Causalized convergent cross-mapping and its approximate equivalence with directed information in causality analysis

Area of Science:

• Complex Systems Science
• Neuroscience
• Information Theory

Background:

• Convergent cross-mapping (CCM) detects causality in deterministic systems, complementing Granger causality.
• Directed Information (DI) quantifies causal information flow from an information-theoretic standpoint.
• The relationship between CCM and DI in non-deterministic systems requires clarification.

Purpose of the Study:

• To investigate whether CCM measures Directed Information (DI) flow.
• To establish and validate the equivalence between causalized CCM (cCCM) and DI.
• To compare the robustness of cCCM and DI in causality detection.

Main Methods:

• Causalization of CCM to align with causality principles.
• Theoretical derivations for approximate equivalence between cCCM and DI under Gaussian variables.
• fMRI-based brain network analysis to validate findings.

Main Results:

• Established and validated the approximate equivalence of cCCM and DI for Gaussian variables.
• Demonstrated that cCCM is generally more robust than DI in causality detection.
• Showcased cCCM's advantage in overcoming probability estimation sensitivities inherent in DI.

Conclusions:

• CCM offers an alternative, robust method for evaluating DI.
• Causalized CCM (cCCM) is a potentially effective technique for identifying linear and nonlinear causal coupling.
• This approach is applicable to brain networks and other complex systems, regardless of their deterministic or random nature.