Large-Scale Nonlinear Granger Causality (lsNGC) is a computational framework designed for inferring directed dependencies from short multivariate time-series data. It addresses the challenge of deriving causal graphs that represent the underlying generative processes of large-scale multivariate data, particularly when the relationships among the data are nonlinear and the observational time series are brief.

To quickly experiment with lsNGC, access our interactive Colab notebook: Demo_lsNGC.ipynb

The task of identifying nonlinear and directed relations among components of complex systems from simultaneous time-series observations is a critical and expanding area of research. lsNGC efficiently identifies causal relations through nonlinear state-space transformations of limited observational data, without relying on explicit a priori assumptions about the functional interdependencies among component time series.

• Introduction of the lsNGC framework for identifying large-scale nonlinear Granger causality.
• Implementation of conditional Granger causality analysis between two multivariate time series, taking into account a large number of confounding time series.
• Adaptation for scenarios with a limited number of time-series samples but large spatial resolution.
• Conversion of multivariate time-series data into a graph adjacency matrix to represent causal relationships.

lsNGC leverages theoretical concepts from Granger causality analysis, focusing on the predictability and precedence of time series. It estimates causal relationships by creating a nonlinear transformation of the state-space representation for each time series, facilitating the measurement of its influence on the system. Detailed theoretical concepts are discussed in the supplementary material available here.

The lsNGC approach has been evaluated against several benchmark simulations, demonstrating its performance in comparison to four state-of-the-art methodologies. Additional implementation details and results are provided in the supplementary material.

If you utilize this code (in whole or part) for your research, please cite our paper:

Wismüller, A., Dsouza, A.M., Vosoughi, M.A., et al. Large-scale nonlinear Granger causality for inferring directed dependence from short multivariate time-series data. Scientific Reports 11, 7817 (2021). DOI: 10.1038/s41598-021-87316-6

Public access to the paper is available here.

@article{wismuller2021large,
  title={Large-scale nonlinear Granger causality for inferring directed dependence from short multivariate time-series data},
  author={Wism{\"u}ller, Axel and Dsouza, Adora M and Vosoughi, M Ali and Abidin, Anas},
  journal={Scientific reports},
  volume={11},
  number={1},
  pages={7817},
  year={2021},
  publisher={Nature Publishing Group UK London}
}