Skip to main content
SpringerLink
Log in

Approximate Inference Method for Dynamic Interactions in Larger Neural Populations

  • Conference paper
  • First Online:
Book cover Neural Information Processing (ICONIP 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9949))

Included in the following conference series:

  • 3076 Accesses

Abstract

The maximum entropy method has been successfully employed to explain stationary spiking activity of a neural population by using fewer features than the number of possible activity patterns. Modeling network activity in vivo, however, has been challenging because features such as spike-rates and interactions can change according to sensory stimulation, behavior, or brain state. To capture the time-dependent activity, Shimazaki et al. (PLOS Comp Biol, 2012) previously introduced a state-space framework for the latent dynamics of neural interactions. However, the exact method suffers from computational cost; therefore its application was limited to only \({\sim }15\) neurons. Here we introduce the pseudolikelihood method combined with the TAP or Bethe approximation to the state-space model, and make it possible to estimate dynamic pairwise interactions of up to 30 neurons. These analytic approximations allow analyses of time-varying activity of larger networks in relation to stimuli or behavior.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Besag, J.: Statistical analysis of non-lattice data. Stat. 24, 179–195 (1975)

    Google Scholar 

  2. Brody, C.D.: Correlations without synchrony. Neural Comput. 11(7), 1537–1551 (1999)

    Article  Google Scholar 

  3. Brown, E.N., Frank, L.M., Tang, D., Quirk, M.C., Wilson, M.A.: A statistical paradigm for neural spike train decoding applied to position prediction from ensemble firing patterns of rat hippocampal place cells. J. Neurosci. 18(18), 7411–7425 (1998)

    Google Scholar 

  4. Granot-Atedgi, E., Tkacik, G., Segev, R., Schneidman, E.: Stimulus-dependent maximum entropy models of neural population codes. PLoS Comput. Biol. 9(3), e1002922 (2013)

    Article  MathSciNet  Google Scholar 

  5. Höfling, H., Tibshirani, R.: Estimation of sparse binary pairwise Markov networks using pseudo-likelihoods. J. Mach. Learn. Res. 10, 883–906 (2009)

    MathSciNet  MATH  Google Scholar 

  6. 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)

    Article  Google Scholar 

  7. Schneidman, E., Berry, M.J., Segev, R., Bialek, W.: Weak pairwise correlations imply strongly correlated network states in a neural population. Nature 440(7087), 1007–1012 (2006)

    Article  Google Scholar 

  8. Shimazaki, H.: Single-trial estimation of stimulus and spike-history effects on time-varying ensemble spiking activity of multiple neurons: a simulation study. J. Phys. Conf. Ser. 473(1), 012009 (2013)

    Article  Google Scholar 

  9. Shimazaki, H., Amari, S.I., Brown, E.N., Grün, S.: State-space analysis on time-varying correlations in parallel spike sequences. In: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 2009, pp. 3501–3504. IEEE (2009)

    Google Scholar 

  10. Shimazaki, H., Amari, S.I., Brown, E.N., Grün, S.: State-space analysis of time-varying higher-order spike correlation for multiple neural spike train data. PLoS Comput. Biol. 8(3), e1002385 (2012)

    Article  MathSciNet  Google Scholar 

  11. Shlens, J., Field, G.D., Gauthier, J.L., Grivich, M.I., Petrusca, D., Sher, A., Litke, A.M., Chichilnisky, E.: The structure of multi-neuron firing patterns in primate retina. J. Neurosci. 26(32), 8254–8266 (2006)

    Article  Google Scholar 

  12. Tanaka, T.: Mean-field theory of Boltzmann machine learning. Phys. Rev. E 58(2), 2302 (1998)

    Article  Google Scholar 

  13. Thouless, D.J., Anderson, P.W., Palmer, R.G.: Solution of ‘solvable model of a spin glass’. Philos. Mag. 35(3), 593–601 (1977)

    Article  Google Scholar 

  14. Tkačik, G., Marre, O., Amodei, D., Schneidman, E., Bialek, W., Berry II, M.J.: Searching for collective behavior in a large network of sensory neurons. PLoS Comput. Biol. 10(1), e1003408 (2014)

    Article  Google Scholar 

  15. Tkačik, G., Mora, T., Marre, O., Amodei, D., Palmer, S.E., Berry, M.J., Bialek, W.: Thermodynamics and signatures of criticality in a network of neurons. Proc. Natl. Acad. Sci. 112(37), 11508–11513 (2015)

    Article  Google Scholar 

  16. Yedidia, J.S., Freeman, W.T., Weiss, Y.: Understanding belief propagation and its generalizations. Explor. Artif. Intell. New Millenn. 8, 236–239 (2003)

    Google Scholar 

  17. Yuille, A.L.: CCCP algorithms to minimize the Bethe and Kikuchi free energies: convergent alternatives to belief propagation. Neural Comput. 14(7), 1691–1722 (2002)

    Article  MATH  Google Scholar 

Download references

Acknowledgments

CD acknowledges T. Toyoizumi for hosting his stay in RIKEN Brain Science Institute and K. Obermayer for valuable ideas and discussions. The custom-made Python programs were developed based on the code originally written by T. Sharp. CD was supported by the Deutsche Forschungsgemeinschaft GRK1589/2.

Author information

Authors and Affiliations

  1. Bernstein Center for Computational Neuroscience, Berlin, Germany

    Christian Donner

  2. Neural Information Processing Group, Technische Universität Berlin, Berlin, Germany

    Christian Donner

  3. RIKEN Brain Science Institute, Saitama, Japan

    Hideaki Shimazaki

Authors
  1. Christian Donner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hideaki Shimazaki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hideaki Shimazaki .

Editor information

Editors and Affiliations

  1. The University of Tokyo , Tokyo, Japan

    Akira Hirose

  2. Kobe University , Kobe, Japan

    Seiichi Ozawa

  3. Okinawa Institute of Science and Technology Graduate University, Onna, Japan

    Kenji Doya

  4. Nara Institute of Science and Technology , Ikoma, Japan

    Kazushi Ikeda

  5. Kyungpook National University , Daegu, Korea (Republic of)

    Minho Lee

  6. Chinese Academy of Sciences , Beijing, China

    Derong Liu

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing AG

About this paper

Cite this paper

Donner, C., Shimazaki, H. (2016). Approximate Inference Method for Dynamic Interactions in Larger Neural Populations. In: Hirose, A., Ozawa, S., Doya, K., Ikeda, K., Lee, M., Liu, D. (eds) Neural Information Processing. ICONIP 2016. Lecture Notes in Computer Science(), vol 9949. Springer, Cham. https://doi.org/10.1007/978-3-319-46675-0_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-46675-0_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46674-3

  • Online ISBN: 978-3-319-46675-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation