1,163 research outputs found
Synergetic and redundant information flow detected by unnormalized Granger causality: application to resting state fMRI
Objectives: We develop a framework for the analysis of synergy and redundancy
in the pattern of information flow between subsystems of a complex network.
Methods: The presence of redundancy and/or synergy in multivariate time series
data renders difficult to estimate the neat flow of information from each
driver variable to a given target. We show that adopting an unnormalized
definition of Granger causality one may put in evidence redundant multiplets of
variables influencing the target by maximizing the total Granger causality to a
given target, over all the possible partitions of the set of driving variables.
Consequently we introduce a pairwise index of synergy which is zero when two
independent sources additively influence the future state of the system,
differently from previous definitions of synergy. Results: We report the
application of the proposed approach to resting state fMRI data from the Human
Connectome Project, showing that redundant pairs of regions arise mainly due to
space contiguity and interhemispheric symmetry, whilst synergy occurs mainly
between non-homologous pairs of regions in opposite hemispheres. Conclusions:
Redundancy and synergy, in healthy resting brains, display characteristic
patterns, revealed by the proposed approach. Significance: The pairwise synergy
index, here introduced, maps the informational character of the system at hand
into a weighted complex network: the same approach can be applied to other
complex systems whose normal state corresponds to a balance between redundant
and synergetic circuits.Comment: 6 figures. arXiv admin note: text overlap with arXiv:1403.515
Multiscale Granger causality analysis by \`a trous wavelet transform
Since interactions in neural systems occur across multiple temporal scales,
it is likely that information flow will exhibit a multiscale structure, thus
requiring a multiscale generalization of classical temporal precedence
causality analysis like Granger's approach. However, the computation of
multiscale measures of information dynamics is complicated by theoretical and
practical issues such as filtering and undersampling: to overcome these
problems, we propose a wavelet-based approach for multiscale Granger causality
(GC) analysis, which is characterized by the following properties: (i) only the
candidate driver variable is wavelet transformed (ii) the decomposition is
performed using the \`a trous wavelet transform with cubic B-spline filter. We
measure GC, at a given scale, by including the wavelet coefficients of the
driver times series, at that scale, in the regression model of the target. To
validate our method, we apply it to publicly available scalp EEG signals, and
we find that the condition of closed eyes, at rest, is characterized by an
enhanced GC among channels at slow scales w.r.t. eye open condition, whilst the
standard Granger causality is not significantly different in the two
conditions.Comment: 4 pages, 3 figure
Kernel method for nonlinear Granger causality
Important information on the structure of complex systems, consisting of more
than one component, can be obtained by measuring to which extent the individual
components exchange information among each other. Such knowledge is needed to
reach a deeper comprehension of phenomena ranging from turbulent fluids to
neural networks, as well as complex physiological signals. The linear Granger
approach, to detect cause-effect relationships between time series, has emerged
in recent years as a leading statistical technique to accomplish this task.
Here we generalize Granger causality to the nonlinear case using the theory of
reproducing kernel Hilbert spaces. Our method performs linear Granger causality
in the feature space of suitable kernel functions, assuming arbitrary degree of
nonlinearity. We develop a new strategy to cope with the problem of
overfitting, based on the geometry of reproducing kernel Hilbert spaces.
Applications to coupled chaotic maps and physiological data sets are presented.Comment: Revised version, accepted for publication on Physical Review Letter
Granger causality and transfer entropy are equivalent for Gaussian variables
Granger causality is a statistical notion of causal influence based on
prediction via vector autoregression. Developed originally in the field of
econometrics, it has since found application in a broader arena, particularly
in neuroscience. More recently transfer entropy, an information-theoretic
measure of time-directed information transfer between jointly dependent
processes, has gained traction in a similarly wide field. While it has been
recognized that the two concepts must be related, the exact relationship has
until now not been formally described. Here we show that for Gaussian
variables, Granger causality and transfer entropy are entirely equivalent, thus
bridging autoregressive and information-theoretic approaches to data-driven
causal inference.Comment: In review, Phys. Rev. Lett., Nov. 200
Neural Networks with Non-Uniform Embedding and Explicit Validation Phase to Assess Granger Causality
A challenging problem when studying a dynamical system is to find the
interdependencies among its individual components. Several algorithms have been
proposed to detect directed dynamical influences between time series. Two of
the most used approaches are a model-free one (transfer entropy) and a
model-based one (Granger causality). Several pitfalls are related to the
presence or absence of assumptions in modeling the relevant features of the
data. We tried to overcome those pitfalls using a neural network approach in
which a model is built without any a priori assumptions. In this sense this
method can be seen as a bridge between model-free and model-based approaches.
The experiments performed will show that the method presented in this work can
detect the correct dynamical information flows occurring in a system of time
series. Additionally we adopt a non-uniform embedding framework according to
which only the past states that actually help the prediction are entered into
the model, improving the prediction and avoiding the risk of overfitting. This
method also leads to a further improvement with respect to traditional Granger
causality approaches when redundant variables (i.e. variables sharing the same
information about the future of the system) are involved. Neural networks are
also able to recognize dynamics in data sets completely different from the ones
used during the training phase
Multivariate contemporaneous threshold autoregressive models
In this paper we propose a contemporaneous threshold multivariate smooth transition autoregressive (C-MSTAR) model in which the regime weights depend on the ex ante probabilities that latent regime-specific variables exceed certain threshold values. The model is a multivariate generalization of the contemporaneous threshold autoregressive model introduced by Dueker et al. (2007). A key feature of the model is that the transition function depends on all the parameters of the model as well as on the data. The stability and distributional properties of the proposed model are investigated. The C-MSTAR model is also used to examine the relationship between US stock prices and interest rates.Time-series analysis ; Capital assets pricing model
Information theoretic interpretation of frequency domain connectivity measures
To provide adequate multivariate measures of information flow between neural
structures, modified expressions of Partial Directed Coherence (PDC) and
Directed Transfer Function (DTF), two popular multivariate connectivity
measures employed in neuroscience, are introduced and their formal relationship
to mutual information rates are proved.Comment: 17 pages, 1 figur
Analyzing Multiple Nonlinear Time Series with Extended Granger Causality
Identifying causal relations among simultaneously acquired signals is an
important problem in multivariate time series analysis. For linear stochastic
systems Granger proposed a simple procedure called the Granger causality to
detect such relations. In this work we consider nonlinear extensions of
Granger's idea and refer to the result as Extended Granger Causality. A simple
approach implementing the Extended Granger Causality is presented and applied
to multiple chaotic time series and other types of nonlinear signals. In
addition, for situations with three or more time series we propose a
conditional Extended Granger Causality measure that enables us to determine
whether the causal relation between two signals is direct or mediated by
another process.Comment: 16 pages, 6 figure
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