Estimating summary statistics in the spike-train space

Journal of Computational Neuroscience

Volumn 34, Issue 3, 2013, Pages 391-410

  Wu, Wei ^a   Srivastava, Anuj ^a  

^a FLORIDA STATE UNIVERSITY   (United States)

Author keywords

Data driven; Estimation; Euclidean metric; Spike train space; Summary statistics; Time warping

Indexed keywords

NEURAL NETWORKS; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES; STATISTICS; STOCHASTIC MODELS; STOCHASTIC SYSTEMS;

COMPUTATIONAL NEUROSCIENCE; DATA DRIVEN; EUCLIDEAN METRICS; NEURAL SPIKE TRAINS; PROBABILITY MODELLING; SAMPLE AVERAGE; SPIKE TRAIN; SPIKE-TRAIN SPACE; SUMMARY STATISTIC; TIME WARPING;

COVARIANCE MATRIX;

ALGORITHM; ARTICLE; CLASSIFICATION; COMPUTER SIMULATION; COVARIANCE; MATCHING CENTERING PRUNING ALGORITHM; MATHEMATICAL COMPUTING; NERVOUS SYSTEM FUNCTION; NEURAL SPIKE TRAIN; PRIMARY MOTOR CORTEX; PRIORITY JOURNAL; PROBABILITY; RHESUS MONKEY; TIME WARPING;

EID: 84877762230     PISSN: 09295313     EISSN: 15736873     Source Type: Journal    
DOI: 10.1007/s10827-012-0427-3     Document Type: Article

References (42)

1. Abbott, L.F.; & Sejnowski, T.J. (1999). Neural codes and distributed representations: foundations of neural computation. The MIT Press.
2. Aronov, D. (2003). Fast algorithm for the metric-space analysis of simultaneous responses of multiple single neurons. Journal of Neuroscience Methods, 124, 175-179.
3. Aronov, D.; & Victor, J. (2004). Non-Euclidean properties of spike train metric spaces. Physical Review E, 69, 061905.
4. Aronov, D.; Reich, D.S.; Mechler, F.; Victor, J. (2003). Neural coding of spatial phase in v1 of the macaque monkey. Journal of Neurophysiology, 89, 3304-3327.
5. Bickel, P.J.; & Levina, E. (2008). Regularized estimation of large covariance matrices. The Annals of Statistics, 36, 199-227.
6. Bilodeau, M.; & Brenner, D. (1999). Theory of multivariate statistics. Springer.
7. Box, G.E.P.; Hunter, W.G.; Hunter, J.S. (1978). Statistics for experimenters: An introduction to design, data analysis, and model building. New York: Wiley.
8. Brown, E.N.; Barbieri, R.; Ventura, V.; Kass, R.E.; Frank, L.M. (2002). The time-rescaling theorem and its applicationto neural spike train data analysis. Neural Computation, 14, 325-346.
9. Dayan, P.; & Abbott, L.F. (2001). Theoretical neuroscience: Computational and mathematical modeling of neural systems. The MIT Press.
10. Dryden, I.L.; Koloydenko, A.; Zhou, D. (2009). Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging. Annals of Applied Statistics, 3, 1102-1123.
11. p spike alighment metric. Neural Computation, 22, 2785-2808.
12. Houghton, C. (2009). Studying spike trains using a van rossum metric with a synapse-like filter. Journal of Computational Neuroscience, 26, 149-155.
13. Houghton, C.; & Sen, K. (2008). A new multineuron spike train metric. Neural Computation, 20, 1495-1511.
14. Hunter, J.D.; & Milton, J.G. (2003). Amplitude and frequency dependence of spike timing: implications for dynamic regulation. Journal of Neurophysiology, 90, 387-394.
15. Karcher, H. (1977). Riemann center of mass and mollifier smoothing. Communications on Pure and Applied Mathematics, 30, 509-541.
16. Kass, R.E.; & Ventura, V. (2001). A spike-train probability model. Neural Computation, 13, 1713-1720.
17. Kass, R.E.; & Vos, P.W. (1997). Geometric foundations of asymptotic inference. Wiley.
18. Kass, R.E.; Ventura, V.; Brown, E.N. (2005). Statistical issues in the analysis of neuronal data. Journal of Neurophysiology, 94, 8-25.
19. Klassen, E.; Srivastava, A.; Mio, W.; Joshi, S.H. (2004). Analysis of planar shapes using geodesic paths on shape spaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26, 372-383.
20. Kreuz, T.; Haas, J.S.; Morelli, A.; Abarbanel, H.; Politi, A. (2007). Measuring spike train synchrony. Journal of Neuroscience Methods, 165, 151-161.
21. Kurtek, S.; Srivastava, A.; Wu, W. (2011). Signal estimation under random time-warpings and nonlinear signal alignment. In Neural Information Processing Systems (NIPS).
22. Levina, E.; Rothman, A.; Zhu, J. (2008). Sparse estimation of large covariance matrices via a nested lasso penalty. The Annals of Applied Statistics, 2, 245-263.
23. Lim, D.; & Capranica, R.R. (1994). Measurement of temporal regularity of spike train responses in auditory nerve fibers of the green treefrog. Journal of Neurosceince Methods, 52, 203-213.
24. MacLeod, K.; Backer, A.; Laurent, G. (1998). Who reads temporal information contained across synchronized and oscillatory spike trains? Nature, 395, 693-698.
25. Michor, P.W.; & Mumford, D. (2007). An overview of the riemannian metrics on spaces of curves using the hamiltonian approach. Applied and Computational Harmonic Analysis, 23, 74-113.
26. Paiva, A.R.C.; Park, I.; Principe, J.C. (2009a). A comparison of binless spike train measures. Neural Computing and Applications. doi: 10.1007/s00521-009-0307-6.
27. Paiva, A.R.C.; Park, I.; Principe, J.C. (2009b). A reproducing kernel hilbert space framework for spike train signal processing. Neural Computation, 21, 424-449.
28. Pennec, X. (2006). Intrinsic statistics on riemannian manifolds: basic tools for geometric measurements. Journal of Mathematical Imaging and Vision, 25, 127-154.
29. Quiroga, R.Q.; Kreuz, T.; Grassberger, P. (2002). Event synchronization: a simple and fast method to measure synchronicity and time delay patterns. Physical Review E, 66, 041904.
30. Ramsay, J.O.; & Silverman, B.W. (2005). Functional data analysis (2nd ed.). Springer Series in Statistics.
31. Rencher, A.C. (2002). Methods of multivariate analysis. Wiley.
32. Rieke, F.; Warland, D.; Ruyter van Steveninck, R.R.; Bialek, W. (1997). Spikes: Exploring the neural code. MIT Press.
33. Schreiber, S.; Fellousb, J.; Whitmerc, D.; Tiesingaa, P.; Sejnowskib, T. (2003). A new correlation-based measure of spike timing reliability. Neurocomputing, 52-54, 925-931.
34. Srivastava, A.; & Jermyn, I.H. (2009). Looking for shapes in two-dimensional, cluttered point clouds. IEEE Transactions on on Pattern Analysis and Machine Intelligence, 31(9), 1616-1629.
35. Tukey, J.W. (1977). Exploratory data analysis. Reading: Addison-Wesley.
36. Valderrama, M.J. (2007). An overview to modelling functional data. Computational Statistics, 22, 331-334.
37. van Rossum, M.C.W. (2001). A novel spike distance. Neural Computation, 13, 751-763.
38. Victor, J.D.; & Purpura, K.P. (1996). Nature and precision of temporal coding in visual cortex: a metric-space analysis. Journal of Neurophysiology, 76, 1310-1326.
39. Victor, J.D.; & Purpura, K.P. (1997). Metric-space analysis of spike trains: theory, algorithms and application. Network, 8, 127-164.
40. Victor, J.D.; Goldberg, D.H.; Gardner, D. (2007). Dynamic programming algorithms for comparing multineuronal spike trains via cost-based metrics and alignments. Journal of Neuroscience Methods, 161, 351-360.
41. Wu, W.; & Srivastava, A. (2011). An information-geometric framework for statistical inferences in the neural spike train space. Journal of Computational Neuroscience, 31, 725-748.
42. Younes, L.; Michor, P.W.; Shah, J.; Mumford, D. (2008). A metric on shape space with explicit geodesics. Rendiconti Lincei Matematica e Applicazioni, 9, 25-57.