On the Role of Entropy-Based Loss for Learning Causal Structure With Continuous Optimization

Area of Science:

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

Background:

• Causal discovery from observational data is crucial but challenging across scientific disciplines.
• Existing methods often rely on least-square loss, assuming Gaussian noise, which limits applicability.
• Violation of Gaussian noise assumption can impede accurate causal direction identification.

Purpose of the Study:

• To theoretically analyze the impact of non-Gaussian noise on causal discovery.
• To propose a more general and robust loss function for causal structure learning.
• To enhance causal direction identification irrespective of noise distribution.

Main Methods:

• Theoretical analysis of causal orientation under non-Gaussian noise assumptions.
• Development of a novel entropy-based loss function for continuous optimization.
• Algebraic characterization of directed acyclic graphs (DAGs) for structure learning.

Main Results:

• Demonstrated that non-Gaussian noise significantly affects causal direction identification.
• Proposed entropy-based loss is theoretically consistent across various noise distributions.
• Empirical evaluations show superior performance in structure Hamming distance, FDR, and TPR.

Conclusions:

• The proposed entropy-based loss function offers a more general solution for causal discovery.
• This method overcomes limitations of least-square loss under non-Gaussian noise.
• The approach is validated on synthetic and real-world data, showing robust performance.