Efficient computation of the maximum a posteriori path and parameter estimation in integrate-and-fire and more general state-space models

Journal of Computational Neuroscience

Volumn 29, Issue 1-2, 2010, Pages 89-105

  Koyama, Shinsuke ^b   Paninski, Liam ^a  

^a Och Spine at New York Presbyterian Hospitals   (United States)

^b NONE

Author keywords

Laplace approximation; Point processes; State space models; Tridiagonal Newton Raphson method

Indexed keywords

PARAMETER ESTIMATION; STATE SPACE METHODS;

EFFICIENT COMPUTATION; LAPLACE'S APPROXIMATION; MAXIMUM A POSTERIORI; NEWTON-RAPHSON'S METHOD; PARAMETERS ESTIMATION; PATH ESTIMATION; POINT PROCESS; STATE-SPACE MODELS; TRIDIAGONAL; TRIDIAGONAL NEWTON-RAPHSON METHOD;

NEWTON-RAPHSON METHOD;

ALGORITHM; ARTICLE; MATHEMATICAL COMPUTING; MATHEMATICAL PARAMETERS; NEUROSCIENCE; PRIORITY JOURNAL; PROBABILITY; SPIKE; STATISTICAL MODEL;

EID: 77956892292     PISSN: 09295313     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10827-009-0150-x     Document Type: Article

References (43)

1. H Abarbanel D Creveling J Jeanne 2008 Estimation of parameters in nonlinear systems using balanced synchronization Physical Review. D. 77 016,208
2. Ahmadian, Y., Pillow, J., & Paninski, L. (2009). Efficient Markov chain Monte Carlo methods for decoding population spike trains. Neural Computation (in press).
3. Ahmed, N. U. (1998). Linear and nonlinear filtering for scientists and engineers. Singapore: World Scientific.
4. A Asif J Moura 2005 Block matrices with l-block banded inverse: Inversion algorithms IEEE Transactions on Signal Processing 53 630 642 10.1109/TSP.2004.840709 (Pubitemid 40181757)
5. L Badel M Richardson W Gerstner 2005 Dependence of the spike-triggered average voltage on membrane response properties Neurocomputing 69 1062 1065 10.1016/j.neucom.2005.12.046
6. BM Bell 1994 The iterated Kalman smoother as Gauss-Newton method SIAM Journal on Optimization 4 626 636 10.1137/0804035
7. Boyd, S., & Vandenberghe, L. (2004). Convex optimization. Cambridge: Cambridge University Press.
8. AE Brockwell AL Rojas RE Kass 2004 Recursive Bayesian decoding of motor cortical signals by particle filtering Journal of Neurophysiology 91 1899 1907 1:STN:280:DC%2BD2c7itVWksA%3D%3D 10.1152/jn.00438.2003 15010499 (Pubitemid 38339355)
9. EN Brown LM Frank D Tang MC Quirk MA Wilson 1998 A statistical paradigm for neural spike train decoding applied to position prediction from ensemble firing patterns of rat hippocampal place cells Journal of Neuroscience 18 7411 7425 1:CAS:528:DyaK1cXmt1Sjtbk%3D 9736661
10. RA Davis G Rodriguez-Yam 2005 Estimation for state-space models based on a likelihood approximation Statistica Sinica 15 381 406
11. AP Dempster NM Laird DB Rubin 1977 Maximum likelihood from incomplete data via the EM algorithm Journal of the Royal Statistical Society. Series B 79 1 38
12. UT Eden LM Frank R Barbieri V Solo EN Brown 2004 Dynamic analyses of neural encoding by point process adaptive filtering Neural Computation 16 971 998 10.1162/089976604773135069 15070506 (Pubitemid 38483047)
13. L Fahrmeir H Kaufmann 1991 On Kalman filtering, posterior mode estimation and fisher scoring in dynamic exponential family regression Metrika 38 37 60 10.1007/BF02613597
14. Fahrmeir, L., & Tutz, G. (1994). Multivariate statistical modelling based on generalized linear models. New York: Springer.
15. Heskes, T., & Zoeter, O. (2002). Expectation propagation for approximate inference in dynamic Bayesian networks. In A. Darwiche & N. Friedman (Eds.), Uncertainty in artificial intelligence: Proceedings of the eighteenth conference (UAI-2002) (pp. 216-233). San Francisco: Morgan Kaufmann.
16. Q Huys M Ahrens L Paninski 2006 Efficient estimation of detailed single-neuron models Journal of Neurophysiology 96 872 890 10.1152/jn.00079.2006 16624998 (Pubitemid 44159755)
17. Izhikevich, E. M. (2007). Dynamical systems in neuroscience: The geometry of excitability and bursting. Cambridge: MIT.
18. B Jungbacker SJ Koopman 2007 Monte Carlo estimation for nonlinear non-Gaussian state-space models Biometrika 94 827 839 10.1093/biomet/asm074
19. S Koyama T Shimokawa S Shinomoto 2007 Phase transitions in the estimation of event rate: A path integral analysis Journal of Physics. A, Mathematical and General 40 383 390 10.1088/1751-8113/40/20/F01
20. S Koyama S Shinomoto 2005 Empirical Bayes interpretations for random point events Journal of Physics. A, Mathematical and General 38 531 537 10.1088/0305-4470/38/29/L04 (Pubitemid 41016426)
21. Minka, T. (2001). Expectation propagation for approximate Bayesian inference. Uncertainty in Artificial intelligence, 17.
22. J Moehlis E Shea-Brown H Rabitz 2006 Optimal inputs for phase models of spiking neurons ASME Journal of Computational and Nonlinear Dynamics 1 358 367 10.1115/1.2338654 (Pubitemid 44762420)
23. RK Olsson KB Petersen T Lehn-Schioler 2007 State-space models: From the EM algorithm to a gradient approach Neural Computation 19 1097 1111 10.1162/neco.2007.19.4.1097
24. L Paninski 2004 Maximum likelihood estimation of cascade point-process neural encoding models Network: Computation in Neural Systems 15 243 262 10.1088/0954-898X/15/4/002 (Pubitemid 39586479)
25. L Paninski 2005 Log-concavity results on Gaussian process methods for supervised and unsupervised learning Advances in Neural Information Processing Systems 17 1025 1032
26. L Paninski 2006 The most likely voltage path and large deviations approximations for integrate-and-fire neurons Journal of Computational Neuroscience 21 71 87 10.1007/s10827-006-7200-4 16633936 (Pubitemid 44028470)
27. L Paninski 2006 The spike-triggered average of the integrate-and-fire cell driven by Gaussian white noise Neural Computation 18 2592 2616 10.1162/neco.2006.18.11.2592 16999572 (Pubitemid 44684600)
28. L Paninski J Pillow E Simoncelli 2004 Maximum likelihood estimation of a stochastic integrate-and-fire neural model Neural Computation 16 2533 2561 10.1162/0899766042321797 15516273 (Pubitemid 39604009)
29. Paninski, L., Brown, E. N., Iyengar, S., & Kass, R. E. (2008). Stochastic methods in neuroscience, chap. Statistical analysis of neuronal data via integrate-and-fire models. Oxford: Oxford University Press.
30. Pillow, J., Ahmadian, Y., & Paninski, L. (2009). Model-based decoding, information estimation, and change-point detection in multi-neuron spike trains. Neural Computation (in press).
31. Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (1992). Numerical recipes in C. Cambridge: Cambridge University Press.
32. L Rabiner 1989 A tutorial on hidden Markov models and selected applications in speech recognition Proceedings of the IEEE 77 257 286 10.1109/5.18626
33. Rasmussen, C. E., & Williams, C. K. I. (2006). Gaussian processes for machine learning. Cambridge: MIT.
34. S Roweis Z Ghahramani 1999 A unifying review of linear Gaussian models Neural Computation 11 305 345 1:STN:280:DyaK1M7js1Slug%3D%3D 10.1162/089976699300016674 9950734
35. G Rybicki D Hummer 1991 An accelerated lambda iteration method for multilevel radiative transfer, appendix b: Fast solution for the diagonal elements of the inverse of a tridiagonal matrix Astronomy and Astrophysics 245 171 1:CAS:528:DyaK3MXlsVGlu70%3D
36. GB Rybicki WH Press 1995 Class of fast methods for processing irregularly sampled or otherwise inhomogeneous one-dimensional data Physical Review Letters 74 7 1060 1063 10.1103/PhysRevLett.74.1060 1:CAS:528:DyaK2MXjs1Kis70%3D 10.1103/PhysRevLett.74.1060 10058924
37. R Salakhutdinov ST Roweis Z Ghahramani 2003 Optimization with EM and expectation-conjugate-gradient International Conference on Machine Learning 20 672 679
38. AC Smith EN Brown 2003 Estimating a state-space model from point process observations Neural Computation 15 965 991 10.1162/089976603765202622 12803953 (Pubitemid 37049798)
39. Snyder, D. L. (1975). Random point processes. New York: Wiley.
40. L Tierney RE Kass JB Kadane 1989 Fully exponential Laplace approximation to posterior expectations and variances Journal of the American Statistical Association 84 710 716 10.2307/2289652
41. M West JP Harrison HS Migon 1985 Dynamic generalized linear models and Bayesian forcasting Journal of the American Statistical Association 80 73 83 10.2307/2288042
42. A Ypma T Heskes 2005 Novel approximations for inference in nonlinear dynamical systems using expectation propagation Neurocomputing 69 85 99 10.1016/j.neucom.2005.02.020 10.1016/j.neucom.2005.02.020 (Pubitemid 41644425)
43. Yu, B. M., Shenoy, K. V., & Sahani, M. (2006). Expectation propagation for inference in non-linear dynamical models with Poisson observations. In Proceedings of the nonlinear statistical signal processing workshop. Piscataway: IEEE.