Discovery of causal relationships from observational data is an important problem in many areas. Several recent results have established the identifiability of causal DAGs with non-Gaussian and/or nonlinear structural equation models (SEMs). In this paper, we focus on nonlinear SEMs defined by non-invertible functions, which exist in many data domains, and propose a novel test for non-invertible bivariate causal models. We further develop a method to incorporate this test in structure learning of DAGs that contain both linear and nonlinear causal relations. By extensive numerical comparisons, we show that our algorithms outperform existing DAG learning methods in identifying causal graphical structures. We illustrate the practical application of our method in learning causal networks for combinatorial binding of transcription factors from ChIP-Seq data.

中文翻译：

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具有不可逆函数关系的因果网络学习

从观测数据中发现因果关系是许多领域的一个重要问题。最近的几个结果已经建立了具有非高斯和/或非线性结构方程模型 (SEM) 的因果 DAG 的可识别性。在本文中，我们关注由存在于许多数据域中的不可逆函数定义的非线性 SEM，并提出了一种对不可逆双变量因果模型的新测试。我们进一步开发了一种方法，将该测试纳入包含线性和非线性因果关系的 DAG 的结构学习中。通过广泛的数值比较，我们表明我们的算法在识别因果图形结构方面优于现有的 DAG 学习方法。