1 Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece.
2 Laboratory of Clinical Neurophysiology, Medical School, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece.
Int J Neural Syst. 2019 May;29(4):1850051. doi: 10.1142/S012906571850051X. Epub 2018 Oct 29.
The study of connectivity patterns of a system's variables, such as multi-channel electroencephalograms (EEG), is of utmost importance towards a better understanding of its internal evolutionary mechanisms. Here, the problem of estimating the connectivity network from multivariate time series in the presence of prominent unobserved variables is addressed. The causality measure of partial mutual information from mixed embedding (PMIME), designed to estimate direct lag-causal effects in the presence of many observed variables, is adapted to estimate also zero-lag effects, the so-called instantaneous causality. We term the proposed advanced method, PMIME0. The estimation of instantaneous causality by PMIME0 is a signature of the presence of hidden source in the observed system, as demonstrated analytically in a toy model. It is further demonstrated that the PMIME0 identifies the true instantaneous with great accuracy in a variety of high-dimensional dynamical systems. The method is applied to EEG data with epileptiform discharges (EDs), and the results imply a strong impact of unobserved confounders during the EDs. This finding comes as a possible explanation for the increased levels of causality during epileptic seizures estimated by some measures affected by the presence of a common source.
研究系统变量（如多通道脑电图（EEG））的连通模式对于更好地理解其内部演化机制至关重要。在这里，解决了在存在显著未观测变量的情况下从多变量时间序列估计连通性网络的问题。混合嵌入的偏互信息因果度量（PMIME）旨在估计存在许多观测变量时的直接滞后因果效应，也被用于估计零滞后效应，即所谓的瞬时因果关系。我们将提出的高级方法称为 PMIME0。PMIME0 对瞬时因果关系的估计是隐藏源在观测系统中存在的特征，这在一个玩具模型中进行了分析。进一步表明，PMIME0 在各种高维动力系统中能够非常准确地识别真实的瞬时。该方法应用于具有癫痫样放电（ED）的 EEG 数据，结果表明在 ED 期间未观察到的混杂因素具有很强的影响。这一发现可能解释了一些受共同源存在影响的因果度量在癫痫发作期间估计的因果关系增加的原因。
