Tree-based additive noise directed acyclic graphical models for nonlinear causal discovery with interactions.

Area of Science:

• Causal Inference
• Machine Learning
• Systems Biology

Background:

• Directed acyclic graphical models with additive noise are crucial for nonlinear causal discovery.
• Existing models often restrict causal functions to be additive, limiting their applicability in the presence of causal interactions.
• Current methods for general nonlinear causal functions can be computationally intensive or lack interpretability.

Purpose of the Study:

• To propose a novel, interpretable, and computationally feasible approach for nonlinear causal discovery that incorporates interactions.
• To develop tree-based additive noise models (TANM) that handle complex causal relationships effectively.
• To establish new identifiability conditions and algorithms for TANMs.

Main Methods:

• Development of tree-based additive noise models (TANM) to represent nonlinear causal functions with interactions.
• Derivation of new causal identifiability conditions specific to piecewise constant causal functions generated by tree structures.
• Implementation of a recursive algorithm for source node identification and a score-based ordering search algorithm.

Main Results:

• Demonstrated the utility and computational feasibility of TANMs through extensive simulations.
• Showcased superior performance of TANMs compared to existing additive noise models, particularly with strong causal interactions.
• Successfully applied the method to infer a protein-protein interaction network relevant to breast cancer.

Conclusions:

• Tree-based additive noise models offer a powerful and interpretable solution for nonlinear causal discovery with interactions.
• The proposed identifiability conditions and algorithms enable robust causal inference in complex systems.
• This approach has significant potential for applications in systems biology and other domains requiring causal network inference.