Causal discovery in symmetric dynamic systems with convergent cross mapping

Area of Science:

• Complex Systems
• Time Series Analysis
• Nonlinear Dynamics

Background:

• Convergent cross mapping (CCM) is a method for inferring causality in time series.
• Symmetric chaotic attractors can cause CCM to incorrectly identify unidirectional causality.

Purpose of the Study:

• To address the limitations of CCM in detecting bidirectional causal relationships when chaotic attractors exhibit symmetry.
• To propose and validate a novel method for accurate causal inference in such scenarios.

Main Methods:

• A novel method based on k-means clustering is proposed.
• The method aims to recover the symmetry of the latent chaotic attractor.
• It discovers causal links without external variable information.

Main Results:

• The proposed method successfully recovers latent chaotic attractor symmetry.
• Accurate bidirectional causal links are identified, correcting CCM errors.
• Validation is performed on simulated and real-world time series data.

Conclusions:

• The novel k-means clustering-based method effectively overcomes CCM limitations caused by symmetric chaotic attractors.
• This approach enhances the reliability of causal discovery from time series data.
• It offers a robust solution for identifying true causal relationships in complex systems.