Nonlinear Causal Discovery for High-Dimensional Deterministic Data.

Area of Science:

• Causal inference
• Machine learning
• Network analysis

Background:

• Causal discovery with high-dimensional, multidimensional data is crucial in fields like social network analysis.
• Existing methods often focus on pairwise causal relationships and lack theoretical validation for multiple variables.
• Violated model assumptions in pairwise methods can lead to incorrect causal ordering.

Purpose of the Study:

• To propose a novel causal functional model, the high-dimensional deterministic model (HDDM), for identifying causal orderings among multiple high-dimensional variables.
• To address limitations of existing methods concerning theoretical validation and assumption violations in multi-variable settings.

Main Methods:

• Developed the high-dimensional deterministic model (HDDM) for nonlinear causal discovery with multidimensional variables.
• Derived two candidate selection rules to mitigate issues arising from violated assumptions in causal pairs.
• Provided theoretical justifications for the proposed candidate selection rules.
• Developed a method for inferring causal orderings in nonlinear multiple-variable data.

Main Results:

• The proposed HDDM method successfully identifies causal orderings among multiple high-dimensional variables.
• Candidate selection rules effectively alleviate problems caused by violated assumptions in specific data pairs.
• Simulations on synthetic and real-world data confirm the method's efficacy.
• The method demonstrates robustness against noise in deterministic relations.

Conclusions:

• The HDDM provides a theoretically justified and practically effective approach for nonlinear causal discovery in high-dimensional, multi-variable settings.
• The method offers improved accuracy and robustness compared to existing techniques, particularly when dealing with complex data structures and potential assumption violations.