On Low-Rank Directed Acyclic Graphs and Causal Structure Learning.

Area of Science:

• Causal Inference
• Machine Learning
• Network Science

Background:

• Learning causal structures from data is crucial but challenging in high-dimensional settings.
• Existing methods struggle with non-sparse directed acyclic graphs (DAGs).

Purpose of the Study:

• To propose and evaluate a novel approach for causal structure learning in DAGs by exploiting a low-rank assumption.
• To adapt existing causal discovery methods using low-rank techniques.

Main Methods:

• Utilized existing low-rank matrix factorization techniques.
• Adapted causal structure learning algorithms to incorporate the low-rank assumption.
• Established theoretical links between graphical properties and the low-rank assumption.

Main Results:

• Demonstrated that the maximum rank of a DAG is related to the presence of hubs.
• Showed that scale-free networks are often low-rank, validating the assumption.
• Experimental results confirm the utility of low-rank adaptations for large, dense graphs.

Conclusions:

• The proposed low-rank adaptations enhance causal structure learning, particularly for complex graph structures.
• The method maintains strong performance even when graphs deviate from strict low-rank properties, offering robustness.