基于à trous小波变换的多尺度Granger因果分析
Multiscale Granger causality analysis by à trous wavelet transform
摘要：
由于神经系统中的相互作用发生在多个时间尺度上，信息流很可能会表现出多尺度结构，因此需要对经典的时间优先因果关系分析进行多尺度推广，如格兰杰方法。然而，信息动力学的多尺度度量的计算由于诸如滤波和欠采样等理论和实际问题而变得复杂：为了克服这些问题，我们提出了一种基于小波的多尺度Granger因果关系（GC）分析方法，其特征在于以下性质：（i）仅对候选驱动变量进行小波变换（ii）使用具有三次B样条滤波器的à trous小波变换来执行分解。我们测量GC，在一个给定的规模，包括小波系数的驱动程序时间序列，在该规模，在回归模型的目标。为了验证我们的方法，我们将其应用到公开可用的头皮EEG信号，我们发现，闭上眼睛，在休息的条件下，其特征在于在慢尺度w.r.t.通道之间的增强GC。睁眼条件下，而标准格兰杰因果关系在两种条件下没有显著差异。
英文摘要：
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 à 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.
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