Estimating Temporal Causal Interaction between Spike Trains with Permutation and Transfer Entropy

Abstract

Estimating the causal interaction between neurons is very important for better understanding the functional connectivity in neuronal networks. We propose a method called normalized permutation transfer entropy (NPTE) to evaluate the temporal causal interaction between spike trains, which quantifies the fraction of ordinal information in a neuron that has presented in another one. The performance of this method is evaluated with the spike trains generated by an Izhikevich’s neuronal model. Results show that the NPTE method can effectively estimate the causal interaction between two neurons without influence of data length. Considering both the precision of time delay estimated and the robustness of information flow estimated against neuronal firing rate, the NPTE method is superior to other information theoretic method including normalized transfer entropy, symbolic transfer entropy and permutation conditional mutual information. To test the performance of NPTE on analyzing simulated biophysically realistic synapses, an Izhikevich’s cortical network that based on the neuronal model is employed. It is found that the NPTE method is able to characterize mutual interactions and identify spurious causality in a network of three neurons exactly. We conclude that the proposed method can obtain more reliable comparison of interactions between different pairs of neurons and is a promising tool to uncover more details on the neural coding.

Statistical Approaches for the Analysis of Dependency Among Neurons Under Noise

“…Wibral et al present a review on the directional information measures, such as time-lagged mutual information (MI), directed information, cross entropy and transfer entropy (TE) [19]. Among these measures, TE is widely preferred in the literature to detect the information flow, and it has many variants, such as the normalized permutation transfer entropy (NPTE) [20], extended TE [21] and trial-shuffle-based TE [22], which are utilized to identify the connectivity between neurons.…”

Effects of Neuronal Noise on Neural Communication

“…Therefore, we generalize the HH model in such a way that the noise can be added to the system beside the coupling among the neurons. In the literature, the effect of coupling among different neurons have been explored by using TE [6], however, to the best of our knowledge, the effects of noise on these interactions have not been fully considered yet.…”

Inferring information flow in spike-train data sets using a trial-shuffle method

“…However, TE values depend on the amount of information present, so neurons with higher firing rates will naturally have higher TE values. Because of this, an effort must be made to normalize the TE values onto the same scale before they can be compared, which previous papers have attempted [ 14 , 15 ]. Our goal is to present a statistical method that circumvents the need to scale TE values before determining significance.…”

“…Furthermore, our method uses neither human intervention (e.g. [ 14 , 15 ]) nor knowledge of the underlying network topology (e.g. [ 17 ]) to determine significance.…”