Improved convergent cross mapping method for causal inference based on decomposition of the Lorenz trajectory

Area of Science:

• Complex systems analysis
• Nonlinear dynamics
• Causal inference

Background:

• Convergent Cross Mapping (CCM) is used for causality detection in dynamical systems.
• Traditional CCM struggles to detect causality when reconstructed manifolds do not fully capture system dynamics, as seen with Lorenz equations.

Purpose of the Study:

• To address limitations of traditional CCM in detecting causal relationships.
• To propose and validate an improved CCM algorithm, LdCCM, for enhanced causal inference.

Main Methods:

• Developed the Local Dynamic Behavior-Consistent CCM (LdCCM) algorithm.
• Focused on selecting nearest neighbors to ensure consistent local dynamic behavior on reconstructed manifolds.
• Applied LdCCM to Lorenz equations and atmospheric observation data.

Main Results:

• LdCCM successfully detected causal influences of variables X and Y on Z in Lorenz equations, which traditional CCM failed to do.
• The LdCCM algorithm demonstrated significantly enhanced performance in identifying causal strength.
• Validated LdCCM's effectiveness and reliability on real-world atmospheric observation data.

Conclusions:

• LdCCM overcomes the limitations of traditional CCM by ensuring local dynamic consistency.
• The improved algorithm offers a more robust tool for causal discovery in complex systems.
• LdCCM shows promise for analyzing causality in various scientific domains, including climate science.