Large-Scale Granger Causality Toolbox
This software was developed using MATLAB* 2014a and contains all the functions required to perform large-scale Granger causality (lsGC) Analysis [1,2]. This method can be used to extract directed influence flow between every pair of time-series in a system. It is an extension to multivariate Granger Causality analysis for very large systems, such as functional MRI data sets. The principle of Granger causality is based on the concept of cross-predictability where the improvement in prediction quality of a time-series in the presence of another time-series is evaluated and quantified, revealing influence direction between the two series.
The flow of influence between individual time-series is obtained using predictive models such as vector auto-regressive (VAR) modelling. For systems with very large number of time-series N as compared to number of time points T (N>>T), calculating a multivariate Granger causality index is not possible as the parameter estimation in multivariate predictive modelling scheme is limited by T resulting in an underdetermined problem. To counter this problem, we introduce a linear dimension reduction step prior to performing VAR. Predictions are performed in the low-dimensional space which are transformed back to the original space using the inverse of the transformation function. This permits us to compare the prediction with the true time-series in the original space, resulting in an lsGC index for each pair of time-series in the system.
 DSouza, Adora M., Anas Z. Abidin, Lutz Leistritz, and Axel Wismueller. "Exploring connectivity with large-scale Granger causality on resting-state functional MRI." Journal of neuroscience methods 287 (2017): 68-79.
 D'Souza, Adora M., Anas Zainul Abidin, Lutz Leistritz, and Axel Wismüller. "Large-scale Granger causality analysis on resting-state functional MRI." In Medical Imaging 2016: Biomedical Applications in Molecular, Structural, and Functional Imaging, vol. 9788, p. 97880L. International Society for Optics and Photonics, 2016.
This software is free for academic non-commercial usage. If you use it, please cite above references [1,2].
Copyright Wismüller Computational Radiology Laboratory, November 2015 University of Rochester, Adora D’Souza (firstname.lastname@example.org)
*MATLAB is a registered trademark of Mathworks, Inc.