This article introduces a causal discovery method to learn nonlinear relationships in a directed acyclic graph with correlated Gaussian errors due to confounding. First, we derive model identifiability under the sublinear growth assumption. Then, we propose a novel method, named the Deconfounded Functional Structure Estimation (DeFuSE), consisting of a deconfounding adjustment to remove the confounding effects and a sequential procedure to estimate the causal order of variables. We implement DeFuSE via feedforward neural networks for scalable computation. Moreover, we establish the consistency of DeFuSE under an assumption called the strong causal minimality. In simulations, DeFuSE compares favorably against state-of-the-art competitors that ignore confounding or nonlinearity. Finally, we demonstrate the utility and effectiveness of the proposed approach with an application to gene regulatory network analysis. The Python implementation is available at https://github.com/chunlinli/defuse.

翻译：本文提出了一种在有向无环图中学习非线性关系的因果发现方法，该方法能够处理由混杂效应引起的相关高斯误差。首先，我们在次线性增长假设下推导了模型的可识别性。随后，我们提出了一种名为"去混杂函数结构估计（DeFuSE）"的新方法，该方法包含两个步骤：通过去混杂调整消除混杂效应，以及通过序贯过程估计变量的因果顺序。我们采用前馈神经网络实现DeFuSE以实现可扩展计算。进一步地，我们在强因果极小性假设下建立了DeFuSE的一致性。仿真实验表明，DeFuSE在性能上优于忽略混杂效应或非线性因素的现有最优方法。最后，我们通过基因调控网络分析的应用案例，展示了所提方法的实用性和有效性。Python代码实现见https://github.com/chunlinli/defuse。