Correlation-based analysis and generation of multiple spike trains using Hawkes models with an exogenous input

Frontiers in Computational Neuroscience

Volumn 4, Issue , 2010, Pages

  Krumin, Michael ^a   Reutsky, Inna ^a   Shoham, Shy ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Correlation functions; Integral equations; Linear system identification; Multi channel recordings; Point process; Recurrent; Retinal ganglion cells; Spike train analysis

Indexed keywords

CORRELATION FUNCTION; MULTI-CHANNEL RECORDING; POINT PROCESS; RECURRENT; RETINAL GANGLION CELLS; SPIKE TRAIN ANALYSIS;

BRAIN; INTEGRAL EQUATIONS; LINEAR SYSTEMS; NEURAL NETWORKS; OPHTHALMOLOGY;

NEURONS;

ACCURACY; ANIMAL CELL; ANIMAL TISSUE; ARTICLE; CELL ACTIVITY; CELL FUNCTION; CORRELATION ANALYSIS; CORRELATION COEFFICIENT; FEEDBACK SYSTEM; HAWKES MODEL; INTERMETHOD COMPARISON; KERNEL METHOD; LINEAR SYSTEM; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MOLECULAR DYNAMICS; MOUSE; NONHUMAN; NONLINEAR SYSTEM; PROCESS MODEL; RETINA GANGLION CELL; SPIKE WAVE; STATISTICAL DISTRIBUTION;

EID: 79958078695     PISSN: 16625188     EISSN: None     Source Type: Journal    
DOI: 10.3389/fncom.2010.00147     Document Type: Article

References (32)

1. Bremaud, P., and Massoulie, L. (2002). Power spectra of general shot noises and Hawkes point processes with a random excitation. Adv. Appl. Probab. 34, 205-222.
2. Brette, R. (2009). Generation of correlated spike trains. Neural. Comput. 21, 188-215.
3. Brillinger, D. (1988). Maximum like-lihood analysis of spike trains of interacting nerve cells. Biol. Cybern. 59, 189-200.
4. Brillinger, D. R. (1975). The identification of point process systems. Ann. Probab. 3, 909-924.
5. Brillinger, D. R., Bryant, H. L., and Segundo, J. P. (1976). Identification of synaptic interactions. Biol. Cybern. 22, 213-228.
6. Brown, E. N., Kass, R. E., and Mitra, P. P. (2004). Multiple neural spike train data analysis: state-of-the-art and future challenges. Nat. Neurosci. 7, 456-461.
7. Cardanobile, S., and Rotter, S. (2010). Multiplicatively interacting point processes and applications to neural modeling. J. Comput. Neurosci. 28, 267-284.
8. Chichilnisky, E. J. (2001). A simple white noise analysis of neuronal light responses. Network 12, 199-213.
9. Chornoboy, E., Schramm, L., and Karr, A. (1988). Maximum likelihood identification of neural point process systems. Biol. Cybern. 59, 265-275.
10. Daley, D. J., and Vere-Jones, D. (2003). An Introduction to the Theory of Point Processes, Vol. 1. New York: Springer.
11. Granger, C. W. J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37, 424-438.
12. Gutnisky, D. A., and Josic, K. (2010). Generation of spatio-temporally correlated spike-trains and local-field potentials using a multivariate autoregressive process. J. Neurophysiol. 103, 2912-2930.
13. Hawkes, A. G. (1971a). Spectra of some self-exciting and mutually exciting point processes. Biometrika 58, 83-90.
14. Hawkes, A. G. (1971b). Point spectra of some mutually exciting point processes. J. R. Stat. Soc. Series B Methodol. 33, 438-443.
15. Johnson, D. H. (1996). Point process models of single-neuron discharges. J. Comput. Neurosci. 3, 275-299.
16. Kailath, T., Sayed, A. H., and Hassibi, B. (2000). Linear Estimation. Upper Saddle River, NJ: Prentice Hall.
17. Krumin, M., Shimron, A., and Shoham, S. (2010). Correlation-distortion based identification of Linear-Nonlinear-Poisson models. J. Comput. Neurosci. 29, 301-308.
18. Krumin, M., and Shoham, S. (2009). Generation of spike trains with controlled auto-and cross-correlation functions. Neural. Comput. 21, 1642-1664.
19. Krumin, M., and Shoham, S. (2010). Multivariate auto-regressive modeling and granger causality analysis of multiple spike trains. Computat. Intell. Neurosci. 2010, Article ID 752428.
20. Ljung, L. (1999). System Identification - Theory for the User, 2nd Edn. Upper Saddle River, NJ: Prentice Hall PTR.
21. Macke, J. H., Berens, P., Ecker, A. S., Tolias, A. S., and Bethge, M. (2009). Generating spike trains with specified correlation coefficients. Neural. Comput. 21, 397-423.
22. Mayers, D. F. (1962). "Part II. Integral equations, Chapters 11-14," in Numerical Solution of Ordinary and Partial Differential Equations, ed. L. Fox (London: Pergamon), 145-183.
23. Noble, B. (1958). Methods Based on the Wiener-Hopf Technique. London: Pergamon.
24. Nykamp, D. Q. (2007). A mathematical framework for inferring connectivity in probabilistic neuronal networks. Math. Biosci. 205, 204-251.
25. Paninski, L., Pillow, J., and Lewi, J. (2007). Statistical models for neural encoding, decoding, and optimal stimulus design. Prog. Brain Res. 165, 493-507.
26. Paninski, L., Shoham, S., Fellows, M. R., Hatsopoulos, N. G., and Donoghue, J. P. (2004). Superlinear population encoding of dynamic hand trajectory in primary motor cortex. J. Neurosci. 24, 8551-8561.
27. Pillow, J. W., Shlens, J., Paninski, L., Sher, A., Litke, A. M., Chichilnisky, E. J., and Simoncelli, E. P. (2008). Spatiotemporal correlations and visual signalling in a complete neuronal population. Nature 454, 995-999.
28. Ringach, D., and Shapley, R. (2004). Reverse correlation in neurophysiology. Cogn. Sci. 28, 147-166.
29. Shoham, S., Paninski, L. M., Fellows, M. R., Hatsopoulos, N. G., Donoghue, J. P., and Normann, R. A. (2005). Statistical encoding model for a primary motor cortical brain-machine interface. IEEE Trans. Biomed. Eng. 52, 1312-1322.
30. Stevenson, I. H., Rebesco, J. M., Miller, L. E., and Koerding, K. P. (2008). Inferring functional connections between neurons. Curr. Opin. Neurobiol. 18, 582-588.
31. Tchumatchenko, T., Malyshev, A., Geisel, T., Volgushev, M., and Wolf, F. (2010). Correlations and synchrony in threshold neuron models. Phys. Rev. Lett. 104, 058102.
32. Toyoizumi, T., Rad, K. R., and Paninski, L. (2009). Mean-field approximations for coupled populations of generalized linear model spiking neurons with Markov refractoriness. Neural. Comput. 21, 1203-1243.