Nonlinear causal discovery with confounders.

Area of Science:

• Causal inference
• Machine learning
• Bioinformatics

Background:

• Learning causal relationships from observational data is challenging due to confounding and nonlinearities.
• Existing methods often struggle with correlated Gaussian errors and complex functional dependencies.

Purpose of the Study:

• To introduce a novel causal discovery method, Deconfounded Functional Structure Estimation (DeFuSE), for learning nonlinear relationships in directed acyclic graphs.
• To address confounding effects and estimate the causal order of variables accurately.

Main Methods:

• Derivation of model identifiability under sublinear growth assumptions.
• Development of DeFuSE, incorporating a deconfounding adjustment and a sequential estimation procedure.
• Implementation of DeFuSE using feedforward neural networks for scalable computation.

Main Results:

• Established theoretical consistency of DeFuSE under the strong causal minimality assumption.
• Demonstrated superior performance of DeFuSE compared to state-of-the-art methods in simulations.
• Validated the method's effectiveness in analyzing gene regulatory networks.

Conclusions:

• DeFuSE provides a robust approach for causal discovery in the presence of confounding and nonlinear relationships.
• The method offers a scalable and effective solution for complex biological network analysis.
• The Python implementation facilitates broader adoption and further research.