Papana Angeliki
Department of Economics, University of Macedonia, 54006 Thessaloniki, Greece.
Entropy (Basel). 2020 Jul 6;22(7):745. doi: 10.3390/e22070745.
Information causality measures have proven to be very effective in uncovering the connectivity patterns of multivariate systems. The non-uniform embedding (NUE) scheme has been developed to address the "curse of dimensionality", since the estimation relies on high-dimensional conditional mutual information (CMI) terms. Although the NUE scheme is a dimension reduction technique, the estimation of high-dimensional CMIs is still required. A possible solution is the utilization of low-dimensional approximation (LA) methods for the computation of CMIs. In this study, we aim to provide useful insights regarding the effectiveness of causality measures that rely on NUE and/or on LA methods. In a comparative study, three causality detection methods are evaluated, namely partial transfer entropy (PTE) defined using uniform embedding, PTE using the NUE scheme (PTENUE), and PTE utilizing both NUE and an LA method (LATE). Results from simulations on well known coupled systems suggest the superiority of PTENUE over the other two measures in identifying the true causal effects, having also the least computational cost. The effectiveness of PTENUE is also demonstrated in a real application, where insights are presented regarding the leading forces in financial data.
信息因果性度量已被证明在揭示多元系统的连接模式方面非常有效。由于估计依赖于高维条件互信息（CMI）项，因此开发了非均匀嵌入（NUE）方案来解决“维数灾难”问题。尽管NUE方案是一种降维技术，但仍需要估计高维CMI。一种可能的解决方案是利用低维近似（LA）方法来计算CMI。在本研究中，我们旨在提供有关依赖于NUE和/或LA方法的因果性度量有效性的有用见解。在一项比较研究中，评估了三种因果性检测方法，即使用均匀嵌入定义的部分转移熵（PTE）、使用NUE方案的PTE（PTENUE）以及同时使用NUE和LA方法的PTE（LATE）。在著名耦合系统上的模拟结果表明，PTENUE在识别真实因果效应方面优于其他两种度量，并且计算成本最低。PTENUE的有效性也在一个实际应用中得到了证明，其中展示了有关金融数据中主导力量的见解。
