Causal discovery from observational data is an important but challenging task in many scientific fields. Recently, NOTEARS [Zheng et al., 2018] formulates the causal structure learning problem as a continuous optimization problem using least-square loss with an acyclicity constraint. 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 the noises of strong non-Gaussianity 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.
翻译:从观测数据中得出的因果发现在许多科学领域是一项重要但具有挑战性的任务。最近,OntaRS[Zheng等人,2018年]将因果结构学习问题作为连续优化问题,使用最不平方的损失,并带有周期性限制。虽然根据标准的高斯噪音假设,最平方的损失功能是完全合理的,但如果这一假设不成立,则其范围有限。在这项工作中,我们理论上表明,违反高斯噪音假设将阻碍因果关系的确定,使因果方向完全取决于因果强度以及线性情况中噪音的差异和非线性情况中强烈的非毛利性噪音的噪音。因此,我们提出了一个在理论上与任何噪音分布下可能得分相一致的更一般性的基于酶损失。我们对合成数据和真实世界数据进行了广泛的经验评估,以证实拟议方法的有效性,并表明我们的方法在结构上取得了最佳的成形距离、虚变异率和真实正正正率矩阵。