Abstract
An algorithm for the estimation of stochastic processes in a neural system is presented. This process is defined here as the continuous stochastic process reflecting the dynamics of the neural system which has some inputs and generates output spike trains. The algorithm proposed here is to identify the system parameters and then estimate the stochastic process called neural system process here. These procedures carried out on the basis of the output spike trains which are supposed to be the data observed in the randomly missing way by the threshold time function in the neural system. The algorithm is constructed with the well-known Kalman filters and realizes the estimation of the neural system process by cooperating with the algorithm for the parameter estimation of the threshold time function presented previously (Nakao et al., 1983). The performance of the algorithm is examined by applying it to the various spike trains simulated by some artificial models and also to the neural spike trains recorded in cat's optic tract fibers. The results in these applications are thought to prove the effectiveness of the algorithm proposed here to some extent. Such attempts, we think, will serve to improve the characterizing and modelling techniques of the stochastic neural systems.
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References
Arimoto, S.: Kalman, filter. Tokyo: Sangyo Tosho 1977 (in Japanese)
Box, G.E.P., Jenkins, G.M.: Time series analysis, forecasting, and control. San Francisco: Holden Day 1970
Brillinger, D.R.: The identification of point process systems. Ann. Probability 3, 909–929 (1975)
Clay, J.R., Goel, N.S.: Diffusion models for firing of a neuron with varying threshold. J. Theor. Biol. 39, 633–644 (1973)
Enroth-Cugell, C., Robson, J.G.: The contrast sensitivity of retinal ganglion cells of the cat. J. Physiol. (London) 187, 517–552 (1966)
Fukushima, Y., Nakao, M., Munemori, J., Hara, K.-I., Kimura, M., Sato, R.: Spatio-temporal organization of the cat retinal ganglion cells. Papers of Tech. Group Med. Electron. Bion. I.E.C.E. Japan, MBE 82-34 (1982)
Hagiwara, S., Omura, Y.: The critical depolarization for the spike in the squid giant axon. Japan J. Physiol. 8, 234–245 (1958)
Inbar, G.F., Milgram, P.: Estimation of intracellular potential from evoked neural pulse trains. IEEE Trans. Biomed. Eng. BME-22, 379–383 (1975)
Jazwinski, A.H.: Stochastic processes and filtering theory. New York: Academic Press 1970
Jenik, F., Hoehne, H.: Über die Impulsverarbeitung eines mathematischen Neuronenmodells. Kybernetik 3, 109–128 (1966)
Kostyukov, A.I.: Curve-crossing problem for Gaussian stochastic processes and its applications to neural modelling. Biol. Cybern. 29, 187–191 (1978)
Kostyukov, A.I., Ivanov, Yu.N., Kryzhanovsky, M.V.: Probability of neural spike initiation as a curve-crossing problem for Gaussian stochastic process. Biol. Cybern. 39, 157–163 (1981)
Marmarelis, P.Z., Marmarelis, V.Z.: Analysis of physiological systems. New York, London: Plenum Press 1978
Maffei, L., Cervetto, L., Fiorentini, A.: Transfer characteristics of excitation and inhibition in cat retinal ganglion cells. J. Neurophysiol 33, 276–284 (1970)
Nakahama, H., Aya, K., Yamamoto, M., Fujii, H., Shima, K.: Dependency representing markov properties of nonstationary spike trains recorded from the cat's optic tract fibers. Biol. Cybern. 35, 43–54 (1979)
Nakao, M., Fukushima, Y., Kimura, M., Sato, R.: Spatiotemporal organization of cat retinal ganglion cells. Papers of Tech. Group on Med. and Bion. I.E.C.E. Japan, MBE80-117 (1981)
Nakao, M., Hara, K.-I., Kimura, M., Sato, R.: Parameter estimation of the threshold time function in the neural system. Biol. Cybern. 48, 131–137 (1983)
Narita, S.: Methods for system engineering. Tokyo: Corona sha 1970 (in Japanese)
Perkel, D.H., Gerstein, G.L., Moore, G.P.: Neuronal spike trains and stochastic point processes. I, II. Biophys. J. 7, 391–440 (1967)
Sakai, H., Soeda, T., Tokumaru, H.: On the relation between fitting autoregression and periodgram with applications. Ann. Statistics 7, 96–107 (1979)
Shapley, R.M., Victor, J.D.: The effect of contrast on the transfer properties of the cat retinal ganglion cells. J. Physiol. (London) 285, 275–298 (1978)
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Nakao, M., Hara, Ki., Kimura, M. et al. Identification and estimation algorithm for stochastic neural system. Biol. Cybern. 50, 241–249 (1984). https://doi.org/10.1007/BF00337074
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DOI: https://doi.org/10.1007/BF00337074