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Journal ArticleDOI

Nonlinear connectivity by Granger causality.

TL;DR: A recently proposed flexible approach has been recently proposed, consisting in the kernel version of Granger causality, to capture nonlinear interactions between even short and noisy time series.
About: This article is published in NeuroImage.The article was published on 2011-09-15. It has received 167 citations till now. The article focuses on the topics: Granger causality & Causality (physics).
Citations
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Journal ArticleDOI
TL;DR: The inception of this journal has been foreshadowed by an ever-increasing number of publications on functional connectivity, causal modeling, connectomics, and multivariate analyses of distributed patterns of brain responses.
Abstract: Over the past 20 years, neuroimaging has become a predominant technique in systems neuroscience. One might envisage that over the next 20 years the neuroimaging of distributed processing and connectivity will play a major role in disclosing the brain's functional architecture and operational principles. The inception of this journal has been foreshadowed by an ever-increasing number of publications on functional connectivity, causal modeling, connectomics, and multivariate analyses of distributed patterns of brain responses. I accepted the invitation to write this review with great pleasure and hope to celebrate and critique the achievements to date, while addressing the challenges ahead.

2,822 citations


Cites background from "Nonlinear connectivity by Granger c..."

  • ...Having said this, each clever refinement and generalization of Granger causality (e.g., Deshpande et al., 2010; Havlicek et al., 2010; Marinazzo et al., 2010) brings it one step closer to DCM (at least from my point of view)....

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Journal ArticleDOI
TL;DR: It is argued that discovering effective connectivity depends critically on state-space models with biophysically informed observation and state equations, and some of the challenges faced in this field have promising solutions and speculate on future developments.

385 citations


Cites background from "Nonlinear connectivity by Granger c..."

  • ..., 2005) GCM has also been extended to cover nonlinear stateequations (Freiwald et al., 1999; Marinazzo et al., 2011)....

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  • ...There are a number of nonlinear WAGS methods that have been proposed for analyzing directed effective connectivity (Freiwald et al., 1999, Solo, 2008; Gourieroux et al., 1987; Marinazzo et al., 2011; Kalitzin et al., 2007) 3....

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Journal ArticleDOI
TL;DR: In this paper, a review of the use of graph analysis in translational neuroscience has been presented, which provides practical indications to make sense of brain network analysis and contrast counterproductive attitudes.
Abstract: The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective, communication is coded by temporal dependence between the activities of different brain areas. In the last decade, the abstract representation of the brain as a graph has allowed to visualize functional brain networks and describe their non-trivial topological properties in a compact and objective way. Nowadays, the use of graph analysis in translational neuroscience has become essential to quantify brain dysfunctions in terms of aberrant reconfiguration of functional brain networks. Despite its evident impact, graph analysis of functional brain networks is not a simple toolbox that can be blindly applied to brain signals. On the one hand, it requires the know-how of all the methodological steps of the pipeline that manipulate the input brain signals and extract the functional network properties. On the other hand, knowledge of the neural phenomenon under study is required to perform physiologically relevant analysis. The aim of this review is to provide practical indications to make sense of brain network analysis and contrast counterproductive attitudes.

342 citations

Journal Article
TL;DR: In this article, the authors extend the framework of nonparametric spectral methods to include the estimation of Granger causality spectra for assessing directional influences, and illustrate the utility of the proposed methods using synthetic data from network models consisting of interacting dynamical systems.
Abstract: Experiments in many fields of science and engineering yield data in the form of time series. The Fourier and wavelet transform-based nonparametric methods are used widely to study the spectral characteristics of these time series data. Here, we extend the framework of nonparametric spectral methods to include the estimation of Granger causality spectra for assessing directional influences. We illustrate the utility of the proposed methods using synthetic data from network models consisting of interacting dynamical systems.

226 citations

Journal ArticleDOI
TL;DR: How the functional connectivity patterns obtained from intracranial and scalp electroencephalographic (EEG) recordings reveal information about the dynamics of the epileptic brain and can be used to predict upcoming seizures and to localize the seizure onset zone is discussed.

217 citations

References
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01 Jan 1998
TL;DR: Presenting a method for determining the necessary and sufficient conditions for consistency of learning process, the author covers function estimates from small data pools, applying these estimations to real-life problems, and much more.
Abstract: A comprehensive look at learning and generalization theory. The statistical theory of learning and generalization concerns the problem of choosing desired functions on the basis of empirical data. Highly applicable to a variety of computer science and robotics fields, this book offers lucid coverage of the theory as a whole. Presenting a method for determining the necessary and sufficient conditions for consistency of learning process, the author covers function estimates from small data pools, applying these estimations to real-life problems, and much more.

26,531 citations


"Nonlinear connectivity by Granger c..." refers methods in this paper

  • ...Kernel algorithms work by embedding data into a Hilbert space, and searching for linear relations in that space (Vapnik, 1998) (for precise information on the geometry of least square regression and projection matrices, see Davidson and MacKinnon, 2004)....

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Journal ArticleDOI
TL;DR: EELAB as mentioned in this paper is a toolbox and graphic user interface for processing collections of single-trial and/or averaged EEG data of any number of channels, including EEG data, channel and event information importing, data visualization (scrolling, scalp map and dipole model plotting, plus multi-trial ERP-image plots), preprocessing (including artifact rejection, filtering, epoch selection, and averaging), Independent Component Analysis (ICA) and time/frequency decomposition including channel and component cross-coherence supported by bootstrap statistical methods based on data resampling.

17,362 citations

Journal ArticleDOI
TL;DR: In this article, the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation, and measures of causal lag and causal strength can then be constructed.
Abstract: There occurs on some occasions a difficulty in deciding the direction of causality between two related variables and also whether or not feedback is occurring. Testable definitions of causality and feedback are proposed and illustrated by use of simple two-variable models. The important problem of apparent instantaneous causality is discussed and it is suggested that the problem often arises due to slowness in recording information or because a sufficiently wide class of possible causal variables has not been used. It can be shown that the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation. Measures of causal lag and causal strength can then be constructed. A generalisation of this result with the partial cross spectrum is suggested.

16,349 citations


"Nonlinear connectivity by Granger c..." refers background in this paper

  • ...Granger causality analysis (Granger, 1969; Wiener, 1956) is an approach that measures the causal association and effective connectivity and can provide information about the dynamics and directionality on both electroencephalography (EEG) (Brovelli et al., 2004; Guo et al., 2008; Kaminski et al.,…...

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Book
01 Jan 1965
TL;DR: This chapter discusses the concept of a Random Variable, the meaning of Probability, and the axioms of probability in terms of Markov Chains and Queueing Theory.
Abstract: Part 1 Probability and Random Variables 1 The Meaning of Probability 2 The Axioms of Probability 3 Repeated Trials 4 The Concept of a Random Variable 5 Functions of One Random Variable 6 Two Random Variables 7 Sequences of Random Variables 8 Statistics Part 2 Stochastic Processes 9 General Concepts 10 Random Walk and Other Applications 11 Spectral Representation 12 Spectral Estimation 13 Mean Square Estimation 14 Entropy 15 Markov Chains 16 Markov Processes and Queueing Theory

13,886 citations


"Nonlinear connectivity by Granger c..." refers background or methods in this paper

  • ...When choosing the kernel for the model, it is important that the model itself will be matched to the dynamical characteristics of the signal, as correctly pointed out in Pereda et al. (2005). In KGC, we deal with problem (i) performing a preliminary analysis in which we look how the causality indices change with the order p of the polynomial kernel, orwith theσ of theGaussian kernel, and theparameter is chosen according to the stability of the results....

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  • ...the function which minimizes the risk functional (Papoulis 1985)) does not change when new variables, statistically independent of input and target variables, are added to the set of input variables....

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Book ChapterDOI
01 Jan 2001
TL;DR: In this article, it is shown that the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation, and measures of causal lag and causal strength can then be constructed.
Abstract: There occurs on some occasions a difficulty in deciding the direction of causality between two related variables and also whether or not feedback is occurring. Testable definitions of causality and feedback are proposed and illustrated by use of simple two-variable models. The important problem of apparent instantaneous causality is discussed and it is suggested that the problem often arises due to slowness in recordhag information or because a sufficiently wide class of possible causal variables has not been used. It can be shown that the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation. Measures of causal lag and causal strength can then be constructed. A generalization of this result with the partial cross spectrum is suggested.The object of this paper is to throw light on the relationships between certain classes of econometric models involving feedback and the functions arising in spectral analysis, particularly the cross spectrum and the partial cross spectrum. Causality and feedback are here defined in an explicit and testable fashion. It is shown that in the two-variable case the feedback mechanism can be broken down into two causal relations and that the cross spectrum can be considered as the sum of two cross spectra, each closely connected with one of the causations. The next three sections of the paper briefly introduce those aspects of spectral methods, model building, and causality which are required later. Section IV presents the results for the two-variable case and Section V generalizes these results for three variables.

11,896 citations


"Nonlinear connectivity by Granger c..." refers background in this paper

  • ...Granger causality analysis (Granger, 1969; Wiener, 1956) is an approach that measures the causal association and effective connectivity and can provide information about the dynamics and directionality on both electroencephalography (EEG) (Brovelli et al., 2004; Guo et al., 2008; Kaminski et al.,…...

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  • ...E-mail address: daniele.marinazzo@gmail.com (Dan 1053-8119/$ – see front matter © 2010 Elsevier Inc. Al doi:10.1016/j.neuroimage.2010.01.099 a b s t r a c t a r t i c l e i n f o...

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