A multivariate additive noise model for complete causal discovery.

Area of Science:

• Causal inference and machine learning
• Statistical modeling and data analysis

Background:

• Traditional bivariate models struggle with multivariate relationships and unmeasured external influences in causal discovery.
• Directed acyclic graphs (DAGs) represent causal relationships but often simplify complex, real-world phenomena.
• Existing methods may fail to capture multiple feature dependencies crucial for accurate causal models.

Purpose of the Study:

• To propose a multivariate additive noise model (MANM) for analyzing multi-nodal causal structures.
• To introduce novel criteria for causal independence and a causal influence factor (CIF) for improved causal discovery.
• To address limitations of bivariate models in capturing complex feature dependencies.

Main Methods:

• Development of the multivariate additive noise model (MANM).
• Introduction of causal independence criteria and causal influence factor (CIF) for qualitative and quantitative analysis.
• Verification of model identifiability for linear and non-linear causal relations using simulated and real-world datasets.

Main Results:

• MANM demonstrated superior performance compared to ICA-LiNGAM, GDS, and RESIT in causal discovery.
• The model effectively handles both Gaussian and non-Gaussian mixture models with correlated and uncorrelated features.
• MANM exhibits enhanced causal model construction ability, with fewer errors and accurate estimation of complex causal directions.

Conclusions:

• MANM offers a robust solution for multivariate causal discovery, outperforming existing methods.
• The proposed causal independence criteria and CIF enhance the accuracy and reliability of causal inference.
• MANM facilitates the construction of complete and accurate causal models even in complex feature sets.