An Information Geometrical Analysis of Neural Spike Sequences

  • Kazushi Ikeda
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3696)


Statistical measures for analyzing neural spikes in cortical areas are discussed from the information geometrical viewpoint. Under the assumption that the interspike intervals of a spike sequence of a neuron obey a gamma distribution with a variable spike rate, we formulate the problem of characterization as a semiparametric statistical estimation. We derive an optimal statistical measure under certain assumptions and also show the meaning of some existing measures, such as the coefficient of variation and the local variation.


Gamma Distribution Spike Train Versus Measure Interspike Interval Spike Rate 
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  1. 1.
    Holt, G.R., et al.: Comparison of discharge variability in vitro and in vivo in cat visual cortex neurons. J. Neurophys. 75, 1806–1814 (1996)Google Scholar
  2. 2.
    Shinomoto, S., Sakai, Y., Funahashi, S.: The Ornstein-Uhlenbeck process does not reproduce spiking statistics of neurons in prefrontal cortex. Neural Comp. 11, 935–951 (1999)CrossRefGoogle Scholar
  3. 3.
    Shinomoto, S., Shima, K., Tanji, J.: New classification scheme of cortical sites with the neuronal spiking characteristics. Neural Networks 15, 1165–1169 (2002)CrossRefGoogle Scholar
  4. 4.
    Shinomoto, S., Shima, K., Tanji, J.: Differences in spiking patterns among cortical neurons. Neural Comp. 15, 2823–2842 (2003)zbMATHCrossRefGoogle Scholar
  5. 5.
    Miura, K., Shinomoto, S., Okada, M.: Search for optimal measure to discriminate random and regular spike trains. Technical Report NC2004-52, IEICE (2004)Google Scholar
  6. 6.
    Tiesinga, P.H.E., Fellous, J.M., Sejnowski, T.J.: Attractor reliability reveals deterministic structure in neuronal spike trains. Neural Comp. 14, 1629–1650 (2002)zbMATHCrossRefGoogle Scholar
  7. 7.
    Amari, S.I.: Differential-Geometrical Methods in Statistics. Lecture Notes in Statistics, vol. 28. Springer, Heidelberg (1985)zbMATHGoogle Scholar
  8. 8.
    Amari, S.I., Nagaoka, H.: Information Geometry. Translations of Mathematical Monographs, vol. 191. AMS and Oxford Univ. Press, Oxford (1999)Google Scholar
  9. 9.
    Shinomoto, S., Tsubo, Y.: Modeling spiking behavior of neurons with time-dependent poisson processes. Physical Review E 64, 041910 (2001)Google Scholar
  10. 10.
    Amari, S.I., Han, T.S.: Statistical inference under multiterminal rate restrictions: A differential geometric approach. IEEE Trans. IT 35, 217–227 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Amari, S.I.: Information geometry on hierarchy of probability distributions. IEEE Trans. IT 47, 1701–1711 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Godambe, V.P.: Conditional likelihood and unconditional optimum estimating equations. Biometrika 63, 277–284 (1976)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Godambe, V.P. (ed.): Estimating Functions. Oxford Univ. Press, Oxford (1991)zbMATHGoogle Scholar
  14. 14.
    Amari, S.I., Kawanabe, M.: Information geometry of estimating functions in semiparametric statistical models. Bernoulli 2(3) (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Kazushi Ikeda
    • 1
  1. 1.Graduate School of InformaticsKyoto UniversityKyotoJapan

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