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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.

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The error of estimation methods for different time delays.(A) NTE. (B) NPTE.
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pone-0070894-g006: The error of estimation methods for different time delays.(A) NTE. (B) NPTE.

Mentions: The methods mentioned in this paper are all able to estimate time delay of the causal interaction between spike trains. A typical distribution of axonal propagation delays between different pairs of cortical neurons is broad, ranging from several tenths to tens of milliseconds. In this study, we only investigate the performance for time delay ranging from 5 ms to 45 ms with a step of 5 ms. Given and spikes/s, spike trains and are generated. 500 realizations for each time delay are implemented by each method. We use Euclidean distance between simulation result and the time delay that used for constructing the model to quantify the error of each realization. The results are considered as outliers if they are larger than or smaller than , where and are the 25th and 75th percentiles, respectively. As shown in Figure 6A), the error and standard deviation of NTE estimation increases with the increase of time delay. In Figure 6(B), it can be seen that the error remains unchanged at 1 ms for the nine delays except for 15 ms, 30 ms and 45 ms. This is caused by the resolution of the NPTE (3 ms in this paper), which is related to the order. In other words, the NPTE is able to estimate precisely for time delays that are multiples of 3 ms, while with a fixed error of 1 ms for others. On the other hand, the PCMI and STE methods can always estimate the time delay without error and it is not plotted because of the zero values. Briefly, the NPTE is superior to the NTE for estimating time delay in terms of robustness and inferior to the PCMI and STE in resolution. The reasons are below. These four methods all use bins to discretize spike trains. In the NPTE and NTE, varying bins and normalization method are used to characterize the causal interaction. As mentioned above, large bins are likely to induce spurious increase of information transferred between spike trains, also bring about unstable and imprecise estimation of time delay. In this study, the NPTE method uses three bins simultaneously to overcome this defect with a little loss of resolution. On the other hand, the PCMI and STE, which employ a fixed bin (1 ms in this paper) and the sliding technique, can supply robust and precise estimation of time delay with a high resolution.


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

Li Z, Li X - PLoS ONE (2013)

The error of estimation methods for different time delays.(A) NTE. (B) NPTE.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0070894-g006: The error of estimation methods for different time delays.(A) NTE. (B) NPTE.
Mentions: The methods mentioned in this paper are all able to estimate time delay of the causal interaction between spike trains. A typical distribution of axonal propagation delays between different pairs of cortical neurons is broad, ranging from several tenths to tens of milliseconds. In this study, we only investigate the performance for time delay ranging from 5 ms to 45 ms with a step of 5 ms. Given and spikes/s, spike trains and are generated. 500 realizations for each time delay are implemented by each method. We use Euclidean distance between simulation result and the time delay that used for constructing the model to quantify the error of each realization. The results are considered as outliers if they are larger than or smaller than , where and are the 25th and 75th percentiles, respectively. As shown in Figure 6A), the error and standard deviation of NTE estimation increases with the increase of time delay. In Figure 6(B), it can be seen that the error remains unchanged at 1 ms for the nine delays except for 15 ms, 30 ms and 45 ms. This is caused by the resolution of the NPTE (3 ms in this paper), which is related to the order. In other words, the NPTE is able to estimate precisely for time delays that are multiples of 3 ms, while with a fixed error of 1 ms for others. On the other hand, the PCMI and STE methods can always estimate the time delay without error and it is not plotted because of the zero values. Briefly, the NPTE is superior to the NTE for estimating time delay in terms of robustness and inferior to the PCMI and STE in resolution. The reasons are below. These four methods all use bins to discretize spike trains. In the NPTE and NTE, varying bins and normalization method are used to characterize the causal interaction. As mentioned above, large bins are likely to induce spurious increase of information transferred between spike trains, also bring about unstable and imprecise estimation of time delay. In this study, the NPTE method uses three bins simultaneously to overcome this defect with a little loss of resolution. On the other hand, the PCMI and STE, which employ a fixed bin (1 ms in this paper) and the sliding technique, can supply robust and precise estimation of time delay with a high resolution.

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