Causal decomposition in the mutual causation system

Abstract

Inference of causality in time series has been principally based on the prediction paradigm. Nonetheless, the predictive causality approach may underestimate the simultaneous and reciprocal nature of causal interactions observed in real-world phenomena. Here, we present a causal-decomposition approach that is not based on prediction, but based on the covariation of cause and effect: cause is that which put, the effect follows; and removed, the effect is removed. Using empirical mode decomposition, we show that causal interaction is encoded in instantaneous phase dependency at a specific time scale, and this phase dependency is diminished when the causal-related intrinsic component is removed from the effect. Furthermore, we demonstrate the generic applicability of our method to both stochastic and deterministic systems, and show the consistency of causal-decomposition method compared to existing methods, and finally uncover the key mode of causal interactions in both modelled and actual predator–prey systems.

Activation of cannabinoid type 1 receptors decreases the synchronization of local field potential oscillations in the hippocampus and entorhinal cortex and prolongs the interresponse time during a differential‐reinforcement‐of‐low‐rate task

“…The causal influence between the CA1 and the MEC (Figure 1d) was analyzed by the causal decomposition developed by Yang, Peng, and Huang (2018). Causal decomposition measures the causality of two time samples by analyzing their instantaneous phase dependency.…”

“…Causal decomposition measures the causality of two time samples by analyzing their instantaneous phase dependency. It is shown to be more accurate for nonlinear stochastic systems or mutual causation systems (Yang et al., 2018). Traditional causality analysis methods such as the Granger causality (Granger, 1969) or the convergent cross‐mapping method (Sugihara et al., 2012) measure whether the history of variable A may predict the value of variable B.…”

“…They calculate the time dependency (Granger causality) (Granger, 1969) or state dependency (convergent cross‐mapping) (Sugihara et al., 2012) between the variables. These methods were relatively difficult to implement in mutual causation systems (Yang et al., 2018). In contrast, causal decomposition uses the ensemble empirical mode decomposition (Huang et al., 1998; Wu & Huang, 2009; Wu, Huang, Long, & Peng, 2007) to decompose the LFP pairs (in our case, LFPs from CA1 and MEC) into a finite number of intrinsic mode functions, and then calculates the phase coherence values between the intrinsic mode functions.…”

“…Therefore, causal decomposition can be applied to analyzing the causal interaction between the CA1 and the MEC. The MATLAB codes of causal decomposition from the original article were downloaded here: https://github.com/accyang/causal-decomposition-analysis (Yang et al., 2018). We considered the LFP that was 1 s previous to lever‐pressing response to be the unit of analysis.…”

Causality Detection Methods Applied to the Investigation of Malaria Epidemics

“…This paper intends to bring to bear a series of methods from this family of time series analysis for causality and to show their efficacy in exploring the linkage between malaria epidemics and climate factors. The methods used are the kernel Granger causality [ 15 , 16 , 17 ], transfer entropy [ 18 , 19 ], recurrence plots [ 20 ], causal decomposition [ 21 ] and complex networks [ 22 ]. The deployment of multiple methods based on independent numerical procedures and providing coherent results, increase significantly the confidence in the conclusions.…”