sci. 109(5), 1731–1736 (2012)

    CrossRef  Google Scholar 

  5. Hamilton, L.S., Sohl-Dickstein, J., Huth, A.G., Carels, V.M., Deisseroth, K., Bao, S.: Optogenetic activation of an inhibitory network enhances feedforward functional connectivity in auditory cortex. Neuron 80, 1066–1076 (2013)

    CrossRef  Google Scholar 

  6. Tkacik, G., Marre, O., Amodei, D., Schneidman, E., Bialek, W., Berry, M.J.: Searching for collective behaviour in a network of real neurons. PloS Comput. Biol. 10(1), e1003408 (2014)

    CrossRef  Google Scholar 

  7. Dehghani, N., Peyrache, A., Telenczuk, B., Le Van Quyen, M., Halgren, E., Cash, S.S., Hatsopoulos, N.G., Destexhe, A.: Dynamic balance of excitation and inhibition in human and monkey neocortex. Sci. Rep. 6 (2016). Article no: 23176. doi:10.1038/srep23176

  8. Gardella, C., Marre, O., Mora, T.: A tractable method for describing complex couplings between neurons and population rate. Eneuro 3(4), 0160 (2016)

    CrossRef  Google Scholar 

  9. Tavoni, G., Ferrari, U., Cocco, S., Battaglia, F.P., Monasson, R.: Functional coupling networks inferred from prefrontal cortex activity show experience-related effective plasticity. Netw. Neurosci. 0(0), 1–27 (2017). doi:10.1162/NETN_a_00014

    Google Scholar 

  10. Jaynes, E.T.: On The rationale of maximum-entropy method. Proc. IEEE 70, 939 (1982)

    CrossRef  Google Scholar 

  11. Ferrari, U., Obuchi, T., Mora, T.: Random versus maximum entropy models of neural population activity. Phys. Rev. E 95, 042321 (2017)

    CrossRef  Google Scholar 

  12. Ackley, D.H., Hinton, G.E., Sejnowski, T.J.: A learning algorithm for Boltzmann machines. Cogn. Sci. 9, 147–169 (1985)

    CrossRef  Google Scholar 

  13. Broderick, T., Dudik, M., Tkacik, G., Schapire, R.E., Bialek, W.: Faster solutions to the inverse pairwise Ising problem. arXiv:0712.2437 (2007)

  14. Cocco, S., Monasson, R.: Adaptive cluster expansion for inferring Boltzmann machines with noisy data. Phys. Rev. Lett. 106, 090601 (2011)

    CrossRef  Google Scholar 

  15. Sohl-Dickstein, J., Battaglino, P.B., DeWeese, M.R.: New method for parameter estimation in probabilistic models: minimum probability flow. Phys. Rev. Lett. 107, 220601 (2011)

    CrossRef  Google Scholar 

  16. Renart, A., De La Rocha, J., Bartho, P., Hollender, L., Parga, N., Reyes, A., Harris, K.D.: The asynchronous state in cortical circuits. Science 327(5965), 587–590 (2010)

    CrossRef  Google Scholar 

  17. Amari, S.: Natural gradient works efficiently in learning. Neural Comput. 10, 251–276 (1998)

    CrossRef  Google Scholar 

  18. Amari, S., Douglas, S.C.: Why natural gradient? Proc. IEEE 2, 1213–1216 (1998)

    Google Scholar 

  19. Le Van Quyen, M., Muller, L.E., Telenczuk, B., Halgren, E., Cash, S., Hatsopoulos, N.G., Dehghani, N., Destexhe, A.: High-frequency oscillations in human and monkey neocortex during the wake-sleep cycle. Proc. Nat. Acad. Sci. 113(33), 9363–93680 (2016)

    CrossRef  Google Scholar 

Download references


We thank B. Telenczuk, G. Tkacik and M. Di Volo for useful discussion. Research funded by European Community (Human Brain Project, H2020-720270), ANR TRAJECTORY, ANR OPTIMA, French State program Investissements dAvenir managed by the Agence Nationale de la Recherche [LIFESENSES: ANR-10-LABX-65] and NIH grant U01NS09050.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Ulisse Ferrari .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Nghiem, TA., Marre, O., Destexhe, A., Ferrari, U. (2017). Pairwise Ising Model Analysis of Human Cortical Neuron Recordings. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2017. Lecture Notes in Computer Science(), vol 10589. Springer, Cham.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68444-4

  • Online ISBN: 978-3-319-68445-1

  • eBook Packages: Computer ScienceComputer Science (R0)