Multivariate Autoregressive Modeling and Granger Causality Analysis of Multiple Spike Trains

Recent years have seen the emergence of microelectrode arrays and optical methods allowing simultaneous recording of spiking activity from populations of neurons in various parts of the nervous system. The analysis of multiple neural spike train data could benefit significantly from existing methods for multivariate time-series analysis which have proven to be very powerful in the modeling and analysis of continuous neural signals like EEG signals. However, those methods have not generally been well adapted to point processes. Here, we use our recent results on correlation distortions in multivariate Linear-Nonlinear-Poisson spiking neuron models to derive generalized Yule-Walker-type equations for fitting ‘‘hidden” Multivariate Autoregressive models. We use this new framework to perform Granger causality analysis in order to extract the directed information flow pattern in networks of simulated spiking neurons. We discuss the relative merits and limitations of the new method.

[1]  M. Wilson,et al.  Analyzing Functional Connectivity Using a Network Likelihood Model of Ensemble Neural Spiking Activity , 2005, Neural Computation.

[2]  Nicholas T. Carnevale,et al.  ModelDB: A Database to Support Computational Neuroscience , 2004, Journal of Computational Neuroscience.

[3]  Shy Shoham,et al.  Correlation-distortion based identification of Linear-Nonlinear-Poisson models , 2009, Journal of Computational Neuroscience.

[4]  Paul H. E. Tiesinga,et al.  A New Correlation-Based Measure of Spike Timing Reliability , 2002, Neurocomputing.

[5]  Fred Wolf,et al.  Correlations and synchrony in threshold neuron models. , 2008, Physical review letters.

[6]  Shy Shoham,et al.  Rapid neurotransmitter uncaging in spatially defined patterns , 2005, Nature Methods.

[7]  F. Helmchen,et al.  In vivo calcium imaging of neural network function. , 2007, Physiology.

[8]  Shy Shoham,et al.  Generation of Spike Trains with Controlled Auto- and Cross-Correlation Functions , 2009, Neural Computation.

[9]  Stefan Rotter,et al.  Analysis of higher-order neuronal interactions based on conditional inference , 2003, Biological Cybernetics.

[10]  Erika E. Fanselow,et al.  Thalamic bursting in rats during different awake behavioral states , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[11]  E. S. Chornoboy,et al.  Maximum likelihood identification of neural point process systems , 1988, Biological Cybernetics.

[12]  P. Whittle On the fitting of multivariate autoregressions, and the approximate canonical factorization of a spectral density matrix , 1963 .

[13]  J. D. Hunter,et al.  Amplitude and frequency dependence of spike timing: implications for dynamic regulation. , 2003, Journal of neurophysiology.

[14]  Shun-ichi Amari,et al.  Information-Geometric Measure for Neural Spikes , 2002, Neural Computation.

[15]  Alexander S. Ecker,et al.  Generating Spike Trains with Specified Correlation Coefficients , 2009, Neural Computation.

[16]  Mark C. W. van Rossum,et al.  A Novel Spike Distance , 2001, Neural Computation.

[17]  Régine Le Bouquin-Jeannès,et al.  Linear and nonlinear causality between signals: methods, examples and neurophysiological applications , 2006, Biological Cybernetics.

[18]  X W Yang,et al.  Identification of connectivity in neural networks. , 1990, Biophysical journal.

[19]  V. I. Kryukov,et al.  A new statistical method for identifying interconnections between neuronal network elements , 1985, Biological Cybernetics.

[20]  C. K. Knox,et al.  Signal transmission in random spike trains with applications to the statocyst neurons of the lobster , 1970, Kybernetik.

[21]  Koichi Sameshima,et al.  Using partial directed coherence to describe neuronal ensemble interactions , 1999, Journal of Neuroscience Methods.

[22]  Uri T Eden,et al.  A point process framework for relating neural spiking activity to spiking history, neural ensemble, and extrinsic covariate effects. , 2005, Journal of neurophysiology.

[23]  Kathryn B. Laskey,et al.  Neural Coding: Higher-Order Temporal Patterns in the Neurostatistics of Cell Assemblies , 2000, Neural Computation.

[24]  G. A. Miller,et al.  Comparison of different cortical connectivity estimators for high‐resolution EEG recordings , 2007, Human brain mapping.

[25]  Eugene M. Izhikevich,et al.  Simple model of spiking neurons , 2003, IEEE Trans. Neural Networks.

[26]  Jonathan D. Victor,et al.  Metric-space analysis of spike trains: theory, algorithms and application , 1998, q-bio/0309031.

[27]  R. Kass,et al.  Multiple neural spike train data analysis: state-of-the-art and future challenges , 2004, Nature Neuroscience.

[28]  S. Shoham,et al.  Patterned Optical Activation of Retinal Ganglion Cells , 2007, 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[29]  H. Boogaard Maximum likelihood estimations in a nonlinear self-exciting point process model , 1986, Biological Cybernetics.

[30]  Ying-Cheng Lai,et al.  Probing Changes in Neural Interaction During Adaptation , 2003, Neural Computation.

[31]  S. Bressler,et al.  Granger Causality: Basic Theory and Application to Neuroscience , 2006, q-bio/0608035.

[32]  Rodrigo Quian Quiroga,et al.  Nonlinear multivariate analysis of neurophysiological signals , 2005, Progress in Neurobiology.

[33]  Mingzhou Ding,et al.  Analyzing multiple spike trains with nonparametric granger causality , 2009, Journal of Computational Neuroscience.

[34]  Jonathan D Victor,et al.  Spike train metrics , 2005, Current Opinion in Neurobiology.

[35]  C. Granger Investigating causal relations by econometric models and cross-spectral methods , 1969 .

[36]  Mingzhou Ding,et al.  Evaluating causal relations in neural systems: Granger causality, directed transfer function and statistical assessment of significance , 2001, Biological Cybernetics.

[37]  Sonja Grün,et al.  Detecting synfire chain activity using massively parallel spike train recording. , 2008, Journal of neurophysiology.

[38]  Andrzej Cichocki,et al.  Quantifying Statistical Interdependence by Message Passing on Graphs—Part I: One-Dimensional Point Processes , 2009, Neural Computation.

[39]  Eero P. Simoncelli,et al.  Spatio-temporal correlations and visual signalling in a complete neuronal population , 2008, Nature.

[40]  David R. Brillinger,et al.  Nerve Cell Spike Train Data Analysis: A Progression of Technique , 1992 .

[41]  L. Paninski,et al.  Superlinear Population Encoding of Dynamic Hand Trajectory in Primary Motor Cortex , 2004, The Journal of Neuroscience.

[42]  Eugene M. Izhikevich,et al.  Polychronization: Computation with Spikes , 2006, Neural Computation.