Efficient Estimation of Directed Connectivity in Nonlinear and Nonstationary Spiking Neuron Networks

Wenjun Chen, Yueming Wang, Yuxiao Yang

Abstract: Objective: Studying directed connectivity within spiking neuron networks can help understand neural mechanisms. Existing methods assume linear time-invariant neural dynamics with a fixed time lag in information transmission, while spiking networks usually involve complex dynamics that are nonlinear and nonstationary, and have varying time lags. Methods: We develop a Gated Recurrent Unit (GRU)-Point Process (PP) method to estimate directed connectivity within spiking networks. We use a GRU to describe the dependency of the target neuron's current firing rate on the source neurons' past spiking events and a PP to relate the target neuron's firing rate to its current 0-1 spiking event. The GRU model uses recurrent states and gate/activation functions to deal with varying time lags, nonlinearity, and nonstationarity in a parameter-efficient manner. We estimate the model using maximum likelihood and compute directed information as our measure of directed connectivity. Results: We conduct simulations using artificial spiking networks and a biophysical model of Parkinson's disease to show that GRU-PP systematically addresses varying time lags, nonlinearity, and nonstationarity, and estimates directed connectivity with high accuracy and data efficiency. We also use a non-human-primate dataset to show that GRU-PP correctly identifies the biophysically-plausible stronger PMd-to-M1 connectivity than M1-to-PMd connectivity during reaching. In all experiments, the GRU-PP consistently outperforms state-of-the-art methods. Conclusion: The GRU-PP method efficiently estimates directed connectivity in varying time lag, nonlinear, and nonstationary spiking neuron networks. Significance: The proposed method can serve as a directed connectivity analysis tool for investigating complex spiking neuron network dynamics.