Advertisement

Journal of Computational Neuroscience

, Volume 29, Issue 1–2, pp 301–308 | Cite as

Correlation-distortion based identification of Linear-Nonlinear-Poisson models

  • Michael Krumin
  • Avner Shimron
  • Shy Shoham
Article

Abstract

Linear-Nonlinear-Poisson (LNP) models are a popular and powerful tool for describing encoding (stimulus-response) transformations by single sensory as well as motor neurons. Recently, there has been rising interest in the second- and higher-order correlation structure of neural spike trains, and how it may be related to specific encoding relationships. The distortion of signal correlations as they are transformed through particular LNP models is predictable and in some cases analytically tractable and invertible. Here, we propose that LNP encoding models can potentially be identified strictly from the correlation transformations they induce, and develop a computational method for identifying minimum-phase single-neuron temporal kernels under white and colored random Gaussian excitation. Unlike reverse-correlation or maximum-likelihood, correlation-distortion based identification does not require the simultaneous observation of stimulus-response pairs—only their respective second order statistics. Although in principle filter kernels are not necessarily minimum-phase, and only their spectral amplitude can be uniquely determined from output correlations, we show that in practice this method provides excellent estimates of kernels from a range of parametric models of neural systems. We conclude by discussing how this approach could potentially enable neural models to be estimated from a much wider variety of experimental conditions and systems, and its limitations.

Keywords

System identification Correlation function Neural population Receptive field Point process Auto-regressive model 

Notes

Acknowledgements

This work was supported by Israeli Science Foundation grant #1248/06 and European Research Council starting grant #211055. We thank the two anonymous reviewers for their comments and suggestions.

References

  1. Adelson, E. & Bergen, J. (1985). Spatiotemporal energy models for the perception of motion. Journal of the Optical Society of America A, 2(2), 284–289.CrossRefGoogle Scholar
  2. Brown, G. D. Yamada, S. & Sejnowski, T. J. (2001). Independent component analysis at the neural cocktail party. Trends in Neurosciences, 24(1), 54–63.CrossRefPubMedGoogle Scholar
  3. Dayan, P. & Abbot, L. F. (2001). Theoretical neuroscience: Computational and mathematical modeling of neural systems. Cambridge: MIT.Google Scholar
  4. Dorn, J. D. & Ringach, D. L. (2003). Estimating membrane voltage correlations from extracellular spike trains. Journal of Neurophysiology, 89(4), 2271–2278.CrossRefPubMedGoogle Scholar
  5. Farah, N., Reutsky, I., & Shoham, S. (2007). Patterned optical activation of retinal ganglion cells. Proc. Engineering in Medicine and Biology Society, 2007. EMBS 2007. 29th Annual International Conference of the IEEE.Google Scholar
  6. Gabbiani, F. Krapp, H. G. Koch, C. & Laurent, G. (2002). Multiplicative computation in a visual neuron sensitive to looming. Nature, 420(6913), 320–324.CrossRefPubMedGoogle Scholar
  7. Johnson, G. E. (1994). Construction of particular random processes. Proceedings of the IEEE, 82(2), 270–285.CrossRefGoogle Scholar
  8. Krumin, M. & Shoham, S. (2009). Generation of spike trains with controlled auto- and cross-correlation functions. Neural Computation, 21(6), 1642–1664.CrossRefPubMedGoogle Scholar
  9. Laubach, M. Shuler, M. & Nicolelis, M. A. L. (1999). Independent component analyses for quantifying neuronal ensemble interactions. Journal of Neuroscience Methods, 94(1), 141–154.CrossRefPubMedGoogle Scholar
  10. Ljung, L. (1999). System identification—theory for the user (2nd ed.). Englewood Cliffs: Prentice Hall PTR.Google Scholar
  11. Macke, J. H. Berens, P. Ecker, A. S. Tolias, A. S. & Bethge, M. (2009). Generating spike trains with specified correlation coefficients. Neural Computation, 21(2), 397–423.CrossRefPubMedGoogle Scholar
  12. Makhoul, J. (1975). Linear prediction: a tutorial review. Proceedings of the IEEE, 63(4), 561–580.CrossRefGoogle Scholar
  13. Nykamp, D. Q. & Ringach, D. L. (2002). Full identification of a linear-nonlinear system via cross-correlation analysis. Journal of Vision, 2(1), 1–11.CrossRefPubMedGoogle Scholar
  14. Paninski, L. Shoham, S. Fellows, M. R. Hatsopoulos, N. G. & Donoghue, J. P. (2004). Superlinear population encoding of dynamic hand trajectory in primary motor cortex. Journal of Neuroscience, 24(39), 8551–8561.CrossRefPubMedGoogle Scholar
  15. Paninski, L., Pillow, J., & Lewi, J. (2007). Statistical models for neural encoding, decoding, and optimal stimulus design. Progress in brain research (Vol. 165, pp. 493–507). The Netherlands: Elsevier.Google Scholar
  16. Pillow, J. W. Shlens, J. Paninski, L. Sher, A. Litke, A. M. Chichilnisky, E. J. et al. (2008). Spatio-temporal correlations and visual signalling in a complete neuronal population. Nature, 454(7207), 995–999.CrossRefPubMedGoogle Scholar
  17. Ringach, D. L. (2004). Mapping receptive fields in primary visual cortex. Journal of Physiology, 558(3), 717–728.CrossRefPubMedGoogle Scholar
  18. Ringach, D. & Shapley, R. (2004). Reverse correlation in neurophysiology. Cognitive Science, 28(2), 147–166.CrossRefGoogle Scholar
  19. Rust, N. C. Mante, V. Simoncelli, E. P. & Movshon, J. A. (2006). How MT cells analyze the motion of visual patterns. Nature Neuroscience, 9(11), 1421–1431.CrossRefPubMedGoogle Scholar
  20. Schwartz, O. Pillow, J. W. Rust, N. C. & Simoncelli, E. P. (2006). Spike-triggered neural characterization. Journal of Vision, 6(4), 484–507.CrossRefPubMedGoogle Scholar
  21. Shoham, S. O’Connor, D. H. Sarkisov, D. V. & Wang, S. S. H. (2005a). Rapid neurotransmitter uncaging in spatially defined patterns. Nature Methods, 2(11), 837–843.CrossRefGoogle Scholar
  22. Shoham, S. Paninski, L. M. Fellows, M. R. Hatsopoulos, N. G. Donoghue, J. P. & Normann, R. A. (2005b). Statistical encoding model for a primary motor cortical brain-machine interface. IEEE Transactions on Biomedical Engineering, 52(7), 1312–1322.CrossRefGoogle Scholar
  23. Simon, B. (1974). The P(ϕ)2 euclidian (Quantum) field theory (pp. 9–11). Princeton: Princeton University Press.Google Scholar
  24. Tchumatchenko, T., Malyshev, A., Geisel, T., Volgushev, M., & Wolf, F. (2008). Correlations and synchrony in threshold neuron models. arXiv:0810.2901v2 [q-bio.NC]. http://arxiv.org/abs/0810.2901. Accessed on December 2008.
  25. Victor, J. D. (1989). Temporal impulse responses from flicker sensitivities: causality, linearity, and amplitude data do not determine phase. Journal of the Optical Society of America A, 6(9), 1302–1303.CrossRefGoogle Scholar
  26. Wu, M. C. K. David, S. V. & Gallant, J. L. (2006). Complete functional characterization of sensory neurons by system identification. Annual Review of Neuroscience, 29(1), 477–505.CrossRefPubMedGoogle Scholar
  27. Yu, Y. & Lee, T. S. (2005). Adaptive contrast gain control and information maximization. Neurocomputing, 65–66, 111–116.CrossRefGoogle Scholar
  28. Yu, Y. Potetz, B. & Lee, T. S. (2005). The role of spiking nonlinearity in contrast gain control and information transmission. Vision Research, 45(5), 583–592.CrossRefPubMedGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Faculty of Biomedical EngineeringTechnion IITHaifaIsrael

Personalised recommendations