The Experts below are selected from a list of 55137 Experts worldwide ranked by ideXlab platform
Mingzhou Ding - One of the best experts on this subject based on the ideXlab platform.
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Analyzing MEG Data with Granger Causality: Promises and Pitfalls
Magnetoencephalography, 2014Co-Authors: Mingzhou Ding, Chao WangAbstract:In this chapter we begin by introducing the basic idea of Granger Causality and discussing its applications to local field potential data. We then proceed to comment on recent results of applying Granger Causality to MEG data. Recognizing that Granger Causality is frequently used to examine neural activity recorded during stimulus processing, we point out the adverse effects of the inevitable trial-to-trial variability of stimulus-evoked responses on Granger cau- sality estimation. We end the chapter by discussing the future prospects of using Granger Causality in basic and clinical neuroscience research.
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Spatio-temporal Granger Causality: a new framework.
NeuroImage, 2013Co-Authors: Qiang Luo, Mingzhou Ding, Wei Cheng, Pedro A. Valdes-sosa, Xiaotong Wen, Jianfeng FengAbstract:That physiological oscillations of various frequencies are present in fMRI signals is the rule, not the exception. Herein, we propose a novel theoretical framework, spatio-temporal Granger Causality, which allows us to more reliably and precisely estimate the Granger Causality from experimental datasets possessing time-varying properties caused by physiological oscillations. Within this framework, Granger Causality is redefined as a global index measuring the directed information flow between two time series with time-varying properties. Both theoretical analyses and numerical examples demonstrate that Granger Causality is a monotonically increasing function of the temporal resolution used in the estimation. This is consistent with the general principle of coarse graining, which causes information loss by smoothing out very fine-scale details in time and space. Our results confirm that the Granger Causality at the finer spatio-temporal scales considerably outperforms the traditional approach in terms of an improved consistency between two resting-state scans of the same subject. To optimally estimate the Granger Causality, the proposed theoretical framework is implemented through a combination of several approaches, such as dividing the optimal time window and estimating the parameters at the fine temporal and spatial scales. Taken together, our approach provides a novel and robust framework for estimating the Granger Causality from fMRI, EEG, and other related data.
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Characterizing Oscillatory Cortical Networks with Granger Causality
Coherent Behavior in Neuronal Networks, 2009Co-Authors: Anil Bollimunta, Yonghong Chen, Charles E. Schroeder, Mingzhou DingAbstract:Multivariate neural recordings are becoming commonplace. Statistical techniques such as Granger Causality promise to reveal the patterns of neural interactions and their functional significance in these data. In this chapter, we start by reviewing the essential mathematical elements of Granger Causality with special emphasis on its spectral representation. Practical issues concerning the estimation of such measures from time series data via autoregressive models are discussed. Simulation examples are used to illustrate the technique. Finally, we analyze local field potential recordings from the visual cortex of behaving monkeys to address the neuronal mechanisms of the alpha oscillation.
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analyzing multiple spike trains with nonparametric Granger Causality
Journal of Computational Neuroscience, 2009Co-Authors: Aatira G Nedungadi, Govindan Rangarajan, Neeraj Jain, Mingzhou DingAbstract:Simultaneous recordings of spike trains from multiple single neurons are becoming commonplace. Understanding the interaction patterns among these spike trains remains a key research area. A question of interest is the evaluation of information flow between neurons through the analysis of whether one spike train exerts causal influence on another. For continuous-valued time series data, Granger Causality has proven an effective method for this purpose. However, the basis for Granger Causality estimation is autoregressive data modeling, which is not directly applicable to spike trains. Various filtering options distort the properties of spike trains as point processes. Here we propose a new nonparametric approach to estimate Granger Causality directly from the Fourier transforms of spike train data. We validate the method on synthetic spike trains generated by model networks of neurons with known connectivity patterns and then apply it to neurons simultaneously recorded from the thalamus and the primary somatosensory cortex of a squirrel monkey undergoing tactile stimulation.
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Analyzing brain networks with PCA and conditional Granger Causality
Human Brain Mapping, 2009Co-Authors: Zhenyu Zhou, Barbara M Wildemuth, Zuhong Lu, Mingzhou Ding, Paul Wright, Yonghong Chen, Yan Zhang, Yijun LiuAbstract:Identifying directional influences in anatomical and functional circuits presents one of the greatest challenges for understanding neural computations in the brain. Granger Causality mapping (GCM) derived from vector autoregressive models of data has been employed for this purpose, revealing complex temporal and spatial dynamics underlying cognitive processes. However, the traditional GCM methods are computationally expensive, as signals from thousands of voxels within selected regions of interest (ROIs) are individually processed, and being based on pairwise Granger Causality, they lack the ability to distinguish direct from indirect connectivity among brain regions. In this work a new algorithm called PCA based conditional GCM is proposed to overcome these problems. The algorithm implements the following two procedures: (i) dimensionality reduction in ROIs of interest with principle component analysis (PCA), and (ii) estimation of the direct causal influences in local brain networks, using conditional Granger Causality. Our results show that the proposed method achieves greater accuracy in detecting network connectivity than the commonly used pairwise Granger Causality method. Furthermore, the use of PCA components in conjunction with conditional GCM greatly reduces the computational cost relative to the use of individual voxel time series.
Daniele Marinazzo - One of the best experts on this subject based on the ideXlab platform.
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On the interpretability and computational reliability of frequency-domain Granger Causality
arXiv: Methodology, 2017Co-Authors: Luca Faes, Sebastiano Stramaglia, Daniele MarinazzoAbstract:This is a comment to the paper 'A study of problems encountered in Granger Causality analysis from a neuroscience perspective'. We agree that interpretation issues of Granger Causality in Neuroscience exist (partially due to the historical unfortunate use of the name 'Causality', as nicely described in previous literature). On the other hand we think that the paper uses a formulation of Granger Causality which is outdated (albeit still used), and in doing so it dismisses the measure based on a suboptimal use of it. Furthermore, since data from simulated systems are used, the pitfalls that are found with the used formulation are intended to be general, and not limited to neuroscience. It would be a pity if this paper, even written in good faith, became a wildcard against all possible applications of Granger Causality, regardless of the hard work of colleagues aiming to seriously address the methodological and interpretation pitfalls. In order to provide a balanced view, we replicated their simulations used the updated State Space implementation, proposed already some years ago, in which the pitfalls are mitigated or directly solved.
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Synergy, redundancy and unnormalized Granger Causality
arXiv: Information Theory, 2015Co-Authors: Sebastiano Stramaglia, Leonardo Angelini, Jesus M. Cortes, Daniele MarinazzoAbstract:We analyze by means of Granger Causality the effect of synergy and redundancy in the inference (from time series data) of the information flow between subsystems of a complex network. Whilst fully conditioned Granger Causality is not affected by synergy, the pairwise analysis fails to put in evidence synergetic effects. We show that maximization of the total Granger Causality to a given target, over all the possible partitions of the set of driving variables, puts in evidence redundant multiplets of variables influencing the target, provided that an {\it unnormalized} definition of Granger Causality is adopted. Along the same lines we also introduce a pairwise index of synergy (w.r.t. to information flow to a third variable) which is zero when two independent sources additively influence a common target, differently from previous definitions of synergy.
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EMBC - Synergy, redundancy and unnormalized Granger Causality
2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 2015Co-Authors: Sebastiano Stramaglia, Leonardo Angelini, Jesus M. Cortes, Daniele MarinazzoAbstract:We analyze by means of Granger Causality the effect of synergy and redundancy in the inference (from time series data) of the information flow between subsystems of a complex network. Whilst fully conditioned Granger Causality is not affected by synergy, the pairwise analysis fails to put in evidence synergetic effects. We show that maximization of the total Granger Causality to a given target, over all the possible partitions of the set of driving variables, puts in evidence redundant multiplets of variables influencing the target, provided that an unnormalized definition of Granger Causality is adopted. Along the same lines we also introduce a pairwise index of synergy (w.r.t. to information flow to a third variable) which is zero when two independent sources additively influence a common target; thus, this definition differs from previous definitions of synergy.
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Nonlinear Granger Causality for brain connectivity
2011 IEEE International Symposium on Medical Measurements and Applications, 2011Co-Authors: Sebastiano Stramaglia, Mario Pellicoro, L. Angelini, Daniele MarinazzoAbstract:The communication among neuronal populations, reflected by transient synchronous activity, is the mechanism underlying the information processing in the brain. Although it is widely assumed that the interactions among those populations (i.e. functional connectivity) are highly nonlinear, the amount of nonlinear information transmission and its functional roles are not clear. Granger Causality constitutes a major tool to reveal effective connectivity, and it is widely used to analyze EEG/MEG data as well as fMRI signals in its linear version. In order to capture nonlinear interactions between even short and noisy time series, a kernel version of Granger Causality has been recently proposed. We review kernel Granger Causality and show the application of this approach on EEG signals.
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Nonlinear connectivity by Granger Causality.
NeuroImage, 2011Co-Authors: Daniele Marinazzo, Wei Liao, Hesheng Chen, Sebastiano StramagliaAbstract:The communication among neuronal populations, reflected by transient synchronous activity, is the mechanism underlying the information processing in the brain. Although it is widely assumed that the interactions among those populations (i.e. functional connectivity) are highly nonlinear, the amount of nonlinear information transmission and its functional roles are not clear. The state of the art to understand the communication between brain systems are dynamic causal modeling (DCM) and Granger Causality. While DCM models nonlinear couplings, Granger Causality, which constitutes a major tool to reveal effective connectivity, and is widely used to analyze EEG/MEG data as well as fMRI signals, is usually applied in its linear version. In order to capture nonlinear interactions between even short and noisy time series, a few approaches have been proposed. We review them and focus on a recently proposed flexible approach has been recently proposed, consisting in the kernel version of Granger Causality. We show the application of the proposed approach on EEG signals and fMRI data.
Sebastiano Stramaglia - One of the best experts on this subject based on the ideXlab platform.
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On the interpretability and computational reliability of frequency-domain Granger Causality
arXiv: Methodology, 2017Co-Authors: Luca Faes, Sebastiano Stramaglia, Daniele MarinazzoAbstract:This is a comment to the paper 'A study of problems encountered in Granger Causality analysis from a neuroscience perspective'. We agree that interpretation issues of Granger Causality in Neuroscience exist (partially due to the historical unfortunate use of the name 'Causality', as nicely described in previous literature). On the other hand we think that the paper uses a formulation of Granger Causality which is outdated (albeit still used), and in doing so it dismisses the measure based on a suboptimal use of it. Furthermore, since data from simulated systems are used, the pitfalls that are found with the used formulation are intended to be general, and not limited to neuroscience. It would be a pity if this paper, even written in good faith, became a wildcard against all possible applications of Granger Causality, regardless of the hard work of colleagues aiming to seriously address the methodological and interpretation pitfalls. In order to provide a balanced view, we replicated their simulations used the updated State Space implementation, proposed already some years ago, in which the pitfalls are mitigated or directly solved.
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Synergy, redundancy and unnormalized Granger Causality
arXiv: Information Theory, 2015Co-Authors: Sebastiano Stramaglia, Leonardo Angelini, Jesus M. Cortes, Daniele MarinazzoAbstract:We analyze by means of Granger Causality the effect of synergy and redundancy in the inference (from time series data) of the information flow between subsystems of a complex network. Whilst fully conditioned Granger Causality is not affected by synergy, the pairwise analysis fails to put in evidence synergetic effects. We show that maximization of the total Granger Causality to a given target, over all the possible partitions of the set of driving variables, puts in evidence redundant multiplets of variables influencing the target, provided that an {\it unnormalized} definition of Granger Causality is adopted. Along the same lines we also introduce a pairwise index of synergy (w.r.t. to information flow to a third variable) which is zero when two independent sources additively influence a common target, differently from previous definitions of synergy.
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EMBC - Synergy, redundancy and unnormalized Granger Causality
2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 2015Co-Authors: Sebastiano Stramaglia, Leonardo Angelini, Jesus M. Cortes, Daniele MarinazzoAbstract:We analyze by means of Granger Causality the effect of synergy and redundancy in the inference (from time series data) of the information flow between subsystems of a complex network. Whilst fully conditioned Granger Causality is not affected by synergy, the pairwise analysis fails to put in evidence synergetic effects. We show that maximization of the total Granger Causality to a given target, over all the possible partitions of the set of driving variables, puts in evidence redundant multiplets of variables influencing the target, provided that an unnormalized definition of Granger Causality is adopted. Along the same lines we also introduce a pairwise index of synergy (w.r.t. to information flow to a third variable) which is zero when two independent sources additively influence a common target; thus, this definition differs from previous definitions of synergy.
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Nonlinear Granger Causality for brain connectivity
2011 IEEE International Symposium on Medical Measurements and Applications, 2011Co-Authors: Sebastiano Stramaglia, Mario Pellicoro, L. Angelini, Daniele MarinazzoAbstract:The communication among neuronal populations, reflected by transient synchronous activity, is the mechanism underlying the information processing in the brain. Although it is widely assumed that the interactions among those populations (i.e. functional connectivity) are highly nonlinear, the amount of nonlinear information transmission and its functional roles are not clear. Granger Causality constitutes a major tool to reveal effective connectivity, and it is widely used to analyze EEG/MEG data as well as fMRI signals in its linear version. In order to capture nonlinear interactions between even short and noisy time series, a kernel version of Granger Causality has been recently proposed. We review kernel Granger Causality and show the application of this approach on EEG signals.
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Nonlinear connectivity by Granger Causality.
NeuroImage, 2011Co-Authors: Daniele Marinazzo, Wei Liao, Hesheng Chen, Sebastiano StramagliaAbstract:The communication among neuronal populations, reflected by transient synchronous activity, is the mechanism underlying the information processing in the brain. Although it is widely assumed that the interactions among those populations (i.e. functional connectivity) are highly nonlinear, the amount of nonlinear information transmission and its functional roles are not clear. The state of the art to understand the communication between brain systems are dynamic causal modeling (DCM) and Granger Causality. While DCM models nonlinear couplings, Granger Causality, which constitutes a major tool to reveal effective connectivity, and is widely used to analyze EEG/MEG data as well as fMRI signals, is usually applied in its linear version. In order to capture nonlinear interactions between even short and noisy time series, a few approaches have been proposed. We review them and focus on a recently proposed flexible approach has been recently proposed, consisting in the kernel version of Granger Causality. We show the application of the proposed approach on EEG signals and fMRI data.
Jianfeng Feng - One of the best experts on this subject based on the ideXlab platform.
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Spatio-temporal Granger Causality: a new framework.
NeuroImage, 2013Co-Authors: Qiang Luo, Mingzhou Ding, Wei Cheng, Pedro A. Valdes-sosa, Xiaotong Wen, Jianfeng FengAbstract:That physiological oscillations of various frequencies are present in fMRI signals is the rule, not the exception. Herein, we propose a novel theoretical framework, spatio-temporal Granger Causality, which allows us to more reliably and precisely estimate the Granger Causality from experimental datasets possessing time-varying properties caused by physiological oscillations. Within this framework, Granger Causality is redefined as a global index measuring the directed information flow between two time series with time-varying properties. Both theoretical analyses and numerical examples demonstrate that Granger Causality is a monotonically increasing function of the temporal resolution used in the estimation. This is consistent with the general principle of coarse graining, which causes information loss by smoothing out very fine-scale details in time and space. Our results confirm that the Granger Causality at the finer spatio-temporal scales considerably outperforms the traditional approach in terms of an improved consistency between two resting-state scans of the same subject. To optimally estimate the Granger Causality, the proposed theoretical framework is implemented through a combination of several approaches, such as dividing the optimal time window and estimating the parameters at the fine temporal and spatial scales. Taken together, our approach provides a novel and robust framework for estimating the Granger Causality from fMRI, EEG, and other related data.
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Granger Causality with signal-dependent noise.
NeuroImage, 2011Co-Authors: Qiang Luo, Jianfeng FengAbstract:It is generally believed that the noise variance in in vivo neuronal data exhibits time-varying volatility, particularly signal-dependent noise. Despite a widely used and powerful tool to detect causal influences in various data sources, Granger Causality has not been well tailored for time-varying volatility models. In this technical note, a unified treatment of the causal influences in both mean and variance is naturally proposed on models with signal-dependent noise in both time and frequency domains. The approach is first systematically validated on toy models, and then applied to the physiological data collected from Parkinson patients, where a clear advantage over the classical Granger Causality is demonstrated.
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Granger Causality: Theory and Applications
Frontiers in Computational and Systems Biology, 2010Co-Authors: Shuixia Guo, Christophe Ladroue, Jianfeng FengAbstract:A question of great interest in systems biology is how to uncover complex network structures from experimental data[1, 3, 18, 38, 55]. With the rapid progress of experimental techniques, a crucial task is to develop methodologies that are both statistically sound and computationally feasible for analysing increasingly large datasets and reliably inferring biological interactions from them [16, 17, 22, 37, 40, 42]. The building block of such enterprise is to being able to detect relations (causal, statistical or functional) between nodes of the network. Over the past two decades, a number of approaches have been developed: information theory ([4]), control theory ([17]) or Bayesian statistics ([35]). Here we will be focusing on another successful alternative approach: Granger Causality. In recent Cell papers [7, 12], the authors have come to the conclusion that the ordinary differential equation approach outperforms the other reverse engineering approaches (Bayesian network and information theory) in building causal networks. We have demonstrated that the Granger Causality achieves better results than the ordinary differential approach [34]. The basic idea of Granger Causality can be traced back to Wiener[47] who conceived the notion that, if the prediction of one time series is improved by incorporating the knowledge of a second time series, then the latter is said to have a causal influence on the first. Granger[23, 24] later formalized Wiener’s idea in the context of linear regression models. Specifically, two auto-regressive models are fitted to the first time series – with and without including the second time series – and the improvement of the prediction is measured by the ratio of the variance of the error terms. A ratio larger than one signifies an improvement, hence a causal connection. At worst, the ratio is 1 and signifies causal independence from the second time series to the first. Geweke’s decomposition of a vector autoregressive process ([20, 21]) led to a set of Causality measures which have a spectral representation and make the interpretation more informative and useful by extending Granger Causality to the frequency domain. In this chapter, we aim to present Granger Causality and how its original formalism has been extended to address biological and computational issues, as summarized in Fig. 5.1.
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partial Granger Causality eliminating exogenous inputs and latent variables
Journal of Neuroscience Methods, 2008Co-Authors: Shuixia Guo, Anil K Seth, Keith M. Kendrick, Cong Zhou, Jianfeng FengAbstract:Attempts to identify causal interactions in multivariable biological time series (e.g., gene data, protein data, physiological data) can be undermined by the confounding influence of environmental (exogenous) inputs. Compounding this problem, we are commonly only able to record a subset of all related variables in a system. These recorded variables are likely to be influenced by unrecorded (latent) variables. To address this problem, we introduce a novel variant of a widely used statistical measure of Causality - Granger Causality - that is inspired by the definition of partial correlation. Our 'partial Granger Causality' measure is extensively tested with toy models, both linear and nonlinear, and is applied to experimental data: in vivo multielectrode array (MEA) local field potentials (LFPs) recorded from the inferotemporal cortex of sheep. Our results demonstrate that partial Granger Causality can reveal the underlying interactions among elements in a network in the presence of exogenous inputs and latent variables in many cases where the existing conditional Granger Causality fails.
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Partial Granger Causality—Eliminating exogenous inputs and latent variables
Journal of Neuroscience Methods, 2008Co-Authors: Shuixia Guo, Anil K Seth, Keith M. Kendrick, Cong Zhou, Jianfeng FengAbstract:Attempts to identify causal interactions in multivariable biological time series (e.g., gene data, protein data, physiological data) can be undermined by the confounding influence of environmental (exogenous) inputs. Compounding this problem, we are commonly only able to record a subset of all related variables in a system. These recorded variables are likely to be influenced by unrecorded (latent) variables. To address this problem, we introduce a novel variant of a widely used statistical measure of Causality - Granger Causality - that is inspired by the definition of partial correlation. Our 'partial Granger Causality' measure is extensively tested with toy models, both linear and nonlinear, and is applied to experimental data: in vivo multielectrode array (MEA) local field potentials (LFPs) recorded from the inferotemporal cortex of sheep. Our results demonstrate that partial Granger Causality can reveal the underlying interactions among elements in a network in the presence of exogenous inputs and latent variables in many cases where the existing conditional Granger Causality fails.
Mehrdad Jafari-mamaghani - One of the best experts on this subject based on the ideXlab platform.
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Non-parametric Wiener-Granger Causality in partially observed systems
2014 IEEE Conference on Norbert Wiener in the 21st Century (21CW), 2014Co-Authors: Mehrdad Jafari-mamaghaniAbstract:Wiener's definition of Causality, commonly known as Wiener-Granger Causality, has become a frequently used quantification of temporally resolved Causality in numerous fields of science. In many empirical studies, the system of interest cannot be observed in its entirety and relevant information may reside outside of the sampled observations. To this end, partial Wiener-Granger Causality has been developed to circumvent this issue. In this paper, we extend partial Wiener-Granger Causality to the non-parametric case and discuss different approaches to estimate it.
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A Treatise on Measuring Wiener-Granger Causality
2014Co-Authors: Mehrdad Jafari-mamaghaniAbstract:Wiener-Granger Causality is a well-established concept of Causality based on stochasticity and the flow of time, with applications in a broad array of quantitative sciences. The majority of methods ...
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Non-parametric analysis of Granger Causality using local measures of divergence
Applied Mathematical Sciences, 2013Co-Authors: Mehrdad Jafari-mamaghaniAbstract:Wiener-Granger Causality is a well-established concept of Causality based on stochasticity and the flow of time, with applications in a broad array of quantitative sciences. The majority of methods used to measure Wiener-Granger Causality are based on linear premises and hence insensitive to non-linear signals. Other frameworks based on non-parametric techniques are often computationally expensive and susceptible to overfitting or lack of sensitivity.In this thesis, Paper I investigates the application of linear Wiener-Granger Causality to migrating cancer cell data obtained using a Systems Microscopy experimental platform. Paper II represents a review of non-parametric measures based on information theory and discusses a number of related bottlenecks and potential routes of circumvention. Paper III studies the properties of a frequently used non-parametric information theoretical measure for a class of non-Gaussian distributions. Paper IV introduces a new efficient scheme for non-parametric analysis of Wiener-Granger Causality based on kernel canonical correlations, and studies the connection between this new scheme and the information theoretical approach. Lastly, Paper V draws upon the results in the preceding paper to discuss non-parametric analysis of Wiener-Granger Causality in partially observed systems.Altogether, the work presented in this thesis constitutes a comprehensive review on measures of Wiener-Granger Causality in general, and in particular, features new insights on efficient non-parametric analysis of Wiener-Granger Causality in high-dimensional settings.
