Estimating spiking irregularities under changing environments

Neural Computation

Volumn 18, Issue 10, 2006, Pages 2359-2386

  Miura, Keiji ^a,b   Okada, Masato ^b,c,d   Amari, Shun Ichi ^d  

^a KYOTO UNIVERSITY   (Japan)

^b JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

^c UNIVERSITY OF TOKYO   (Japan)

^d RIKEN BRAIN SCIENCE INSTITUTE   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ACTION POTENTIAL; ANIMAL; ARTICLE; BIOLOGICAL MODEL; COMPARATIVE STUDY; ENVIRONMENT; HUMAN; NERVE CELL; PHYSIOLOGY; SIGNAL PROCESSING; STATISTICAL MODEL; TIME;

ACTION POTENTIALS; ANIMALS; ENVIRONMENT; HUMANS; LIKELIHOOD FUNCTIONS; MODELS, NEUROLOGICAL; MODELS, STATISTICAL; NEURONS; SIGNAL PROCESSING, COMPUTER-ASSISTED; TIME FACTORS;

FISHER INFORMATION MATRIX; MAXIMUM LIKELIHOOD ESTIMATION; PARAMETER ESTIMATION; POISSON DISTRIBUTION;

CHANGING ENVIRONMENT; ESTIMATING FUNCTIONS; FIRING RATES; GAMMA DISTRIBUTION; INTER SPIKE INTERVALS; NATURAL EXTENSION; SHAPE PARAMETERS; SPIKE GENERATION; STATISTIC MODELING; TIME DEPENDENT;

NEURONS;

EID: 33749438552     PISSN: 08997667     EISSN: 1530888X     Source Type: Journal    
DOI: 10.1162/neco.2006.18.10.2359     Document Type: Article

References (31)

1. Amari, S. (1982). Differential geometry of curved exponential families - curvatures and information loss. Ann. Statist., 10, 357-385.
2. Amari, S. (1985). Differential-geometrical methods in statistics. New York: Springer-Verlag.
3. Amari, S. (1987). Dual connections on the Hilbert bundles of statistical models. In C. T. J. Dodson (Ed.), Geometrization of statistical theory. Lancaster: University of Lancaster, Department of Mathematics.
4. Amari, S. (1998). Natural gradient works efficiently in learning. Neural Comput., 10, 251-276.
5. Amari, S., & Kawanabe, M. (1997). Information geometry of estimating functions in semi-parametric statistical models. Bernoulli, 3, 29-54.
6. Amari, S., & Kumon, M. (1988). Estimation in the presence of infinitely many nuisance parameters-geometry of estimating functions. Ann. Statist., 16, 1044-1068.
7. Amari, S., Kurata, K., & Nagaoka, H. (1992). Information geometry of Boltzmann machines. IEEE Trans. on Neural Networks, 3, 26-271.
8. Amari, S., & Nagaoka, H. (2001). Methods of information geometry. Providence, RI: American Mathematical Society.
9. Baker, S. N., & Lemon, R. N. (2000). Precise spatiotemporal repeating patterns in monkey primary and supplementary motor areas occur at chance levels. J. Neurophysiol., 84, 1770-1780.
10. Bickel, P. J., Klaassen, C. A. J., Ritov, Y., & Wellner, J. A. (1993). Efficient and adaptive estimation for semiparametric models. Baltimore, MD: Johns Hopkins University Press.
11. Brown, E. N., Barbieri, R., Ventura, V., Kass, R. E., & Frank, L. M. (2002). The time-rescaling theorem and its application to neural spike train data analysis. Neural Comput., 14, 325-346.
12. Cox, D. R., & Lewis, P. A. W. (1966). The statistical analysis of series of events. London: Methuen.
13. Godambe, V. P. (1960). An optimum property of regular maximum likelihood estimation. Ann. Math. Statist., 31, 1208-1211.
14. Godambe, V. P. (1976). Conditional likelihood and unconditional optimum estimating equations. Biometrika, 63, 277-284.
15. Godambe, V. P. (Ed.). (1991). Estimating functions. New York: Oxford University Press.
16. Groeneboom, P., & Wellner, J. A. (1992). Information bounds and nonparametric maximum likelihood estimation. Basel: Birkhauser.
17. Havil, J. (2003). Gamma: Exploring Euler's constant. Princeton, NJ: Princeton University Press.
18. Holt, G. R., Softky, W. R., Koch, C., & Douglas, R. J. (1996). Comparison of discharge variability in vitro and in vivo in cat visual cortex neurons. J. Neurophysiol., 75, 1806-1814.
19. Ikeda, K. (2005). Information geometry of interspike intervals in spiking neurons. Neural Comput., 17, 2719-2735.
20. Mukhopadhyay, P. (2004). An introduction to estimating functions. Harrow: Alpha Science International.
21. Murray, M. K., & Rice, J. W. (1993). Differential geometry and statistics. New York: Chapman and Hall.
22. Neyman, J., & Scott, E. L. (1948). Consistent estimates based on partially consistent observations. Econometrica, 32, 1-32.
23. Pfanzagl, J. (1990). Estimation in semiparametric models. Berlin: Springer-Verlag.
24. Reich, D. S., Victor, J. D., & Knight, B. W. (1998). The power ratio and the interval map: Spiking models and extracellular recordings, J. Neurosci., 18, 10090-100104.
25. Ritov, Y., & Bickel, P. J. (1990). Achieving information bounds in non and semiparametric models. Ann. Statist., 18, 925-938.
26. Sakai, Y., Funahashi, S., & Shinomoto, S. (1999). Temporally correlated inputs to leaky integrate-and-fire models can reproduce spiking statistics of cortical neurons. Neural Netw., 12, 1181-1190.
27. Shinomoto, S., Miura, K., & Koyama, S. (2005). A measure of local variation of inter-spike intervals. Biosystems, 79, 67-72.
28. Shinomoto, S., Miyazaki, Y., Tamura, H., & Fujita, I. (2005). Regional and laminar differences in in vivo firing patterns of primate cortical neurons. J. Neurophysiol., 94, 567-576.
29. Shinomoto, S., Shima, K., & Tanji, J. (2003). Differences in spiking patterns among cortical neurons, Neural Comput., 15, 2823-2842.
30. Tuckwell, H. C. (1988). Introduction to theoretical neurobiology: Vol 2, nonlinear and stochastic theories. Cambridge: Cambridge University Press.
31. van der Vaart, A. W. (1998). A symptotic statistics. Cambridge: Cambridge University Press.