10 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 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
Multivariate Granger causality unveils directed parietal to prefrontal cortex connectivity during task-free MRI.
While a large body of research has focused on the study of functional brain "connectivity", few investigators have focused on directionality of brain-brain interactions which, in spite of the mostly bidirectional anatomical substrates, cannot be assumed to be symmetrical. We employ a multivariate Granger Causality-based approach to estimating directed in-network interactions and quantify its advantages using extensive realistic synthetic BOLD data simulations to match Human Connectome Project (HCP) data specification. We then apply our framework to resting state functional MRI (rs-fMRI) data provided by the HCP to estimate the directed connectome of the human brain. We show that the functional interactions between parietal and prefrontal cortices commonly observed in rs-fMRI studies are not symmetrical, but consists of directional connectivity from parietal areas to prefrontal cortices rather than vice versa. These effects are localized within the same hemisphere and do not generalize to cross-hemispheric functional interactions. Our data are consistent with neurophysiological evidence that posterior parietal cortices involved in processing and integration of multi-sensory information modulate the function of more anterior prefrontal regions implicated in action control and goal-directed behaviour. The directionality of functional connectivity can provide an additional layer of information in interpreting rs-fMRI studies both in health and disease
Algorithms of causal inference for the analysis of effective connectivity among brain regions
In recent years, powerful general algorithms of causal inference have been developed. In particular, in the framework of Pearl’s causality, algorithms of inductive causation (IC and IC*) provide a procedure to determine which causal connections among nodes in a network can be inferred from empirical observations even in the presence of latent variables, indicating the limits of what can be learned without active manipulation of the system. These algorithms can in principle become important complements to established techniques such as Granger causality and Dynamic Causal Modeling (DCM) to analyze causal influences (effective connectivity) among brain regions. However, their application to dynamic processes has not been yet examined. Here we study how to apply these algorithms to time-varying signals such as electrophysiological or neuroimaging signals. We propose a new algorithm which combines the basic principles of the previous algorithms with Granger causality to obtain a representation of the causal relations suited to dynamic processes. Furthermore, we use graphical criteria to predict dynamic statistical dependencies between the signals from the causal structure. We show how some problems for causal inference from neural signals (e.g., measurement noise, hemodynamic responses, and time aggregation) can be understood in a general graphical approach. Focusing on the effect of spatial aggregation, we show that when causal inference is performed at a coarser scale than the one at which the neural sources interact, results strongly depend on the degree of integration of the neural sources aggregated in the signals, and thus characterize more the intra-areal properties than the interactions among regions. We finally discuss how the explicit consideration of latent processes contributes to understand Granger causality and DCM as well as to distinguish functional and effective connectivity
Evaluation of Granger causality measures for constructing networks from multivariate time series
Granger causality and variants of this concept allow the study of complex
dynamical systems as networks constructed from multivariate time series. In
this work, a large number of Granger causality measures used to form causality
networks from multivariate time series are assessed. These measures are in the
time domain, such as model-based and information measures, the frequency domain
and the phase domain. The study aims also to compare bivariate and multivariate
measures, linear and nonlinear measures, as well as the use of dimension
reduction in linear model-based measures and information measures. The latter
is particular relevant in the study of high-dimensional time series. For the
performance of the multivariate causality measures, low and high dimensional
coupled dynamical systems are considered in discrete and continuous time, as
well as deterministic and stochastic. The measures are evaluated and ranked
according to their ability to provide causality networks that match the
original coupling structure. The simulation study concludes that the Granger
causality measures using dimension reduction are superior and should be
preferred particularly in studies involving many observed variables, such as
multi-channel electroencephalograms and financial markets.Comment: 24 pages, 5 figures, to be published in Entrop
Causal Information Approach to Partial Conditioning in Multivariate Data Sets
When evaluating causal influence from one time series to another in a multivariate data set it is necessary to take into account
the conditioning effect of the other variables. In the presence of many variables and possibly of a reduced number of samples, full
conditioning can lead to computational and numerical problems. In this paper, we address the problem of partial conditioning to
a limited subset of variables, in the framework of information theory. The proposed approach is tested on simulated data sets and
on an example of intracranial EEG recording from an epileptic subject. We show that, in many instances, conditioning on a small
number of variables, chosen as the most informative ones for the driver node, leads to results very close to those obtained with
a fully multivariate analysis and even better in the presence of a small number of samples. This is particularly relevant when the
pattern of causalities is sparse
Statistical approaches for resting state fMRI data analysis
This doctoral dissertation investigates the methodology to explore brain dynamics from resting state fMRI data. A standard resting state fMRI study gives rise to massive amounts of noisy data with a complicated spatio-temporal correlation structure. There are two main objectives in the analysis of these noisy data: establishing the link between neural activity and the measured signal, and determining distributed brain networks that correspond to brain function. These measures can then be used as indicators of psychological, cognitive or pathological states. Two main issues will be addressed: retrieving and interpreting the hemodynamic response function (HRF) at rest, and dealing with the redundancy inherent to fMRI data. Novel approaches are introduced, discussed and validated on simulated data and on real datasets, in health and disease, in order to track modulation of brain dynamics and HRF across different pathophysiological conditions