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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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Related in: MedlinePlus

Causal graph for two coupled systems .Illustration of d-separation of  and  by . Arrows indicate a causal influence (directed interaction). Solid lines indicate a single time step, broken lines an arbitrary number of time steps. The black circle is the state to be predicted in Wiener’s sense, the red circles indicate the states that form its set of parents in the graphs. These states are also the ones conditioned upon in the novel estimator . The blue circle indicates the state in the graph for which we want to determine that forms a Markov chain: . For  all sequential paths from  into  are blocked, as are the divergent paths between these nodes. All convergent paths (e.g. via  in (B)) are not blocked. This holds for  (A) and  (B).
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pone-0055809-g002: Causal graph for two coupled systems .Illustration of d-separation of and by . Arrows indicate a causal influence (directed interaction). Solid lines indicate a single time step, broken lines an arbitrary number of time steps. The black circle is the state to be predicted in Wiener’s sense, the red circles indicate the states that form its set of parents in the graphs. These states are also the ones conditioned upon in the novel estimator . The blue circle indicates the state in the graph for which we want to determine that forms a Markov chain: . For all sequential paths from into are blocked, as are the divergent paths between these nodes. All convergent paths (e.g. via in (B)) are not blocked. This holds for (A) and (B).

Mentions: From figure 2, representing the causal graph of the two random processes , we see that:


Measuring information-transfer delays.

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

Causal graph for two coupled systems .Illustration of d-separation of  and  by . Arrows indicate a causal influence (directed interaction). Solid lines indicate a single time step, broken lines an arbitrary number of time steps. The black circle is the state to be predicted in Wiener’s sense, the red circles indicate the states that form its set of parents in the graphs. These states are also the ones conditioned upon in the novel estimator . The blue circle indicates the state in the graph for which we want to determine that forms a Markov chain: . For  all sequential paths from  into  are blocked, as are the divergent paths between these nodes. All convergent paths (e.g. via  in (B)) are not blocked. This holds for  (A) and  (B).
© Copyright Policy
Related In: Results  -  Collection

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

pone-0055809-g002: Causal graph for two coupled systems .Illustration of d-separation of and by . Arrows indicate a causal influence (directed interaction). Solid lines indicate a single time step, broken lines an arbitrary number of time steps. The black circle is the state to be predicted in Wiener’s sense, the red circles indicate the states that form its set of parents in the graphs. These states are also the ones conditioned upon in the novel estimator . The blue circle indicates the state in the graph for which we want to determine that forms a Markov chain: . For all sequential paths from into are blocked, as are the divergent paths between these nodes. All convergent paths (e.g. via in (B)) are not blocked. This holds for (A) and (B).
Mentions: From figure 2, representing the causal graph of the two random processes , we see that:

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