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Quantifying 'causality' in complex systems: understanding transfer entropy.

Abdul Razak F, Jensen HJ - PLoS ONE (2014)

Bottom Line: Often big volumes of data in the form of time series are available and it is important to develop methods that can inform about possible causal connections between the different observables.We do this by firstly applying Transfer Entropy to an amended Ising model.In particular we systematically study the effect of the finite size of data sets.

View Article: PubMed Central - PubMed

Affiliation: Complexity & Networks Group and Department of Mathematics, Imperial College London, London, United Kingdom; School of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, Bangi, Selangor, Malaysia.

ABSTRACT
'Causal' direction is of great importance when dealing with complex systems. Often big volumes of data in the form of time series are available and it is important to develop methods that can inform about possible causal connections between the different observables. Here we investigate the ability of the Transfer Entropy measure to identify causal relations embedded in emergent coherent correlations. We do this by firstly applying Transfer Entropy to an amended Ising model. In addition we use a simple Random Transition model to test the reliability of Transfer Entropy as a measure of 'causal' direction in the presence of stochastic fluctuations. In particular we systematically study the effect of the finite size of data sets.

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Related in: MedlinePlus

Transfer Entropy  on the Ising model of lengths L=10,25,50,100 obtained using equation (5).Peaks can be seen at respective , similar to Ising model results in Figure (6).
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pone-0099462-g012: Transfer Entropy on the Ising model of lengths L=10,25,50,100 obtained using equation (5).Peaks can be seen at respective , similar to Ising model results in Figure (6).

Mentions: We simulated the amended Ising model with for different lattice lengths . Figures (7) display the values of susceptibility on the model and the peaks clearly show the presence of in our model just like Figure (1) of the Ising model. Figures (8) and (9) display the values of the covariance and the Mutual Information respectively. We reiterate that our correlations reach across the system for [2], [31]. While covariance and Mutual Information gives similar results to those of the standard Ising model as in Figures (2) and (3), a difference is clearly seen in Transfer Entropy values. Figure (10–12) displays the contrasts of and on the amended Ising model which explicitly indicates the direction of ‘causality’ . While Figure (12) is not very different from Figure (6), Figures (10) and (11) are clearly different from their counterparts in the Ising model, Figures (4) and (5). Transfer Entropy captures the effect of the amendment.


Quantifying 'causality' in complex systems: understanding transfer entropy.

Abdul Razak F, Jensen HJ - PLoS ONE (2014)

Transfer Entropy  on the Ising model of lengths L=10,25,50,100 obtained using equation (5).Peaks can be seen at respective , similar to Ising model results in Figure (6).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4067287&req=5

pone-0099462-g012: Transfer Entropy on the Ising model of lengths L=10,25,50,100 obtained using equation (5).Peaks can be seen at respective , similar to Ising model results in Figure (6).
Mentions: We simulated the amended Ising model with for different lattice lengths . Figures (7) display the values of susceptibility on the model and the peaks clearly show the presence of in our model just like Figure (1) of the Ising model. Figures (8) and (9) display the values of the covariance and the Mutual Information respectively. We reiterate that our correlations reach across the system for [2], [31]. While covariance and Mutual Information gives similar results to those of the standard Ising model as in Figures (2) and (3), a difference is clearly seen in Transfer Entropy values. Figure (10–12) displays the contrasts of and on the amended Ising model which explicitly indicates the direction of ‘causality’ . While Figure (12) is not very different from Figure (6), Figures (10) and (11) are clearly different from their counterparts in the Ising model, Figures (4) and (5). Transfer Entropy captures the effect of the amendment.

Bottom Line: Often big volumes of data in the form of time series are available and it is important to develop methods that can inform about possible causal connections between the different observables.We do this by firstly applying Transfer Entropy to an amended Ising model.In particular we systematically study the effect of the finite size of data sets.

View Article: PubMed Central - PubMed

Affiliation: Complexity & Networks Group and Department of Mathematics, Imperial College London, London, United Kingdom; School of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, Bangi, Selangor, Malaysia.

ABSTRACT
'Causal' direction is of great importance when dealing with complex systems. Often big volumes of data in the form of time series are available and it is important to develop methods that can inform about possible causal connections between the different observables. Here we investigate the ability of the Transfer Entropy measure to identify causal relations embedded in emergent coherent correlations. We do this by firstly applying Transfer Entropy to an amended Ising model. In addition we use a simple Random Transition model to test the reliability of Transfer Entropy as a measure of 'causal' direction in the presence of stochastic fluctuations. In particular we systematically study the effect of the finite size of data sets.

Show MeSH
Related in: MedlinePlus