Robust Model-Free Identification of the Causal Networks Underlying Complex Nonlinear Systems

Area of Science:

• Network science
• Causal inference
• Dynamical systems

Background:

• Inferring causal networks from observational data is crucial across many scientific fields.
• Existing methods often require specific model assumptions or struggle with complex, nonlinear dynamics.
• Reconstructing accurate network structures, especially direct relationships, remains a significant challenge.

Purpose of the Study:

• To develop a universal and feasible model-free framework for uncovering direct causal relationships in networked systems.
• To introduce novel inference algorithms, Polynomial Conditional Granger Causality (PCGC) and sparse PCGC (SPCGC).
• To effectively distinguish direct interactions from indirect influences in nonlinear dynamical systems.

Main Methods:

• Developed a model-free framework that approximates system dynamics using polynomial functions.
• Introduced PCGC for nonlinear Granger causality analysis to identify direct interactions.
• Utilized Lasso optimization in SPCGC for dimension reduction prior to PCGC analysis.
• Integrated conditional variables to reconcile direct and indirect influences.

Main Results:

• Demonstrated the effectiveness of PCGC and SPCGC in inferring direct causal relationships from nonlinear dynamics.
• Verified the performance of the proposed methods on various classical dynamical systems.
• Showcased the framework's ability to handle complex systems without prior model knowledge.

Conclusions:

• The proposed model-free framework offers a promising approach for network reconstruction from observational data.
• PCGC and SPCGC provide effective tools for identifying direct causal links in systems with unknown models.
• This work offers guidance for data-driven modeling and causal discovery in complex dynamical systems.