Abstract
Causality detection likely misidentifies indirect causations as direct ones, due to the effect of causation transitivity. Although several methods in traditional frameworks have been proposed to avoid such misinterpretations, there still is a lack of feasible methods for identifying direct causations from indirect ones in the challenging situation where the variables of the underlying dynamical system are non-separable and weakly or moderately interacting. Here, we solve this problem by developing a data-based, model-independent method of partial cross mapping based on an articulated integration of three tools from nonlinear dynamics and statistics: phase-space reconstruction, mutual cross mapping, and partial correlation. We demonstrate our method by using data from different representative models and real-world systems. As direct causations are keys to the fundamental underpinnings of a variety of complex dynamics, we anticipate our method to be indispensable in unlocking and deciphering the inner mechanisms of real systems in diverse disciplines from data.
Highlights
Causality detection likely misidentifies indirect causations as direct ones, due to the effect of causation transitivity
Identifying causal relations among the dynamical variables generating the time series provides a window through which the inner dynamics of the target system may be probed into, and a number of previous methods were developed, such as those based on the celebrated Granger causality[1,2,3,4,5], the entropy[6,7,8,9,10,11], the dynamical Bayesian inference[12,13,14,15], and the mutual cross mapping (MCM)[16,17,18,19,20,21], with applications to real-world systems[5,7,22,23,24,25,26,27,28,29,30,31]
If only two variables interact in one direction and the third one is isolated (Fig. 1a), the previous methods can be effective for identifying the direct causal link[16,17,18,19,20,21]
Summary
Causality detection likely misidentifies indirect causations as direct ones, due to the effect of causation transitivity. There were previous studies of significant advance in detecting direct causal links to reconstruct the underlying true causal network based on the concept of partial transfer entropy or its linear Gaussian version, the conditional Granger causality, which resulted in many successful data mining in related fields[32,33,34,35,36,37,38] Combining these methods with graphical models, recent studies further provided a visible and comprehensive description of causal relations among interested variables[36,38,39]. Because of its unprecedented ability to eliminate indirect causation, this method can be a powerful tool to understand and model complex dynamical systems
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