Abstract
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.
Highlights
The analysis of multivariate neurophysiological signals at the cellular and population scales (EEG/MEG, LFP, and ECOG) has developed almost independently, largely due to the mathematical differences between continuous and point-process signals
The multivariate autoregressive (MVAR) framework is associated with a powerful set of time- and frequency-domain statistical tools for inferring directional and causal information flow based on Granger’s framework [5], including linear and nonlinear Granger causality, directed transfer function, directed coherence, and partial directed coherence
We introduced a new method for modeling multineuron spike train data, and its application to the identification of information flow structure among interacting neuronal populations
Summary
The analysis of multivariate neurophysiological signals at the cellular (spike trains) and population scales (EEG/MEG, LFP, and ECOG) has developed almost independently, largely due to the mathematical differences between continuous and point-process signals. Scattered attempts at applying this general framework to neural spike trains have relied on smoothing the spike trains to obtain a continuous process that can be fit with an MVAR model [9,10,11,12]. This approach has the clear disadvantage of being highly kernel dependent and of introducing unwanted distortions. The inability to estimate multivariate autoregressive models for spike trains has recently motivated Nedungadi et al [13] to develop an alternative nonparametric procedure for computing Granger causality based on spectral matrix factorization (without fitting the data with an autoregressive model)
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