Frequency Domain Repercussions of Instantaneous Granger Causality

Using directed transfer function (DTF) and partial directed coherence (PDC) in the information version, this paper extends the theoretical framework to incorporate the instantaneous Granger causality (iGC) frequency domain description into a single unified perspective. We show that standard vector autoregressive models allow portraying iGC’s repercussions associated with Granger connectivity, where interactions mediated without delay between time series can be easily detected.

Granger-Causality Inference of the Existence of Unobserved Important Components in Network Analysis

Detecting causal interrelationships in multivariate systems, in terms of the Granger-causality concept, is of major interest for applications in many fields. Analyzing all the relevant components of a system is almost impossible, which contrasts with the concept of Granger causality. Not observing some components might, in turn, lead to misleading results, particularly if the missing components are the most influential and important in the system under investigation. In networks, the importance of a node depends on the number of nodes connected to this node. The degree of centrality is the most commonly used measure to identify important nodes in networks. There are two kinds of degree centrality, which are in-degree and out-degree. This manuscrpt is concerned with finding the highest out-degree among nodes to identify the most influential nodes. Inferring the existence of unobserved important components is critical in many multivariate interacting systems. The implications of such a situation are discussed in the Granger-causality framework. To this end, two of the most recent Granger-causality techniques, renormalized partial directed coherence and directed partial correlation, were employed. They were then compared in terms of their performance according to the extent to which they can infer the existence of unobserved important components. Sub-network analysis was conducted to aid these two techniques in inferring the existence of unobserved important components, which is evidenced in the results. By comparing the results of the two conducted techniques, it can be asserted that renormalized partial coherence outperforms directed partial correlation in the inference of existing unobserved important components that have not been included in the analysis. This measure of Granger causality and sub-network analysis emphasizes their ubiquitous successful applicability in such cases of the existence of hidden unobserved important components.

Frequency Domain Repercussions of Instantaneous Granger Causality

Using Directed Transfer Function (DTF) and Partial Directed Coherence (PDC) in their information version, this paper extends their theoretical framework to incorporate instantaneous Granger Causality (iGC)’s frequency domain description into a single unified perspective. We show that standard vector autoregressive models allow portraying iGC’s repercussions associated with Granger Connectivity where interactions mediated without delay between time series can be easily detected.

An Interpretable Machine Learning Method for the Detection of Schizophrenia Using EEG Signals

In this work we propose a machine learning (ML) method to aid in the diagnosis of schizophrenia using electroencephalograms (EEGs) as input data. The computational algorithm not only yields a proposal of diagnostic but, even more importantly, it provides additional information that admits clinical interpretation. It is based on an ML model called random forest that operates on connectivity metrics extracted from the EEG signals. Specifically, we use measures of generalized partial directed coherence (GPDC) and direct directed transfer function (dDTF) to construct the input features to the ML model. The latter allows the identification of the most performance-wise relevant features which, in turn, provide some insights about EEG signals and frequency bands that are associated with schizophrenia. Our preliminary results on real data show that signals associated with the occipital region seem to play a significant role in the diagnosis of the disease. Moreover, although every frequency band might yield useful information for the diagnosis, the beta and theta (frequency) bands provide features that are ultimately more relevant for the ML classifier that we have implemented.