Neural Networks for Modeling Granger Causality

Marwala, Tshilidzi

doi:10.1142/9789814630870_0005

Cited by 3 publications

References 39 publications

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Echo state network models for nonlinear Granger causality

Duggento

Guerrisi

Toschi

2021

Phil. Trans. R. Soc. A.

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While Granger causality (GC) has been often employed in network neuroscience, most GC applications are based on linear multivariate autoregressive (MVAR) models. However, real-life systems like biological networks exhibit notable nonlinear behaviour, hence undermining the validity of MVAR-based GC (MVAR-GC). Most nonlinear GC estimators only cater for additive nonlinearities or, alternatively, are based on recurrent neural networks or long short-term memory networks, which present considerable training difficulties and tailoring needs. We reformulate the GC framework in terms of echo-state networks-based models for arbitrarily complex networks, and characterize its ability to capture nonlinear causal relations in a network of noisy Duffing oscillators, showing a net advantage of echo state GC (ES-GC) in detecting nonlinear, causal links. We then explore the structure of ES-GC networks in the human brain employing functional MRI data from 1003 healthy subjects drawn from the human connectome project, demonstrating the existence of previously unknown directed within-brain interactions. In addition, we examine joint brain-heart signals in 15 subjects where we explore directed interaction between brain networks and central vagal cardiac control in order to investigate the so-called central autonomic network in a causal manner. This article is part of the theme issue ‘Advanced computation in cardiovascular physiology: new challenges and opportunities’.

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Echo state network models for nonlinear Granger causality

Duggento

Guerrisi

Toschi

2021

Phil. Trans. R. Soc. A.

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Echo State Network models for nonlinear Granger causality

Duggento

Guerrisi

Toschi

2019

Preprint

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While Granger Causality (GC) has been employed in a large number of problems in network neuroscience, the vast majority of GC applications are based on linear multivariate autoregressive (MVAR) models. However, it is well known that real-life systems (and biological networks in particular) exhibit notable nonlinear behavior, hence undermining that validity of MVAR-based GC (MVAR-GC) approaches. Current nonlinear approaches to GC estimation only cater for additive nonlinearities or, alternatively, are based on recurrent neural networks (RNN) or Long short-term memory (LSTM) networks, which present considerable training difficulties and/or the need to be carefully tailored to specific applications. We define a novel approach to estimating nonlinear, directed within-network interactions based on a specific class of RNNs termed echo-state networks (ESN), where training is replaced by random initialization and the internal basis is built through orthonormal matrices. We reformulate the classical GC framework in terms of ESN-based models for arbitrarily complex networks, and characterize the ability of our ESN-based Granger Causality (ES-GC) estimator to capture nonlinear causal relations in a network of noisy Duffing oscillators, showing a net advantage of ES-GC in detecting nonlinear, causal links. We then explore the structure of ES-GC networks in the human brain employing functional MRI data from 1003 healthy subjects scanned at rest at 3T within the human connectome project, demonstrating the existence of previously unknown directed within-brain interactions. In summary, ES-GC performs better than commonly used and recently developed GC detection approaches, making it a valuable tool for the analysis of e.g. multivariate biological networks.

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A fuzzy sensitivity analysis approach to estimate brain effective connectivity and its application to epileptic seizure detection

Moharamzadeh

Nasrabadi

2021

Biomedical Engineering / Biomedizinische Technik

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The brain is considered to be the most complicated organ in human body. Inferring and quantification of effective (causal) connectivity among regions of the brain is an important step in characterization of its complicated functions. The proposed method is comprised of modeling multivariate time series with Adaptive Neurofuzzy Inference System (ANFIS) and carrying out a sensitivity analysis using Fuzzy network parameters as a new approach to introduce a connectivity measure for detecting causal interactions between interactive input time series. The results of simulations indicate that this method is successful in detecting causal connectivity. After validating the performance of the proposed method on synthetic linear and nonlinear interconnected time series, it is applied to epileptic intracranial Electroencephalography (EEG) signals. The result of applying the proposed method on Freiburg epileptic intracranial EEG data recorded during seizure shows that the proposed method is capable of discriminating between the seizure and non-seizure states of the brain.

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Neural Networks for Modeling Granger Causality

Cited by 3 publications

References 39 publications

Echo state network models for nonlinear Granger causality

Echo state network models for nonlinear Granger causality

Echo State Network models for nonlinear Granger causality

A fuzzy sensitivity analysis approach to estimate brain effective connectivity and its application to epileptic seizure detection

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