  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.
