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Bayesian decoding of neural spike trains

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Abstract

Perception, memory, learning, and decision making are processes carried out in the brain. The performance of such intelligent tasks is made possible by the communication of neurons through sequences of voltage pulses called spike trains. It is of great interest to have methods of extracting information from spike trains in order to learn about their relationship to behavior. In this article, we review a Bayesian approach to this problem based on state-space representations of point processes. We discuss some of the theory and we describe the way these methods are used in decoding motor cortical activity, in which the hand motion is reconstructed from neural spike trains.

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References

  • Akaike H. (1974) A new look at the statistical model identification. IEEE Transactions on Automatic Control, AC- 19: 716–723

    Article  MATH  MathSciNet  Google Scholar 

  • Akaike, H. (1994). Experiences on the development of time series models. In H. Bozdogan (Ed.), Proceedings of the first US/Japan conference on the frontiers of statistical modeling: an informational approach (pp. 33–42). Dordrecht: Kluwer. Reprinted in E. Parzen, K. Tanabe, G. Kitagawa (Eds.) (1998). Selected papers of Hirotugu Akaike. New York: Springer.

  • Barbieri R., Quirk M.C., Frank L.M., Wilson M.A., Brown E.N. (2001) Construction and analysis on non-Poisson stimulus-response models of neural spiking activity. Journal of Neuroscience Methods 105: 25–37

    Article  Google Scholar 

  • Barbieri R., Frank L.M., Nguyen D.P., Quirk M.C., Solo V., Wilson M.A., Brown E.N. (2004) Dynamic analyses of information encoding by neural ensembles. Neural Computation 16: 277–307

    Article  MATH  Google Scholar 

  • Berman M. (1983) Comment on Likelihood analysis of point processes and its applications to seismological dat by Ogata. Bulletin of the International Statistical institute 50: 412–418

    Google Scholar 

  • Brockwell A.E., Kass R.E., Schwartz A.B. (2007) Statistical signal processing and the motor cortex. Proceedings of the IEEE 95: 881–898

    Article  Google Scholar 

  • Brown E.N., Frank L.M., Tang D., Quirk M.C., Wilson M.A. (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

    Google Scholar 

  • Brown E.N., Nguyen D.P., Frank L.M., Wilson M.A., Solo V. (2001) An analysis of neural receptive field plasticity by point process adaptive filtering. Proceedings of the National Academy of Sciences 98: 12261–12266

    Article  Google Scholar 

  • 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 Computation 14: 325–346

    Article  MATH  Google Scholar 

  • Brown E.N., Barbieri R., Eden U.T., Frank L.M. (2003) Likelihood methods for neural data analysis. In: Feng J. (eds) Computational Neuroscience: a comprehensive approach. CRC, London, pp 253–286

    Google Scholar 

  • Chapin J.K., Moxon K.A., Markowitz R.S., Nicolelis M.A.L. (1999) Real-time control of a robot arm using simultaneously recorded neurons in the motor cortex. Nature Neuroscience 2: 664–670

    Article  Google Scholar 

  • Daley D.J., Vere-Jones D. (2003) An introduction to the theory of point processes (2nd ed.). Springer, New York

    MATH  Google Scholar 

  • Dayan P., Abbot L.F. (2001) Theoretical neuroscience: computational and mathematical modeling of neural systems. The MIT Press, Cambridge

    MATH  Google Scholar 

  • Doucet A., de Nando F., Gordon N. (2001) Sequential Monte Carlo methods in practice. Springer, Berlin

    MATH  Google Scholar 

  • Durbin J., Coopman S.J. (1997) Monte Carlo maximum likelihood estimation for non-Gaussian state space models. Biometrika 84: 669–684

    Article  MATH  MathSciNet  Google Scholar 

  • Edeline J.M. (1999) Learning-induced physiological plasticity in the thalamo-cortical sensory sytems: a critical evaluation of receptive field plasticity, map changes and their potential mechanisms. Progress in Neurobiology 57: 165–224

    Article  Google Scholar 

  • Eden U.T., Brown E.N. (2008) Continuous-time filters for state estimation from point process models of neural data. Statistica Sinica 18: 1293–1310

    MATH  MathSciNet  Google Scholar 

  • Eden, U. T., Brown, E. N. (2008b). Mixed observation filtering for neural data. In 33rd International conference on acoustics, speech, and signal processing, Las Vegas, NV. March 30–April 4.

  • Eden U.T., Frank L.M., Barbieri R., Solo V., Brown E.N. (2004) Dynamic analyses of neural encoding by point process adaptive filtering. Neural Computation 16: 971–998

    Article  MATH  Google Scholar 

  • Erdélyi A. (1956) Asymptotic expansions. Dover, New York

    MATH  Google Scholar 

  • Frank L.M., Eden U.T., Solo V., Wilson M.A., Brown E.N. (2002) Contrasting patterns of receptive field plasticity in the hippocampus and the entorhinalcortex: an adaptive filtering approach. Journal of Neuroscience 22: 3817–3830

    Google Scholar 

  • Frank L.M., Stanley G.B., Brown E.N. (2004) Hippocampal plasticity across multiple days of exposure to novel environments. Journal of Neuroscience 24: 7681–7689

    Article  Google Scholar 

  • Fruhwirth-Schnatter S. (1994) Applied State space modeling of non-Gaussian Time series using integration-based Kalman-filtering. Statistics and Computing 4: 259–269

    Article  Google Scholar 

  • Georgopoulos A.B., Schwartz A.B., Kettner R.E. (1986) Neural population coding of movement direction. Science, 233: 1416–1419

    Article  Google Scholar 

  • Hastie T.J., Tibshirani R.J. (1990) Generalized additive models. Florida, Chapman & Hall/CRC

    MATH  Google Scholar 

  • Haynes J., Sakai K., Rees G., Gilbert S., Firth C., Passingham R.E. (2007) Reading hidden intentions in the human brain. Current Biology 17: 323–328

    Article  Google Scholar 

  • Johnson A., Kotz S. (1970) Distributions in statistics: continuous univariate distributions (vol. 2). Wiley, New York

    Google Scholar 

  • Julier, S. J., Uhlmann, J. K. (1997). A new extension of the Kalman filter to nonlinear systems. In The proceedings of aerosense: the 11th international symposium on aerospace/defense sensing, simulation and controls, multi sensor fusion, tracking and resource management II.

  • Kaas J.H., Florence S.L., Jain N. (1999) Subcortical contributions to massive cortical reorganizations. Neuron 22: 657–660

    Article  Google Scholar 

  • Kandel E.R. (2000) Principles of Neural Science (4th ed). McGraw-Hill, New York

    Google Scholar 

  • Kass R.E., Raftery A.E. (1995) Bayes factor. Journal of the American Statistical Association 90: 773–795

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Kay K.N., Naselaris T., Prenger R.J., Gallant J.L. (2008) Identifying natural images from human brain activity. Nature 452: 352–356

    Article  Google Scholar 

  • Kitagawa G. (1996) Monte Carlo flter and smoother for non-Gaussian nonlinear state space models. Journal of Computational and Graphical Statistics 5: 1–25

    Article  MathSciNet  Google Scholar 

  • Kitagawa G., Gersh W. (1996) Smoothness priors analysis of time series. Springer, New York

    MATH  Google Scholar 

  • Koyama S., Kass R.E. (2008) Spike-train probability models for stimulus-driven leaky integrate-and-fire neurons. Neural Computation 20: 1776–1795

    Article  MATH  MathSciNet  Google Scholar 

  • Koyama S., Shinomoto S. (2005) Empirical Bayes interpretations of random point events. Journal of Physics A: Mathematical and General 38: L531–L537

    Article  MATH  MathSciNet  Google Scholar 

  • Koyama, S., Pérez-Bolde, L. C., Shalizi, C. R., Kass, R. E. (2008). Approximate methods for state-space models (submitted).

  • Koyama, S., Chase, S. M., Whitford, A. S., Velliste, M., Schwartz, A. B., Kass, R. E. (2009). Comparison of brain-computer interface decoding algorithms in open-loop and closed-loop control (submitted).

  • Lebedev M.A., Nicolelis A.L. (2006) Brain-machine interfaces: past, present and future. Trends in Neuroscience 29: 536–546

    Article  Google Scholar 

  • Li C., Padoa-Schioppa C., Bizzi E. (2001) Neuronal correlates of motor performance and motor learning in the primary motor cortex of monkeys adapting to an external force field. Neuron 30: 593–607

    Article  Google Scholar 

  • McCullagh P., Nelder J.A. (1989) Generalized linear models (2nd edn). Chapman & Hall, New York

    MATH  Google Scholar 

  • Mehta M.R., Quirk M.C., Wilson M.A. (2000) Experience-dependent asymmetric shape of Hippocampal receptive fields. Neuron 25: 707–715

    Article  Google Scholar 

  • Merzenich M.M., Kaas J.H., Wall J.T., Sur M., Nelson R.J., Felleman D.J. (1984) Progression of change following median nerve section in the cortical representation of the hand in areas 3b and 1 in adult owl and squirrel monkeys. Neuroscience 10: 639–665

    Article  Google Scholar 

  • Ogata Y. (1988) Statistical models for earthquake occurrences and residual analysis for point processes. Journal of American Statistical Association 83: 9–27

    Article  Google Scholar 

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

    Google Scholar 

  • Paninski L., Fellows M., Hatsopoulos N., Donoghue J. (2004) Spatiotemporal tuning properties for hand position and velocity in motor cortical neurons. Journal of Neurophysiology 91: 515–532

    Article  Google Scholar 

  • Papangelou F. (1972) Integrability of expected increments of point processes and a related random change of scale. Transactions of the American Mathematical Society 165: 483–506

    Article  MATH  MathSciNet  Google Scholar 

  • Pillow J., Shlens J., Paninski L., Sher A., Litke A., Chichilnisky E., Simoncelli E. (2008) Spatiotemporal correlations and visual signaling in a complete neuronal population. Nature 454: 995–999

    Article  Google Scholar 

  • Reich D.S., Victor J.D., Knight B.W. (1998) The power ratio and interval map: Spiking models and extracellular recordings. Journal of Neuroscience 18: 10090–10104

    Google Scholar 

  • Rieke F., Warland D., de van Ruyter Steveninck R.R., Bialek W. (1997) Spikes: Exploring the neural code. MIT Press, Cambridge

    Google Scholar 

  • Schnatter S. (1992) Integration-based Kalman-filtering for a dynamic generalized linear trend model. Computational Statistics and Data Analysis 13: 447–459

    Article  MATH  MathSciNet  Google Scholar 

  • Schwartz G. (1978) Estimating the dimension of a model. The Annals of Statistics 6: 461–464

    Article  MathSciNet  Google Scholar 

  • Schwartz A.B. (2004) Cortical neural prosthetics. Annual Review of Neuroscience 27: 487–507

    Article  Google Scholar 

  • Serruya M., Hatsopoulos N.G., Paninski L., Fellows M.R., Donoghue J.P. (2002) Brain-machine interface: instant neural control of a movement signal. Nature 416: 141–142

    Article  Google Scholar 

  • Smith M.A., Kohn A. (2008) Spatial and temporal scales of neuronal correlation in primary visual cortex. Journal of Neuroscience 28: 12591–12603

    Article  Google Scholar 

  • Snyder D.L. (1972) Random point processes. Wiley, New York

    Google Scholar 

  • Snyder D.L., Miller M.I. (1991) Random point processes in time and space. Springer, New York

    MATH  Google Scholar 

  • Solo, V. (2000). Unobserved Monte Carlo Method for identification of partially observed nonlinear State space systems, Part II: counting process observations. In Proceedings of the 39th IEEE conference on decision and control (pp. 3331–3336). Sydney, Australia.

  • Srinivasan L., Eden U.T., Mitter S.K., Brown E.N. (2007) General-purpose filter design for neural prosthetic devices. Journal of Neurophysiology 98: 2456–2475

    Article  Google Scholar 

  • Tanner M.A. (1996) Tools for statistical inference. Springer, New York

    MATH  Google Scholar 

  • Taylor D.M., Tillery H., Stephen I., Schwartz A.B. (2002) Direct cortical control of 3D neuroprosthetic devices. Science 296: 1829–1832

    Article  Google Scholar 

  • Tierney L., Kass R.E., Kadane J.B. (1989) Fully exponential Laplace approximations to expectations and variances of nonpositive functions. Journal of the American Statistical Association 84: 710–716

    Article  MATH  MathSciNet  Google Scholar 

  • Truccolo W., Eden U.T., Fellows M.R., Donoghue J.P., Brown E.N. (2005) A point process framework for relating neural spiking activity to spiking history, neural ensemble, and extrinsic covariate effects. Journal of Neurophysiology 93: 1074–1089

    Article  Google Scholar 

  • Velliste, M., Perel, S., Spalding, M. C., Whitford, A. S., Schwartz, A. B. (2008). Cortical control of a prosthetic arm for self-feeding. Nature. doi:10.1038/nature06996.

  • Weinberger N.M. (1993) Leaning-induced changes of auditory receptive fields. Current Opinion in Neurobiology 3: 570–577

    Article  Google Scholar 

  • Wu W., Gao Y., Biemenstock E., Donoghue J.P., Black M.J. (2005) Bayesian population decoding of motor cortical activity using a Kalman filter. Neural Computation 18: 80–118

    Article  Google Scholar 

  • Yu B.M., Kemere C., Santhanam G., Afshar A., Ryu S.I., Meng T.H., Sahani M., Shenoy K.V. (2007) Mixture of trajectory models for neural decoding of goal-directed movements. Journal of Neurophysiology 97: 3763–3780

    Article  Google Scholar 

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Correspondence to Shinsuke Koyama.

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Koyama, S., Eden, U.T., Brown, E.N. et al. Bayesian decoding of neural spike trains. Ann Inst Stat Math 62, 37–59 (2010). https://doi.org/10.1007/s10463-009-0249-x

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  • DOI: https://doi.org/10.1007/s10463-009-0249-x

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