Transfer entropy (TE) captures the directed relationships between two variables. Partial transfer entropy (PTE) accounts for the presence of all confounding variables of a multivariate system and infers only about direct causality. However, the computation of partial transfer entropy involves high dimensional distributions and thus may not be robust in case of many variables. In this work, different variants of the partial transfer entropy are introduced, by building a reduced number of confounding variables based on different scenarios in terms of their interrelationships with the driving or response variable. Connectivity-based PTE variants utilizing the random forests (RF) methodology are evaluated on synthetic time series. The empirical findings indicate the superiority of the suggested variants over transfer entropy and partial transfer entropy, especially in the case of high dimensional systems. The above findings are further highlighted when applying the causality measures on financial time series.

中文翻译：

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转移熵和部分转移熵的缺点：扩展它们以逃避维度的诅咒

转移熵 (TE) 捕获两个变量之间的有向关系。部分转移熵 (PTE) 解释了多元系统中所有混杂变量的存在，并且仅推断直接因果关系。然而，部分转移熵的计算涉及高维分布，因此在变量很多的情况下可能不稳健。在这项工作中，通过根据不同场景在与驱动或响应变量的相互关系方面构建减少数量的混杂变量，引入了部分转移熵的不同变体。使用随机森林 (RF) 方法的基于连接的 PTE 变体在合成时间序列上进行评估。实证结果表明，建议的变体优于转移熵和部分转移熵，尤其是在高维系统的情况下。在对金融时间序列应用因果关系度量时，上述发现得到了进一步的强调。