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Estimating temporal causal interaction between spike trains with permutation and transfer entropy.

Li Z, Li X - PLoS ONE (2013)

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Institute of Information Science and Engineering, Yanshan University, Qinhuangdao, China.

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.

Show MeSH
Removal of the bias and normalization of the PTE.(A) Permutation transfer entropy. (B) Unbiased permutation transfer entropy. (C) Conditional entropy. (D) Normalized permutation transfer entropy.
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pone-0070894-g002: Removal of the bias and normalization of the PTE.(A) Permutation transfer entropy. (B) Unbiased permutation transfer entropy. (C) Conditional entropy. (D) Normalized permutation transfer entropy.

Mentions: Before discussing the parameter choice, we first investigate the necessity of removing bias and the effect of normalization. Given and spike trains and are generated. In the calculation, the lag is set as . As shown in Figure 2(A), when the PTE value increases with the increase of bin, which is caused by the sparse joint distribution of , , and . As can be seen in Figure 2(B), removal of this bias eliminates the spurious increase and the PTE stays close to 0 for large bins. Figure 2(C) shows that the amount of information available in and also increases with the increase of the bins. In Figure 2(D), the normalization of PTE by the conditional entropy highlights the main peak at


Estimating temporal causal interaction between spike trains with permutation and transfer entropy.

Li Z, Li X - PLoS ONE (2013)

Removal of the bias and normalization of the PTE.(A) Permutation transfer entropy. (B) Unbiased permutation transfer entropy. (C) Conditional entropy. (D) Normalized permutation transfer entropy.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3733844&req=5

pone-0070894-g002: Removal of the bias and normalization of the PTE.(A) Permutation transfer entropy. (B) Unbiased permutation transfer entropy. (C) Conditional entropy. (D) Normalized permutation transfer entropy.
Mentions: Before discussing the parameter choice, we first investigate the necessity of removing bias and the effect of normalization. Given and spike trains and are generated. In the calculation, the lag is set as . As shown in Figure 2(A), when the PTE value increases with the increase of bin, which is caused by the sparse joint distribution of , , and . As can be seen in Figure 2(B), removal of this bias eliminates the spurious increase and the PTE stays close to 0 for large bins. Figure 2(C) shows that the amount of information available in and also increases with the increase of the bins. In Figure 2(D), the normalization of PTE by the conditional entropy highlights the main peak at

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Institute of Information Science and Engineering, Yanshan University, Qinhuangdao, China.

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.

Show MeSH