Detecting causality based on state space reconstruction from interspike intervals for neural spike trains

System analysis depends critically on the identification of the connections-especially the causal relationships-that exist between the components of the system. In particular, the causal relationships connecting neurons in brains, whose activities are typically observed as spike trains (a type of point process), need to be elucidated. Although various causality detection methods have been developed for time series signals, an effective causality detection method for spike trains has not been developed yet. To this end, we propose a causality detection method for spike trains based on the theory of nonlinear dynamical systems. We use the mutual prediction accuracy of the interspike intervals of spike trains for causality detection. Furthermore, we test the prediction accuracy obtained by the proposed method using the method of surrogate data from nonlinear dynamical systems theory. Numerical experiments revealed that the proposed method provides accurate causality detection for a small number of neural spike trains generated by the mathematical model.