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Measuring information-transfer delays.

Wibral M, Pampu N, Priesemann V, Siebenhühner F, Seiwert H, Lindner M, Lizier JT, Vicente R - PLoS ONE (2013)

Bottom Line: In complex networks such as gene networks, traffic systems or brain circuits it is important to understand how long it takes for the different parts of the network to effectively influence one another.We also show the ability of the extended transfer entropy to detect the presence of multiple delays, as well as feedback loops.While evaluated on neuroscience data, we expect the estimator to be useful in other fields dealing with network dynamics.

View Article: PubMed Central - PubMed

Affiliation: MEG Unit, Brain Imaging Center, Goethe University, Frankfurt, Germany. wibral@em.uni-frankfurt.de

ABSTRACT
In complex networks such as gene networks, traffic systems or brain circuits it is important to understand how long it takes for the different parts of the network to effectively influence one another. In the brain, for example, axonal delays between brain areas can amount to several tens of milliseconds, adding an intrinsic component to any timing-based processing of information. Inferring neural interaction delays is thus needed to interpret the information transfer revealed by any analysis of directed interactions across brain structures. However, a robust estimation of interaction delays from neural activity faces several challenges if modeling assumptions on interaction mechanisms are wrong or cannot be made. Here, we propose a robust estimator for neuronal interaction delays rooted in an information-theoretic framework, which allows a model-free exploration of interactions. In particular, we extend transfer entropy to account for delayed source-target interactions, while crucially retaining the conditioning on the embedded target state at the immediately previous time step. We prove that this particular extension is indeed guaranteed to identify interaction delays between two coupled systems and is the only relevant option in keeping with Wiener's principle of causality. We demonstrate the performance of our approach in detecting interaction delays on finite data by numerical simulations of stochastic and deterministic processes, as well as on local field potential recordings. We also show the ability of the extended transfer entropy to detect the presence of multiple delays, as well as feedback loops. While evaluated on neuroscience data, we expect the estimator to be useful in other fields dealing with network dynamics.

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Test case (IV).Transfer entropy () values and significance as a function of the assumed delay  for two unidirectionally coupled autoregressive systems with multiple delays. The simulated delays  were 18, 19, 20, 21 and 22 sampling points. The rest of the parameters and criteria used are the same as those in Figure 5.
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pone-0055809-g007: Test case (IV).Transfer entropy () values and significance as a function of the assumed delay for two unidirectionally coupled autoregressive systems with multiple delays. The simulated delays were 18, 19, 20, 21 and 22 sampling points. The rest of the parameters and criteria used are the same as those in Figure 5.

Mentions: A more complex case (IV) is encountered when dealing with a smooth distribution of delays. Figure 7 demonstrates that in this case, a peak of is attained near to the mean of the distribution of delays. The width of the peak is proportional to the width of the delay distribution. However, an exact estimation of the range of delays is difficult since single delays are also associated with broad peaks in the versus assumed delay curves (see figure 5, but note the different scale of the time axes). We note that the peak of is skewed towards the shorter of the actual interaction delays, and this may be due to: (a) the longer delays providing less novel information from the source given that it is already contained in the target state from the shorter delays (as discussed in the above paragraph); and/or (b) the persistence of information of the current influential component of the source state in several following source states (as discussed in the preceding subsection).


Measuring information-transfer delays.

Wibral M, Pampu N, Priesemann V, Siebenhühner F, Seiwert H, Lindner M, Lizier JT, Vicente R - PLoS ONE (2013)

Test case (IV).Transfer entropy () values and significance as a function of the assumed delay  for two unidirectionally coupled autoregressive systems with multiple delays. The simulated delays  were 18, 19, 20, 21 and 22 sampling points. The rest of the parameters and criteria used are the same as those in Figure 5.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3585400&req=5

pone-0055809-g007: Test case (IV).Transfer entropy () values and significance as a function of the assumed delay for two unidirectionally coupled autoregressive systems with multiple delays. The simulated delays were 18, 19, 20, 21 and 22 sampling points. The rest of the parameters and criteria used are the same as those in Figure 5.
Mentions: A more complex case (IV) is encountered when dealing with a smooth distribution of delays. Figure 7 demonstrates that in this case, a peak of is attained near to the mean of the distribution of delays. The width of the peak is proportional to the width of the delay distribution. However, an exact estimation of the range of delays is difficult since single delays are also associated with broad peaks in the versus assumed delay curves (see figure 5, but note the different scale of the time axes). We note that the peak of is skewed towards the shorter of the actual interaction delays, and this may be due to: (a) the longer delays providing less novel information from the source given that it is already contained in the target state from the shorter delays (as discussed in the above paragraph); and/or (b) the persistence of information of the current influential component of the source state in several following source states (as discussed in the preceding subsection).

Bottom Line: In complex networks such as gene networks, traffic systems or brain circuits it is important to understand how long it takes for the different parts of the network to effectively influence one another.We also show the ability of the extended transfer entropy to detect the presence of multiple delays, as well as feedback loops.While evaluated on neuroscience data, we expect the estimator to be useful in other fields dealing with network dynamics.

View Article: PubMed Central - PubMed

Affiliation: MEG Unit, Brain Imaging Center, Goethe University, Frankfurt, Germany. wibral@em.uni-frankfurt.de

ABSTRACT
In complex networks such as gene networks, traffic systems or brain circuits it is important to understand how long it takes for the different parts of the network to effectively influence one another. In the brain, for example, axonal delays between brain areas can amount to several tens of milliseconds, adding an intrinsic component to any timing-based processing of information. Inferring neural interaction delays is thus needed to interpret the information transfer revealed by any analysis of directed interactions across brain structures. However, a robust estimation of interaction delays from neural activity faces several challenges if modeling assumptions on interaction mechanisms are wrong or cannot be made. Here, we propose a robust estimator for neuronal interaction delays rooted in an information-theoretic framework, which allows a model-free exploration of interactions. In particular, we extend transfer entropy to account for delayed source-target interactions, while crucially retaining the conditioning on the embedded target state at the immediately previous time step. We prove that this particular extension is indeed guaranteed to identify interaction delays between two coupled systems and is the only relevant option in keeping with Wiener's principle of causality. We demonstrate the performance of our approach in detecting interaction delays on finite data by numerical simulations of stochastic and deterministic processes, as well as on local field potential recordings. We also show the ability of the extended transfer entropy to detect the presence of multiple delays, as well as feedback loops. While evaluated on neuroscience data, we expect the estimator to be useful in other fields dealing with network dynamics.

Show MeSH
Related in: MedlinePlus