Skip to main content
SpringerLink
Log in
Book cover

Analysis of Parallel Spike Trains pp 321–341Cite as

Stochastic Models for Multivariate Neural Point Processes: Collective Dynamics and Neural Decoding

  • Chapter

Part of the book series: Springer Series in Computational Neuroscience ((NEUROSCI,volume 7))

Abstract

This chapter reviews a stochastic point process framework for the modeling, analysis and decoding of neuronal ensembles. The spiking probability of any neuron in an ensemble is computed recursively via a system of stochastic nonlinear equations with delays in discrete time. These equations are expressed in terms of conditional intensity functions, which capture the effects of the neuron’s own spiking history (intrinsic dynamics), ensemble history (collective dynamics), and dependencies on stimuli and behavioral covariates. Four related approaches for the statistical modeling of conditional intensity functions are presented: generalized linear models (GLM), penalized splines, hierarchical Bayesian P-splines, and nonparametric function approximation. Decoding of neuronal ensemble spike trains is implemented via stochastic state-space models with point process observations. The framework is illustrated with examples of neural decoding of hand velocities and assessment of collective dynamics in primary motor cortex.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Barbieri R, Quirk MC, Frank LM, Wilson MA, Brown EN (2001) Construction and analysis on non-Poisson stimulus-response models of neural spiking activity. J Neurosci Methods 105:25–37

    Article  CAS  PubMed  Google Scholar 

  • Brezger A, Kneib T, Lang S (2005) BayesX: analyzing Bayesian structured additive regression models. J Statist Software 14(11):1–22

    Google Scholar 

  • Brezger A, Lang S (2006) Generalized structured additive regression based on Bayesian P-splines. Comput Stat Data Anal 50:967–991

    Article  Google Scholar 

  • Brillinger DR (1988) Maximum likelihood analysis of spike trains of interacting nerve cells. Biol Cybern 59:189–200

    Article  CAS  PubMed  Google Scholar 

  • Brockwell AE, Rojas AL, Kass RE (2004) Recursive Bayesian decoding of motor cortical signals by particle filtering. J Neurophys 91(2):1899–1907

    Google Scholar 

  • Brockwell AE, Kass RE, Schwartz AB (2007) Statistical signal processing and the motor cortex. Proc IEEE 95(5):881–897

    Article  Google Scholar 

  • Brockwell AE (2007) Universal residuals: a multivariate transformation. Stat Probab Lett 77:1473–1478

    Article  PubMed  Google Scholar 

  • Brown EN, Frank LM, Tang D, Quirk MC, Wilson MA (1998) A statistical paradigm for neural spike train decoding applied to position prediction from ensemble firing patterns of rat hippocampal place cells. J Neurosci 18:7411–7425

    CAS  PubMed  Google Scholar 

  • Brown EN, Barbieri R, Ventura V, Kass RE, Frank LM (2001) The time-rescaling theorem and its application to neural spike train data analysis. Neural Comput 14:325–346

    Article  Google Scholar 

  • Cardanobile S, Rotter S (2010) Multiplicatively interacting point processes and applications to neural modeling. J Comput Neurosci 28(2):267–284

    Article  PubMed  Google Scholar 

  • Chen Z, Kloosterman F, Wilson M, Brown EN (2010) Variational Bayesian inference for point process generalized linear models in neural spike train analysis. In: Proc. IEEE ICASSP’10, Dallas, TX, pp 2086–2089

    Google Scholar 

  • Chornoboy ES, Schramm PL, Karr AF (1988) Maximum likelihood identification of neuronal point process systems. Biol Cybern 59:265–275

    Article  CAS  PubMed  Google Scholar 

  • Coleman T, Sarma S (2007) A computationally efficient method for modeling neural spiking activity with point processes nonparametrically. In: Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans

    Google Scholar 

  • Cunningham JP, Yu BM, Shenoy KV (2008) Inferring neural firing rates from spike trains using Gaussian processes. In: Platt JC, Koller D, Singer Y, Roweis S (eds) Advances in neural information processing systems, vol 20. MIT Press, Cambridge

    Google Scholar 

  • Czanner G, Eden UT, Wirth S, Yanike M, Suzuki W, Brown E (2008) Analysis of between-trial and within-trial neural spiking dynamics. J Neurophys 99:2672–2693

    Article  Google Scholar 

  • Daley D, Vere-Jones D (2003) An introduction to the theory of point processes. Springer-Verlag, New York

    Google Scholar 

  • DiMatteo I, Genovese C, Kass R (2001) Bayesian curve fitting with free-knot splines. Biometrika 88:1055–1073

    Article  Google Scholar 

  • Donoghue JP (2008) Bridging the brain to the world: a perspective on neural interface systems. Neuron 60:511–521

    Article  CAS  PubMed  Google Scholar 

  • Doucet A, de Freitas N, Gordon N (2001) Sequential Monte Carlo methods in practice. Springer-Verlag, New York

    Google Scholar 

  • Eden UT, Frank LM, Barbieri T, Solo V, Brown EN (2004) Dynamic analyses of neural encoding by point process adaptive filtering. Neural Comput 16(5):971–998

    Article  PubMed  Google Scholar 

  • Eilers PHC, Marx BD (1996) Flexible smoothing with B-splines and penalties. Statist Sci 11:89–102

    Article  Google Scholar 

  • Ergun A, Barbieri R, Eden UT, MA Wilson, Brown EN (2007) Construction of point process adaptive filter algorithms for neural systems using sequential Monte Carlo methods. IEEE Trans Biomed Eng 54(3):416–428

    Article  Google Scholar 

  • Friedman JH (2001) Greedy function approximation: a gradient boosting machine. Ann Statist 29(5):1189–1232

    Article  Google Scholar 

  • Friedman J, Hastie T, Tibshirani R (2008) Regularization paths for generalized linear models via coordinate descent. Available online at http://www-stat.stanford.edu/~hastie/Papers/glmnet.pdf

  • Gamerman D (1997) Sampling from the posterior distribution in generalized linear mixed models. Stat Comput 7:57–68

    Article  Google Scholar 

  • Ginzburg I, Sompolinsky H (1994) Theory of correlations in stochastic neural networks. Phys Rev E 50(4):3171–3191

    Article  CAS  Google Scholar 

  • Harris K, Csicsvari J, Hirase H, Dragoi G, Buzsaki G (2003) Organization of cell assemblies in the hippocampus. Nature 424:552–556

    Article  CAS  PubMed  Google Scholar 

  • Haslinger R, Brown EN, Pipa G (2009) Discrete time rescaling theorem: determining goodness of fit for discrete time models of neural spiking. Abstract No 789.9. Society for Neuroscience, Washington

    Google Scholar 

  • Hastie T, Tibshirani R, Friedman J (2001) The elements of statistical learning. Springer-Verlag, New York

    Google Scholar 

  • Hatsopoulos NG, Ojakangas CL, Paninski L, Donoghue JP (1998) Information about movement direction obtained from synchronous activity of motor cortical neurons. Proc Natl Acad Sci USA 95:15706–15711

    Article  CAS  PubMed  Google Scholar 

  • Hatsopoulos NG, Xu Q, Amit Y (2007) Encoding of movement fragments in the motor cortex. J Neurosci 27(19):5105–5114

    Article  CAS  PubMed  Google Scholar 

  • Hochberg LR, Serruya MD, Friehs GM, Mukand JA, Saleh M, Caplan AH, Branner A, Chen D, Penn RD, Donoghue JP (2006) Neuronal ensemble control of prosthetic devices by a human with tetraplegia. Nature 442:164–171

    Article  CAS  PubMed  Google Scholar 

  • Jaynes ET (1982) On the rationale of maximum entropy methods. Proc IEEE 70:939–952

    Article  Google Scholar 

  • Jermakowicz WJ, Chen X, Khaytin I, Bonds AB, Casagrande VA (2009) Relationship between spontaneous and evoked spike-time correlations in primate visual cortex. J Neurophysiol 101:2279–2289

    Article  PubMed  Google Scholar 

  • Johnson DH (1996) Point process models of single-neuron discharges. J Comput Neurosci 3(4):275–299

    Article  CAS  PubMed  Google Scholar 

  • Kass RE, Ventura V (2001) A spike-train probability model. Neural Comput 13:1713–1720

    Article  CAS  PubMed  Google Scholar 

  • Kass R, Ventura V, Brown EN (2005) Statistical issues in the analysis of neuronal data. J Neurophys 94:8–25

    Article  Google Scholar 

  • Koyama S, Paninski L (2009) Efficient computation of the maximum a posteriori path and parameter estimation in integrate-and-fire and more general state-space models. J Comput Neurosci. doi:10.1007/s10827-009-0150. Advance online publication

    Google Scholar 

  • Koyama S, Perez-Bolde LC, Shalizi CR, Kass RE (2010) Approximate methods for state-space models. J Amer Statist Assoc 105(489):170–180

    Article  CAS  Google Scholar 

  • Kulkarni J, Paninski L (2007) Common-input models for multiple neural spike-train data. Network Comput Neural Syst 18:375–407

    Article  Google Scholar 

  • Kulkarni J, Paninski L (2008) State-space decoding of goal-directed movements. IEEE Signal Process Mag Jan:78–86

    Article  Google Scholar 

  • Landau LD, Lifshitz EM (1958) Statistical physics. Pergamon, London

    Google Scholar 

  • Lawhern V, Wu W, Hatsopoulos NG, Paninski L (2010) Population decoding of motor cortical activity using a generalized linear model with hidden states. J Neurosci Methods 189(2):267–280

    Article  PubMed  Google Scholar 

  • Lesaffre E, Marx BD (1993) Collinearity in generalized linear regression. Commun Stat Theory Methods 22(7):1933–1952

    Article  Google Scholar 

  • Marre O, El Boustani S, Fregnac Y, Dextexhe A (2009) Prediction of spatiotemporal patterns of neural activity from pairwise correlation. Phys Rev Lett 102(138101):1–4

    Google Scholar 

  • Marmarelis VZ (2004) Nonlinear dynamic modeling of physiological systems. Wiley, Hoboken,

    Google Scholar 

  • McCullagh P, Nelder JA (1989) Generalized linear models, 2nd edn. Chapman & Hall/CRC, Boca Raton

    Google Scholar 

  • Martignon L, Deco G, Laskey K, Diamond M, Freiwald W, Vaadia E (2000) Neural coding: higher-order temporal patterns in the neuro-statistics of cell assemblies. Neural Comput 12:2621–2653

    Article  CAS  PubMed  Google Scholar 

  • Meyer C, van Vreeswijk C (2002) Temporal correlations in stochastic networks of spiking neurons. Neural Comput 14:369–404

    Article  PubMed  Google Scholar 

  • Nicolelis MAL, Dimitrov D, Carmena JM, Crist R, Lehew G, Kralik JD, Wise SP (2003) Chronic, multisite, multielectrode recordings in macaque monkeys. Proc Natl Acad Sci USA 100(19):11041–11046

    Article  CAS  PubMed  Google Scholar 

  • Nicolelis MAL, Lebedev MA (2009) Principles of neural ensemble physiology underlying the operation of brain-machine interfaces. Nature Rev Neurosci 10:530–540

    Article  CAS  Google Scholar 

  • Nykamp D (2007) A mathematical framework for inferring connectivity in probabilistic neuronal networks. Math Biosci 205:204–251

    Article  PubMed  Google Scholar 

  • Okatan M, Wilson MA, Brown EN (2005) Analyzing functional connectivity using a network likelihood model of ensemble neural spiking activity. Neural Comput 9:1927–1961

    Article  Google Scholar 

  • Paninski L, Ahmadian Y, Ferreira DG, Koyama S, Rahnama Rad K, Vidne M, Vogelstein J, Wu W (2009a) A new look at state-space models for neural data. J Comput Neurosci. doi:10.1007/s10827-009-0179. Advance online publication

    Google Scholar 

  • Paninski L, Kass R, Brown E, Iyengar I (2009b) Statistical analysis of neuronal data via integrate-and-fire models. In: Laing, C, Lord, G (eds) Stochastic methods in neuroscience. Oxford University Press, London

    Google Scholar 

  • Paninski L (2004) Maximum likelihood estimation of cascade point-process neural encoding models. Network Comput Neural Syst 15:243–262

    Article  Google Scholar 

  • Pillow JW, Shlens J, Paninski L, Sher A, Litke AM, Chichilnisky EJ, Simoncelli EP (2008) Spatio-temporal correlations and visual signaling in a complete neuronal population. Nature 454:995–999

    Article  CAS  PubMed  Google Scholar 

  • Rahnama Rad K, Paninski L (2008) Efficient estimation of two dimensional firing rate surfaces via Gaussian process methods. In: Computational systems neuroscience (COSYNE) conference

    Google Scholar 

  • Riehle A, Grun S, Diesmann M, Aertsen A (1997) Spike synchronization and rate modulation differentially involved in motor cortical function. Science 278:1950–1953

    Article  CAS  PubMed  Google Scholar 

  • Rigat F, de Gunst M, van Pelt J (2006) Bayesian modelling and analysis of spatio-temporal neuronal networks. Bayesian Anal 1(1):733–764

    Google Scholar 

  • Schneidman E, Berry M, Segev R, Bialek W (2006) Weak pairwise correlations imply strongly correlated network states in a neural population. Nature 440:1007–1012

    Article  CAS  PubMed  Google Scholar 

  • Shlens J, Field GD, Gauthier JL, Grivich MI, Petrusca D, Sher A, Litke AM, Chichilnisky EJ (2006) The structure of multi-neuron firing patterns in primate retina. J Neurosci 26:8254–8266

    Article  CAS  PubMed  Google Scholar 

  • Smith AC, Brown EN (2003) Estimating a state-space model from point process observations. Neural Comput 15:965–991

    Article  PubMed  Google Scholar 

  • Spiegelhalter D, Thomas A, Best N, Lunn D (2003) WinBUGS user manual (Version 1.4). Medical Research Council Biostatistics Unit, Cambridge

    Google Scholar 

  • Srinivasan L, Eden UT, Mitter SK, Brown EN (2007) General-purpose filter design for neural prosthetic devices. J Neurophysiol 98:2456–2475

    Article  PubMed  Google Scholar 

  • Stevenson IH, Rebesco JM, Hatsopoulos NG, Haga Z, Miller LE, Körding KP (2009) Bayesian inference of functional connectivity and network structure from spikes. IEEE Trans Neural Syst Rehabil Eng 17(3):203–213

    Article  PubMed  Google Scholar 

  • Tierney L, Kass RE, Kadane JB (1989) Fully exponential Laplace approximations to expectations and variances of nonpositive functions. J Amer Statist Assoc 84:710–716

    Article  Google Scholar 

  • Toyoizumi T, Rahnama Rad K, Paninski L (2009) Mean-field approximations for coupled populations of generalized linear model spiking neurons with Markov refractoriness. Neural Comput 21:1203–1243

    Article  PubMed  Google Scholar 

  • Truccolo W, Eden UT, Fellows MR, Donoghue JP, Brown EN (2004) A point process framework for relating neural spiking activity to spiking history, neural ensemble, and extrinsic covariate effects. J Neurophysiol 93:1074–1089. doi:10.1152/jn.00697.2004

    Article  PubMed  Google Scholar 

  • Truccolo W, Donoghue JP (2007) Non-parametric modeling of neural point processes via stochastic gradient boosting regression. Neural Comput 19(3):672–705

    Article  PubMed  Google Scholar 

  • Truccolo W, Friehs GM, Donoghue JP, Hochberg LR (2008a) Primary motor cortex tuning to intended movement kinematics in humans with tetraplegia. J Neurosci 28(5):1163–1178

    Article  CAS  PubMed  Google Scholar 

  • Truccolo W, Hochberg LR, Eskandar E, Cole A, Cash SS (2008b) Multielectrode array recordings of single unit activity in humans with epilepsy. In: Neural interfaces conference. Cleveland

    Google Scholar 

  • Truccolo W, Hochberg LR, Donoghue JP (2009) Collective dynamics in human and monkey sensorimotor cortex: predicting single neuron spikes. Nature Neurosci. doi:10.1038/nn.2455. Advance online publication, 6 Dec 2009

    PubMed  Google Scholar 

  • Wedderburn RWM (1976) On the existence and uniqueness of the maximum likelihood estimates for certain generalized linear models. Biometrika 63:27–32

    Article  Google Scholar 

  • Wilson MA, McNaughton BL (1993) Dynamics of the hippocampal ensemble code for space. Science 261:1055–1058

    Article  CAS  PubMed  Google Scholar 

  • Wood SN (2006) Generalized additive models. Chapman & Hall/CRC, Boca Raton

    Google Scholar 

  • Wu W, Kulkarni JE, Hatsopoulos NG, Paninski L (2009) Neural decoding of hand motion using a linear state-space model with hidden states. IEEE Trans Neural Syst Rehabil Eng 17(4):370–378

    Article  PubMed  Google Scholar 

  • Yu BM, Afshar A, Santhanam G, Ryu S, Shenoy K, Sahani M (2006) Extracting dynamical structure embedded in neural activity. In: Advances in neural information processing systems, vol 18. MIT Press, Cambridge, pp 1545–1552

    Google Scholar 

  • Zhao M, Iyengar S (2010) Nonconvergence in logistic and Poisson models for neural spiking. Neural Comput 22:1231–1244

    Article  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Neuroscience and Brown Institute for Brain Science, Brown University, S.E. Frank Hall, 185 Meeting Street, Office 583, Providence, RI, 02912, USA

    Wilson Truccolo

  2. Department of Neurology, Massachusetts General Hospital, Boston, MA, 02114, USA

    Wilson Truccolo

Authors
  1. Wilson Truccolo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wilson Truccolo .

Editor information

Editors and Affiliations

  1. Computational Neuroscience Group, RIKEN Brain Science Institute, Hirosawa 2-1, Saitama, 351-0198, Japan

    Sonja Grün

  2. Bernstein-Zentrum für Computational Neur, Neuroscience, Universität Freiburg, Hansastrasse 9A 9a, Freiburg, 79104, Germany

    Stefan Rotter

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Truccolo, W. (2010). Stochastic Models for Multivariate Neural Point Processes: Collective Dynamics and Neural Decoding. In: Grün, S., Rotter, S. (eds) Analysis of Parallel Spike Trains. Springer Series in Computational Neuroscience, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5675-0_15

Download citation

Publish with us

Policies and ethics

Search

Navigation