Point-Process Principal Components Analysis via Geometric Optimization

Neural Computation

Volumn 25, Issue 1, 2013, Pages 101-122

  Solo, Victor ^a   Pasha, Syed Ahmed ^b  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

^b UNIVERSITY OF SYDNEY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC ANALYSIS; MAXIMUM LIKELIHOOD ESTIMATION;

ANALYSIS TOOLS; GEOMETRIC OPTIMIZATION; GROWING DEMAND; HIGH-FREQUENCY FINANCE; MAXIMUM LIKELIHOOD ESTIMATOR; PRELIMINARY PROCESSING; PRINCIPAL COMPONENTS ANALYSIS; STIEFEL MANIFOLD;

PRINCIPAL COMPONENT ANALYSIS;

ACTION POTENTIAL; ALGORITHM; ANIMAL; ARTICLE; ARTIFICIAL NEURAL NETWORK; COMPUTER SIMULATION; HUMAN; MULTIVARIATE ANALYSIS; NERVE CELL; PHYSIOLOGY; PRINCIPAL COMPONENT ANALYSIS; STATISTICAL MODEL;

ACTION POTENTIALS; ALGORITHMS; ANIMALS; COMPUTER SIMULATION; HUMANS; LIKELIHOOD FUNCTIONS; MULTIVARIATE ANALYSIS; NEURAL NETWORKS (COMPUTER); NEURONS; PRINCIPAL COMPONENT ANALYSIS;

EID: 84878183663     PISSN: 08997667     EISSN: 1530888X     Source Type: Journal    
DOI: 10.1162/NECO_a_00382     Document Type: Article

References (35)

1. Aitchison, J., & Silvey, S. (1958). Maximum likelihood estimation of parameters subject to restraints. Ann. Math. Stat., 29, 813-833.
2. Andersen, P., Borgan, O., Gill, R., & Keiding, N. (1993). Statistical models based on counting processes. Berlin: Springer-Verlag.
3. Brillinger, D. (1975). The identification of point process systems. Ann. Prob., 3, 909- 929.
4. Brillinger, D. (1981). Time series: Data analysis and theory. San Francisco: Holden-Day.
5. Brillinger, D. (1988). Maximum likelihood analysis of spike trains of interacting nerve cells. Biol. Cybern., 59, 189-200.
6. Brown, E., Frank, L., Tang, D., Quirk, M., &Wilson, M. (1998). A statistical paradigm for neural spike train decoding applied to position prediction from ensemble firing patterns of rat hippocampal place cells. J. Neuroscience, 18, 7411-7425.
7. Brown, E., Kass, R., & Mitra, P. (2004). Multiple neural spike train data analysis: State-of-the-art and future challenges. Nature Neurosci., 7, 456-461.
8. Daley, D., & Vere-Jones, D. (2003). An introduction to the theory of point processes (2nd ed.). New York: Springer-Verlag.
9. Dayan, P., & Abbott, L. (2001). Theoretical neuroscience. Cambridge MA: MIT Press.
10. Edelman, A., Arias, T., & Smith, S. (1998). The geometry of algorithms with orthogonality constraints. SIAM J. Matrix Anal. Appl., 20, 303-353.
11. Grün, S., Diesmann, M., & Aertsen, A. (2002). Unitary events in multiple singleneuron spiking activity: II. Nonstationary data. Neural Comput., 14, 81-119.
12. Hannan, E. (1970). Multiple time series. NewYork: Wiley.
13. Hansen, L., Larsen, J., Nielsen, F., Strother, S., Rostrup, E., Savoy, R., et al. (1999). Generalizable patterns in neuroimaging:How many principal components? NeuroImage, 9, 534-544.
14. Hautsch, N. (2004). Modelling irregularly spaced financial data. New York: Springer.
15. Joliffe, I. (1986). Principal components analysis. Heidelberg: Springer-Verlag.
16. Kass, R., Kelly, R., & Loh, W. (2011). Assessment of synchrony in multiple neural spike trains using loglinear point process models. Ann. Appl. Stat., 5, 1262-1292.
17. Kim, S., Putrino, D., Ghosh, S., & Brown, E. (2011). A Granger causality measure for point process models of ensemble neural spiking activity. PLoS Comput Biol, 7(3), e1001110.
18. Klebaner, F. (2005). Introduction to stochastic calculus with applications. London: Imperial College Press.
19. Kshirsagar, A. (1972). Multivariate analysis. New York: Marcel Dekker.
20. Luenberger, D. (1972). The gradient projection method along geodesics. Management Science, 18, 620-631.
21. Luenberger, D. (1974). Linear and non-linear programming. New York:Wiley.
22. Magnus, J., & Neudecker, H. (1999). Matrix differential calculus with applications in statistics and econometrics. New York:Wiley.
23. Manton, J. (2002). Optimization algorithms exploiting unitary constraints. IEEE Trans. Signal Processing, 50, 635-650.
24. McCullagh, P., & Nelder, J. (1983). Generalized linear models. London: Chapman and Hall.
25. McKeown, M., Jung, T., Makeig, S., Brown, G., Kindermann, S., Lee, T., et al. (1998). Spatially independent activity patterns in functional MRI data during the Stroop color-naming task. Proc. Natl. Acad. Sci. USA, 95, 803-810.
26. Mitra, P., & Pesaran, B. (1999). Analysis of dynamic brain imaging data. Biophysical Journal, 76, 691-708.
27. Okatan, M., Wilson, M., & Brown, E. (2005). Analyzing functional connectivity using a network likelihood model of ensemble neural spiking activity. Neural Comput., 17, 1927-1961.
28. Reinsel, G., & Velu, R. (1998). Multivariate reduced rank regression. Berlin: Springer.
29. Rieke, F., Warland, D., de Ruyter van Stevenink, R., & Bialek, W. (1997). Spikes: Exploring the neural code. Cambridge, MA: MIT Press.
30. Silvey, S. (1959). The Lagrangian multiplier test. Ann. Math. Stat., 30, 389-407.
31. Snyder, D. (1975). Random point processes. New York:Wiley.
32. Solo, V. (2005). System identification with analog and counting process observations I: Hybrid stochastic intensity and likelihood ratios. In Proc. IEEE Conf. Decision and Control (pp. 3105-3110). Piscataway, NJ: IEEE.
33. Solo, V. (2006). High dimensional point process system identification: PCA and dynamic index models. In Proc. IEEE Conf. Decision and Control (pp. 829-833). Piscataway, NJ: IEEE.
34. Truccolo, W., Eden, U., Fellows, M., Donoghue, J., &Brown, E. (2005).Apoint process framework for relating neural spiking activity to spiking history, neural ensemble and extrinsic covariate effects. J. Neurophys., 93, 1074-1089.
35. Truccolo, W., Hochberg, L., &Donoghue, J. (2010).Collective dynamics in humanand monkey sensorimotor cortex: Predicting single neuron spikes. Nature Neurosci., 13, 105-111.