@article {pub3837,
	title = {Large-scale directed network inference with multivariate transfer entropy and hierarchical statistical testing},
	author = {Leonardo Novelli AND Patricia Wollstadt AND Pedro Mediano AND Michael Wibral AND Joseph Troy Lizier},
	year = {2019},
	month = {April},
	abstract = {Network inference algorithms are valuable tools for the study of large-scale neuroimaging datasets. Multivariate transfer entropy is a model-free measure that can capture nonlinear and lagged dependencies between time series to infer a minimal directed network model.Greedy algorithms have been proposed to efficiently deal with high-dimensional datasets,in a fashion that avoids redundant inferences and captures synergistic effects. Statistical testing of estimates using shuffled surrogate time series is necessary to handle estimator bias, however poses practical problems: multiple statistical comparisons may cause an inflated false positive rate (type I errors) and are computationally demanding, limiting the size of previous validation studies. The algorithm presented in this paper, as implemented in the IDTxl open-source software, addresses these challenges by employing hierarchical statistical tests to control the family-wise error rate and to allow for efficient parallelization. The method was validated on synthetic datasets involving random networks of increasing size (up to 100 nodes) and different types of dynamics (vector autoregressive processes and coupled logistic maps). The performance increased with the length of the time series,reaching consistently high precision and recall (>\%) for 10000 time samples. The influence of the statistical significance threshold was further investigated, showing a more favourable precision-recall trade-off for longer time series. Both the network size and the sample size that could be analysed in acceptable time were one order of magnitude larger than previously demonstrated, demonstrating feasibility for typical EEG and MEG experiments.},
	publisher = {MIT Press},
	journal = {Network Neuroscience},
	editor = {Olaf Sporns}
}