On the Role of Entropy-based Loss for Learning Causal Structures with Continuous Optimization
This work improves causal structure learning for scientific fields by providing a more robust method that handles non-Gaussian noise, though it is incremental as it builds on the NOTEARS framework.
The authors tackled the problem of causal discovery from observational data by addressing the limitation of existing methods that rely on Gaussian noise assumptions, proposing an entropy-based loss function that works under any noise distribution and achieving the best performance in Structure Hamming Distance, False Discovery Rate, and True Positive Rate metrics.
Causal discovery from observational data is an important but challenging task in many scientific fields. Recently, a method with non-combinatorial directed acyclic constraint, called NOTEARS, formulates the causal structure learning problem as a continuous optimization problem using least-square loss. Though the least-square loss function is well justified under the standard Gaussian noise assumption, it is limited if the assumption does not hold. In this work, we theoretically show that the violation of the Gaussian noise assumption will hinder the causal direction identification, making the causal orientation fully determined by the causal strength as well as the variances of noises in the linear case and by the strong non-Gaussian noises in the nonlinear case. Consequently, we propose a more general entropy-based loss that is theoretically consistent with the likelihood score under any noise distribution. We run extensive empirical evaluations on both synthetic data and real-world data to validate the effectiveness of the proposed method and show that our method achieves the best in Structure Hamming Distance, False Discovery Rate, and True Positive Rate matrices.