Inferring Causality from Noisy Time Series Data - A Test of Convergent Cross-Mapping

Abstract

Abstract:Convergent Cross-Mapping (CCM) has shown high potential to perform causal inference in the absence of models. We assess the strengths and weaknesses of the method by varying coupling strength and noise levels in coupled logistic maps. We find that CCM fails to infer accurate coupling strength and even causality direction in synchronized time-series and in the presence of intermediate coupling. We find that the presence of noise deterministically reduces the level of cross-mapping fidelity, while the convergence rate exhibits higher levels of robustness. Finally, we propose that controlled noise injections in intermediate-to-strongly coupled systems could enable more accurate causal inferences. Given the inherent noisy nature of real-world systems, our findings enable a more accurate evaluation of CCM applicability and advance suggestions on how to overcome its weaknesses.

Multidimensional Recurrence Quantification Analysis (MdRQA) for the Analysis of Multidimensional Time-Series: A Software Implementation in MATLAB and Its Application to Group-Level Data in Joint Action

“…It is also not possible to test the specific influence that one component signal has on another over time as with convergent cross-mapping (Mønster et al, 2016b). Solutions to this problem could be comparisons of different MdRPs with and without the specific signal of interest, such as in Joint Recurrence Analysis (Romano et al, 2004), or investigating the effects of time-shifting individual signals systematically and comparing the resulting MdRPs (as has been suggested by Marwan et al (2007) for JRPs with two variables).…”

Modeling interaction as a complex system

“…In fact, the study of causality has brought forward a variety of statistical approaches aimed at this goal [30]. Such approaches are typically based on a combination of a model and corresponding measurements of the system [27]. However, as indicated by Mønster [27], in many cases such a model of the system is not available, or the multiple available models provide conflicting information -this is especially true in the field of complex natural, technical, and social systems.…”

Reverse-engineering biological networks from large data sets

“…First, it seems that the outcome is quite sensitive to the sampling methods used to obtain training data (for example, eliminating nonstationarity on the way to the attractor is key) [237]. Second, CCM fails to infer the accurate coupling strengths and even the direction of causal interaction when time series are synchronous [246]. Third, it has been shown that the predictions made by CCM do not always conform to our intuitive notions of causality, even for certain rudimentary systems like a simple resistorinductor (R-L) circuit with a sinusoidal driving voltage, where CCM does not unequivocally determine the causal dependence of the current on the voltage [244].…”

“…Indeed, Takens' original theorems allow for noise in the measurement procedure only (i. e., intrinsic stochasticity is prohibited; the breakdown of inference based on CCM in the presence of intrinsic noise has been demonstrated explicitly [244][245][246], and a thorough analysis of state space reconstruction in the presence of noise can be found in [241]). Nevertheless, artificially added measurement noise can actually improve the detection of causality [247].…”