On directed information theory and Granger causality graphs

Amblard, Pierre‐Olivier; Michel, Olivier

doi:10.1007/s10827-010-0231-x

Cited by 124 publications

(122 citation statements)

References 44 publications

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“…It is now clear that there is no single universal approach to understanding connectivity in the brain (Amblard and Michel 2011) and approaches extend from non-directional measures such as mutual information (Jirsa and McIntosh 2007) to measures that utilize directional information flow such as transfer entropy (Lungarella and Sporns 2006). Lungarella and Sporns (2006) show that there is a distinct link between the morphology of sensors and information flow and that coding depends on the morphology and dynamics of sensory systems.…”

Section: Computational Models and Network Inferencementioning

confidence: 99%

Delayed mutual information infers patterns of synaptic connectivity in a proprioceptive neural network

et al. 2015

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Understanding the patterns of interconnections between neurons in complex networks is an enormous challenge using traditional physiological approaches. Here we combine the use of an information theoretic approach with intracellular recording to establish patterns of connections between layers of interneurons in a neural network responsible for mediating reflex movements of the hind limb of an insect. By analysing delayed mutual information of the synaptic and spiking responses of sensory neurons, spiking and nonspiking interneurons in response to movement of a joint receptor that monitors the position of the tibia relative to the femur, we are able to predict the patterns of interconnections between the layers of sensory neurons and interneurons in the network, with results matching closely those known from the literature. In addition, we use cross-correlation methods to establish the sign of those interconnections and show that they also show a high degree of similarity with those established for these networks over the last 30 years. The method proposed in this paper has great potential to elucidate functional connectivity at the neuronal level in many different neuronal networks.

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Section: Computational Models and Network Inferencementioning

confidence: 99%

Delayed mutual information infers patterns of synaptic connectivity in a proprioceptive neural network

et al. 2015

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“…Similarly, we can also quantify a degree of causation in bits through calculating the directed information. It is demonstrated by Amblard et al [20]: for linear Gaussian processes, directed information and Granger causality are equivalent. Note that the transfer entropy defined in Eq.…”

Section: Causal Inference: Granger Causality Transfer Entropy and Dmentioning

confidence: 95%

“…Directed information, proposed by Marko [18] and re-formalized by others [19,20], is more general for quantifying directional dependencies, and has recently attracted attention [10,21]. It is modified from the mutual information to capture causal influences, denoted as I(X → Y) for two stochastic processes X and Y.…”

Section: Causal Inference: Granger Causality Transfer Entropy and Dmentioning

confidence: 99%

“…Prominently involved areas for the changes include left temporal pole and cerebellum, which have previously been implied to be involved in auditory short-term or working memory. Amblard and Michel [20] extracted Granger causality graphs using directed information, and such techniques were shown to be necessary to analyze the structure of systems with feedback in general, and neural systems specifically. Quinn et al [10] proposed a nonlinear robust extension of the linear Granger tools also based directed information.…”

Section: Applications and Validity In Neuroscience And Aging Researchmentioning

confidence: 99%

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Multi-Scale Information, Network, Causality, and Dynamics: Mathematical Computation and Bayesian Inference to Cognitive Neuroscience and Aging

Wang¹

2013

Functional Brain Mapping and the Endeavor to Understand the Working Brain

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“…(1), (2), (3) and (4) with effective partial symbolic transfer entropy. For challenge (5), i.e., statistical significance, it may be evaluated by using bootstrapping strategies, surrogate data or random permutations [50,51]. Under the surrogate-based testing scheme, we will assess the significance with kernel density estimation.…”

Section: Drive-response Network Inferencementioning

confidence: 99%

Inferring a Drive-Response Network from Time Series of Topological Measures in Complex Networks with Transfer Entropy

2014

Entropy

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Topological measures are crucial to describe, classify and understand complex networks. Lots of measures are proposed to characterize specific features of specific networks, but the relationships among these measures remain unclear. Taking into account that pulling networks from different domains together for statistical analysis might provide incorrect conclusions, we conduct our investigation with data observed from the same network in the form of simultaneously measured time series. We synthesize a transfer entropy-based framework to quantify the relationships among topological measures, and then to provide a holistic scenario of these measures by inferring a drive-response network. Techniques from Symbolic Transfer Entropy, Effective Transfer Entropy, and Partial Transfer Entropy are synthesized to deal with challenges such as time series being nonstationary, finite sample effects and indirect effects. We resort to kernel density estimation to assess significance of the results based on surrogate data. The framework is applied to study 20 measures across 2779 records in the Technology Exchange Network, and the results are consistent with some existing knowledge. With the drive-response network, we evaluate the influence of each measure by calculating its strength, and cluster them into three classes, i.e., driving measures, responding measures and standalone measures, according to the network communities.

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On directed information theory and Granger causality graphs

Cited by 124 publications

References 44 publications

Delayed mutual information infers patterns of synaptic connectivity in a proprioceptive neural network

Delayed mutual information infers patterns of synaptic connectivity in a proprioceptive neural network

Multi-Scale Information, Network, Causality, and Dynamics: Mathematical Computation and Bayesian Inference to Cognitive Neuroscience and Aging

Inferring a Drive-Response Network from Time Series of Topological Measures in Complex Networks with Transfer Entropy

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