Characterization of the causality between spike trains with permutation conditional mutual information

Uncovering the causal relationship between spike train recordings from different neurons is a key issue for understanding the neural coding. This paper presents a method, called permutation conditional mutual information (PCMI), for characterizing the causality between a pair of neurons. The performance of this method is demonstrated with the spike trains generated by the Poisson point process model and the Izhikevich neuronal model, including estimation of the directionality index and detection of the temporal dynamics of the causal link. Simulations show that the PCMI method is superior to the transfer entropy and causal entropy methods at identifying the coupling direction between the spike trains. The advantages of PCMI are twofold: It is able to estimate the directionality index under the weak coupling and against the missing and extra spikes.