Limits...
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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Transfer Entropy  on the Ising model of lengths L=10,25,50,100 obtained using equation (5).Peaks can be seen at respective .
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pone-0099462-g005: Transfer Entropy on the Ising model of lengths L=10,25,50,100 obtained using equation (5).Peaks can be seen at respective .

Mentions: Using time shifted variables we obtained the Transfer Entropy in Figures (4–6). By looking at Figure (4) and then contrasting Figures (5) and (6), one can see that there is no clear difference between and in the figures thus no direction of ‘causality’ can be established between and . This is expected due to the symmetry of the lattice. More interestingly, the fact that Transfer Entropy peaks near can be due to the fact that at the correlations span across the entire lattice. Therefore, one may say that the critical transition and collective behaviour in the Ising model is detected by Transfer Entropy as a type of ‘causality’ that is symmetric in both directions. It is logical to interpret collective behaviour as a type of ‘causality’ in all directions since information is disseminated throughout the whole lattice when it is fully connected. This is an important fact to take into account when estimating Transfer Entropy on complex systems.


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 .
© Copyright Policy
Related In: Results  -  Collection

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

pone-0099462-g005: Transfer Entropy on the Ising model of lengths L=10,25,50,100 obtained using equation (5).Peaks can be seen at respective .
Mentions: Using time shifted variables we obtained the Transfer Entropy in Figures (4–6). By looking at Figure (4) and then contrasting Figures (5) and (6), one can see that there is no clear difference between and in the figures thus no direction of ‘causality’ can be established between and . This is expected due to the symmetry of the lattice. More interestingly, the fact that Transfer Entropy peaks near can be due to the fact that at the correlations span across the entire lattice. Therefore, one may say that the critical transition and collective behaviour in the Ising model is detected by Transfer Entropy as a type of ‘causality’ that is symmetric in both directions. It is logical to interpret collective behaviour as a type of ‘causality’ in all directions since information is disseminated throughout the whole lattice when it is fully connected. This is an important fact to take into account when estimating Transfer Entropy on complex systems.

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