299 research outputs found
Multiscale Information Decomposition: Exact Computation for Multivariate Gaussian Processes
Exploiting the theory of state space models, we derive the exact expressions
of the information transfer, as well as redundant and synergistic transfer, for
coupled Gaussian processes observed at multiple temporal scales. All of the
terms, constituting the frameworks known as interaction information
decomposition and partial information decomposition, can thus be analytically
obtained for different time scales from the parameters of the VAR model that
fits the processes. We report the application of the proposed methodology
firstly to benchmark Gaussian systems, showing that this class of systems may
generate patterns of information decomposition characterized by mainly
redundant or synergistic information transfer persisting across multiple time
scales or even by the alternating prevalence of redundant and synergistic
source interaction depending on the time scale. Then, we apply our method to an
important topic in neuroscience, i.e., the detection of causal interactions in
human epilepsy networks, for which we show the relevance of partial information
decomposition to the detection of multiscale information transfer spreading
from the seizure onset zone
On the interpretability and computational reliability of frequency-domain Granger causality
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formulation of Granger causality which is outdated (albeit still used), and in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
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
Multiscale Granger causality
In the study of complex physical and biological systems represented by
multivariate stochastic processes, an issue of great relevance is the
description of the system dynamics spanning multiple temporal scales. While
methods to assess the dynamic complexity of individual processes at different
time scales are well-established, multiscale analysis of directed interactions
has never been formalized theoretically, and empirical evaluations are
complicated by practical issues such as filtering and downsampling. Here we
extend the very popular measure of Granger causality (GC), a prominent tool for
assessing directed lagged interactions between joint processes, to quantify
information transfer across multiple time scales. We show that the multiscale
processing of a vector autoregressive (AR) process introduces a moving average
(MA) component, and describe how to represent the resulting ARMA process using
state space (SS) models and to combine the SS model parameters for computing
exact GC values at arbitrarily large time scales. We exploit the theoretical
formulation to identify peculiar features of multiscale GC in basic AR
processes, and demonstrate with numerical simulations the much larger
estimation accuracy of the SS approach compared with pure AR modeling of
filtered and downsampled data. The improved computational reliability is
exploited to disclose meaningful multiscale patterns of information transfer
between global temperature and carbon dioxide concentration time series, both
in paleoclimate and in recent years
Multivariate Frequency Domain Analysis of Causal Interactions in Physiological Time Series
The mission of this chapter is to enhance the theoretical interpretability of the available frequency domain measures of coupling and causality derived from the MVAR representation of multiple time series
Multiscale Analysis of Information Dynamics for Linear Multivariate Processes
In the study of complex physical and physiological systems represented by
multivariate time series, an issue of great interest is the description of the
system dynamics over a range of different temporal scales. While
information-theoretic approaches to the multiscale analysis of complex dynamics
are being increasingly used, the theoretical properties of the applied measures
are poorly understood. This study introduces for the first time a framework for
the analytical computation of information dynamics for linear multivariate
stochastic processes explored at different time scales. After showing that the
multiscale processing of a vector autoregressive (VAR) process introduces a
moving average (MA) component, we describe how to represent the resulting VARMA
process using state-space (SS) models and how to exploit the SS model
parameters to compute analytical measures of information storage and
information transfer for the original and rescaled processes. The framework is
then used to quantify multiscale information dynamics for simulated
unidirectionally and bidirectionally coupled VAR processes, showing that
rescaling may lead to insightful patterns of information storage and transfer
but also to potentially misleading behaviors
Information decomposition of multichannel EMG to map functional interactions in the distributed motor system
The central nervous system needs to coordinate multiple muscles during postural control. Functional coordination is established through the neural circuitry that interconnects different muscles. Here we used multivariate information decomposition of multichannel EMG acquired from 14 healthy participants during postural tasks to investigate the neural interactions between muscles. A set of information measures were estimated from an instantaneous linear regression model and a time-lagged VAR model fitted to the EMG envelopes of 36 muscles. We used network analysis to quantify the structure of functional interactions between muscles and compared them across experimental conditions. Conditional mutual information and transfer entropy revealed sparse networks dominated by local connections between muscles. We observed significant changes in muscle networks across postural tasks localized to the muscles involved in performing those tasks. Information decomposition revealed distinct patterns in task-related changes: unimanual and bimanual pointing were associated with reduced transfer to the pectoralis major muscles, but an increase in total information compared to no pointing, while postural instability resulted in increased information, information transfer and information storage in the abductor longus muscles compared to normal stability. These findings show robust patterns of directed interactions between muscles that are task-dependent and can be assessed from surface EMG recorded during static postural tasks. We discuss directed muscle networks in terms of the neural circuitry involved in generating muscle activity and suggest that task-related effects may reflect gain modulations of spinal reflex pathways
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
MuTE: a new matlab toolbox for estimating the multivariate transfer entropy in physiological variability series
We present a new time series analysis toolbox, developed in Matlab, for the estimation of the Transfer entropy (TE) between time series taken from a multivariate dataset. The main feature of the toolbox is its fully multivariate implementation, that is made possible by the design of an approach for the non-uniform embedding (NUE) of the observed time series. The toolbox is equipped with parametric (linear) and non-parametric (based on binning or nearest neighbors) entropy estimators. All these estimators, implemented using the NUE approach in comparison with the classical approach based on uniform embedding, are tested on RR interval, systolic pressure and respiration variability series measured from healthy subjects during head-up tilt. The results support the necessity of resorting to NUE for obtaining reliable estimates of the multivariate TE in short-term cardiovascular and cardiorespiratory variability
Measuring Connectivity in Linear Multivariate Processes: Definitions, Interpretation, and Practical Analysis
This tutorial paper introduces a common framework for the evaluation of widely used frequency-domain measures of coupling (coherence, partial coherence) and causality (directed coherence, partial directed coherence) from the parametric representation of linear multivariate (MV) processes. After providing a comprehensive time-domain definition of the various forms of connectivity observed in MV processes, we particularize them to MV autoregressive (MVAR) processes and derive the corresponding frequency-domain measures. Then, we discuss the theoretical interpretation of these MVAR-based connectivity measures, showing that each of them reflects a specific time-domain connectivity definition and how this results in the description of peculiar aspects of the information transfer in MV processes. Furthermore, issues related to the practical utilization of these measures on real-time series are pointed out, including MVAR model estimation and significance assessment. Finally, limitations and pitfalls arising from model mis-specification are discussed, indicating possible solutions and providing practical recommendations for a safe computation of the connectivity measures. An example of estimation of the presented measures from multiple EEG signals recorded during a combined visuomotor task is also reported, showing how evaluation of coupling and causality in the frequency domain may help describing specific neurophysiological mechanisms
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