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：本文提出了一种因果发现方法，用于在存在相关高斯误差（由混杂因素引起）的有向无环图中学习非线性关系。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，该方法包含去除混杂效应的去混杂调整步骤，以及用于估计变量因果顺序的序贯程序。我们通过前馈神经网络实现DeFuSE以实现可扩展计算，并在强因果极小性假设下建立了DeFuSE的一致性。在仿真实验中，DeFuSE相较于忽略混杂或非线性的现有最优方法展现出显著优势。最后，我们通过基因调控网络分析的应用案例验证了所提方法的实用性与有效性。Python实现代码见https://github.com/chunlinli/defuse。