Detecting and tracking time-varying causality with applications to EEG data

This paper introduces a novel method called the ERR-Causality, or Error Reduction Ratio Causality test, that can be used to detect and track causal relationships between two signals using a new adaptive forward orthogonal least squares (Adaptive-Forward-OLS) algorithm. In comparison to the traditional Granger method, one advantage of the new ERR-Causality test is that it can effectively detect the time-varying direction of linear or nonlinear causality between two signals without fitting a complete model. Another important advantage is that the ERR-Causality test can detect both the direction of interactions and estimate the relative time shift between the two signals. Several numerical examples are provided to illustrate the effectiveness of the new method for causal relationship detection between two signals. An important real application, relating to the analysis of the causality of EEG signals from different cortical sites which can be very useful for understanding brain activity during an epileptic seizure by inspecting the high-resolution time varying directed information flow, is also discussed

A parametric time frequency-conditional Granger causality method using ultra-regularized orthogonal least squares and multiwavelets for dynamic connectivity analysis in EEGs

Objective: This study proposes a new para-metric TF-CGC (time-frequency conditional Granger causality) method for high-precision connectivity analysis over time and frequency domain in multivariate coupling nonstationary systems, and applies it to source EEG signals to reveal dynamic interaction patterns in oscillatory neo-cortical sensorimotor networks. Methods: The Geweke's spectral measure is combined with the TVARX (time-varying autoregressive with exogenous input) model-ling approach, which uses multiwavelet-based ul-tra-regularized orthogonal least squares (UROLS) algo-rithm aided by APRESS (adjustable prediction error sum of squares), to obtain high-resolution time-varying CGC representations. The UROLS-APRESS algorithm, which adopts both the regularization technique and the ultra-least squares criterion to measure not only the signal themselves but also the weak derivatives of them, is a novel powerful method in constructing time-varying models with good generalization performance, and can accurately track smooth and fast changing causalities. The generalized measurement based on CGC decomposition is able to eliminate indirect influences in multivariate systems. Re-sults: The proposed method is validated on two simulations and then applied to source level motor imagery (MI) EEGs, where the predicted distributions are well recovered with high TF precision, and the detected connectivity patterns of MI-EEGs are physiologically interpretable and yield new insights into the dynamical organization of oscillatory cor-tical networks. Conclusion: Experimental results confirm the effectiveness of the TF-CGC method in tracking rapidly varying causalities of EEG-based oscillatory networks. Significance: The novel TF-CGC method is expected to provide important information of neural mechanisms of perception and cognition

Supervised estimation of Granger-based causality between time series

Brain effective connectivity aims to detect causal interactions between distinct brain units and it is typically studied through the analysis of direct measurements of the neural activity, e.g., magneto/electroencephalography (M/EEG) signals. The literature on methods for causal inference is vast. It includes model-based methods in which a generative model of the data is assumed and model-free methods that directly infer causality from the probability distribution of the underlying stochastic process. Here, we firstly focus on the model-based methods developed from the Granger criterion of causality, which assumes the autoregressive model of the data. Secondly, we introduce a new perspective, that looks at the problem in a way that is typical of the machine learning literature. Then, we formulate the problem of causality detection as a supervised learning task, by proposing a classification-based approach. A classifier is trained to identify causal interactions between time series for the chosen model and by means of a proposed feature space. In this paper, we are interested in comparing this classification-based approach with the standard Geweke measure of causality in the time domain, through simulation study. Thus, we customized our approach to the case of a MAR model and designed a feature space which contains causality measures based on the idea of precedence and predictability in time. Two variations of the supervised method are proposed and compared to a standard Granger causal analysis method. The results of the simulations show that the supervised method outperforms the standard approach, in particular it is more robust to noise. As evidence of the efficacy of the proposed method, we report the details of our submission to the causality detection competition of Biomag2014, where the proposed method reached the 2nd place. Moreover, as empirical application, we applied the supervised approach on a dataset of neural recordings of rats obtaining an important reduction in the false positive rate