IDTxl

The Information Dynamics Toolkit xl (IDTxl) is a comprehensive software package for efficient inference of networks and their node dynamics from multivariate time series data using information theory. IDTxl provides functionality to estimate the following measures:

1. For network inference:
   • multivariate transfer entropy (TE)/Granger causality (GC)
   • multivariate mutual information (MI)
   • bivariate TE/GC
   • bivariate MI
2. For analysis of node dynamics:
   • active information storage (AIS)
   • partial information decomposition (PID)

IDTxl implements estimators for discrete and continuous data with parallel computing engines for both GPU and CPU platforms. Written for Python3.4.3+.

To get started have a look at the wiki and the documentation. For further discussions, join IDTxl's google group.

How to cite

P. Wollstadt, J. T. Lizier, R. Vicente, C. Finn, M. Martinez-Zarzuela, P. Mediano, L. Novelli, M. Wibral (2018). IDTxl: The Information Dynamics Toolkit xl: a Python package for the efficient analysis of multivariate information dynamics in networks. Journal of Open Source Software, 4(34), 1081. https://doi.org/10.21105/joss.01081.

Contributors

• Patricia Wollstadt, Brain Imaging Center, MEG Unit, Goethe-University, Frankfurt, Germany; Honda Research Institute Europe GmbH, Offenbach am Main, Germany
• Michael Wibral, Campus Institute for Dynamics of Biological Networks, Georg August University, Göttingen, Germany
• David Alexander Ehrlich, Campus Institute for Dynamics of Biological Networks, Georg August University, Göttingen, Germany; Max Planck Institute for Dynamics and Self-Organization, Goettingen, Germany
• Joseph T. Lizier, Centre for Complex Systems, The University of Sydney, Sydney, Australia
• Raul Vicente, Computational Neuroscience Lab, Institute of Computer Science, University of Tartu, Tartu, Estonia
• Abdullah Makkeh, Campus Institute for Dynamics of Biological Networks, Georg August University, Göttingen, Germany
• Conor Finn, Centre for Complex Systems, The University of Sydney, Sydney, Australia
• Mario Martinez-Zarzuela, Department of Signal Theory and Communications and Telematics Engineering, University of Valladolid, Valladolid, Spain
• Leonardo Novelli, Centre for Complex Systems, The University of Sydney, Sydney, Australia
• Pedro Mediano, Computational Neurodynamics Group, Imperial College London, London, United Kingdom
• Dr. Michael Lindner, Campus Institute for Dynamics of Biological Networks, Georg August University, Göttingen, Germany
• Dr. Aaron J. Gutknecht, Campus Institute for Dynamics of Biological Networks, Georg August University, Göttingen, Germany
• Prof. Viola Priesemann, Theory of Neural Systems, Faculty of Physics, Georg August University and Max Planck Institute for Dynamics and Self-Organization, Göttingen
• Dr. Lucas Rudelt, Max Planck Institute for Dynamics and Self-Organization, Göttingen

How to contribute? We are happy about any feedback on IDTxl. If you would like to contribute, please open an issue or send a pull request with your feature or improvement. Also have a look at the developer's section in the Wiki for details.

Acknowledgements

This project has been supported by funding through:

• Universities Australia - Deutscher Akademischer Austauschdienst (German Academic Exchange Service) UA-DAAD Australia-Germany Joint Research Co-operation grant "Measuring neural information synthesis and its impairment", Wibral, Lizier, Priesemann, Wollstadt, Finn, 2016-17
• Australian Research Council Discovery Early Career Researcher Award (DECRA) "Relating function of complex networks to structure using information theory", Lizier, 2016-19
• Deutsche Forschungsgemeinschaft (DFG) Grant CRC 1193 C04, Wibral
• Funding from the Ministry for Science and Education of Lower Saxony and the Volkswagen Foundation through the "Niedersächsisches Vorab" under the program "Big Data in den Lebenswissenschaften"-project "Deep learning techniques for association studies of transcriptome and systems dynamics in tissue morphogenesis".

Key References

• Multivariate transfer entropy: Lizier & Rubinov, 2012, Preprint, Technical Report 25/2012, Max Planck Institute for Mathematics in the Sciences. Available from: http://www.mis.mpg.de/preprints/2012/preprint2012_25.pdf
• Hierarchical statistical testing for multivariate transfer entropy estimation: Novelli et al., 2019, Network Neurosci 3(3)
• Kraskov estimator: Kraskov et al., 2004, Phys Rev E 69, 066138
• Nonuniform embedding: Faes et al., 2011, Phys Rev E 83, 051112
• Faes' compensated transfer entropy: Faes et al., 2013, Entropy 15, 198-219
• PID:
  • Williams & Beer, 2010, arXiv:1004.2515 [cs.IT]
  • Makkeh et al., 2021, Phys Rev E 103, 032149
  • Gutknecht et al., 2021, Proc. R. Soc. A: Math. Phys. Eng, 477(2251), 20210110.
• PID estimators:
  • Bertschinger et al., 2014, Entropy, 16(4)
  • Makkeh et al., 2017, Entropy, 19(10)
  • Makkeh et al., 2018, Entropy, 20(271)
  • Makkeh et al., 2018, Phys. Rev. E 103, 032149
• History-dependence estimator for neural spiking data: Rudelt et al., 2021, PLOS Computational Biology, 17(6)
• Significant subgraph mining: Gutknecht et al., 2021, bioRxiv