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Netw Neurosci. 2019 Jul 1;3(3):827-847. doi: 10.1162/netn_a_00092. eCollection 2019.

Large-scale directed network inference with multivariate transfer entropy and hierarchical statistical testing.

Author information

1
Centre for Complex Systems, Faculty of Engineering, The University of Sydney, Sydney, Australia.
2
Honda Research Institute Europe, Offenbach am Main, Germany.
3
Computational Neurodynamics Group, Department of Computing, Imperial College London, London, United Kingdom.
4
Campus Institute for Dynamics of Biological Networks, Georg-August University, Göttingen, Germany.

Abstract

Network inference algorithms are valuable tools for the study of large-scale neuroimaging datasets. Multivariate transfer entropy is well suited for this task, being a model-free measure that captures 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 while avoiding redundant inferences and capturing synergistic effects. However, multiple statistical comparisons may inflate the false positive rate and are computationally demanding, which limited the size of previous validation studies. The algorithm we present-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), for both linear and nonlinear dynamics. The performance increased with the length of the time series, reaching consistently high precision, recall, and specificity (>98% on average) for 10,000 time samples. Varying the statistical significance threshold showed a more favorable precision-recall trade-off for longer time series. Both the network size and the sample size are one order of magnitude larger than previously demonstrated, showing feasibility for typical EEG and magnetoencephalography experiments.

KEYWORDS:

Directed connectivity; Effective network; Information theory; Multivariate transfer entropy; Neuroimaging; Nonlinear dynamics; Nonparametric tests; Statistical inference

Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

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