Discrimination of coupling structures using causality networks from multivariate time series

Abstract

Measures of Granger causality on multivariate time series have been used to form the so-called causality networks. A causality network represents the interdependence structure of the underlying dynamical system or coupled dynamical systems, and its properties are quantified by network indices. In this work, it is investigated whether network indices on networks generated by an appropriate Granger causality measure can discriminate different coupling structures. The information based Granger causality measure of partial mutual information from mixed embedding (PMIME) is used to form causality networks, and a large number of network indices are ranked according to their ability to discriminate the different coupling structures. The evaluation of the network indices is done with a simulation study based on two dynamical systems, the coupled Mackey-Glass delay differential equations and the neural mass model, both of 25 variables, and three prototypes of coupling structures, i.e., random, small-world, and scale-free. It is concluded that the setting of PMIME combined with a network index attains high level of discrimination of the coupling structures solely on the basis of the observed multivariate time series. This approach is demonstrated to identify epileptic seizures emerging during electroencephalogram recordings.

Reconstructing dynamical networks via feature ranking

“…Finally, we check how our method compares to existing data-driven methods. For comparison we selected the Partial Mutual Information from Mixed Embedding (PMIME) method [35] that is built around an entropy-based measure that can detect directionality of links [37]. The method, like ours, does not require any strong assumptions on the nature of the reconstructed system, and its usefulness has been demonstrated on Mackey-Glass delay differential equations and neural mass models.…”

“…Another family of methods require that the mathematical form of interaction function is sparse in non-zero terms [9]. While such data-driven methods are elegant and in principle efficient [5,32,35,37,40,63,65,75], these methods often require long data-sets and/or the implicit assumptions about the signals that can be limiting to their usage in some situations of practical interest. In fact, latest results emphasize the importance of model-free reconstruction methods [9,10,52], which is the context of our present contribution.Moreover, relevance network approach (RNA) follows the statistical perspective of the network reconstruction task and is often used for inferring gene regulatory networks from expression data [14,27].…”

Reconstruction of Complex Dynamical Systems from Time Series using Reservoir Computing

“…The functional connectivity may reveal connections where there are no physical information pathways, and vice versa. Common methods to arrive at such a connectivity are correlations, transfer entropy, and Granger causality [15], [16].…”

Inferring directed networks using a rank-based connectivity measure

“…However, these measures are not able to determine the direction of interaction between nodes. Partial mutual information from mixed embedding is able to infer networks which have almost the same topological structures like the original ones [18,19]. Furthermore, measures like partial directed coherence and partial transfer entropy were used for small systems with particular topologies [20][21][22][23][24].…”