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:本文引入了一种因果发现方法, 用于在定向循环图中学习非线性关系, 与相关Gaussian错误因混为一谈而发生。 首先, 我们在亚线性增长假设下得出模型可识别性。 然后, 我们提出了一个新颖的方法, 名为“ 分解功能结构估计( DeFuse) ”, 名为“ 分解功能结构估计( DeFuse ), 由分解调整法组成, 以消除混杂效应, 并采用一个顺序程序来估计变量的因果关系。 我们通过 feedforward 神经网络实施 DeFuse, 以便进行可缩放的计算。 此外, 我们根据一个称为强因果最小性的假设, 将 DeFuse 建立一致性。 在模拟中, DeFuse 与忽略混杂或非线性的最新竞争者相比, 。 最后, 我们展示了拟议方法的实用性和有效性, 并应用基因管理网络分析。 Python 的落实情况可在 https://github.com/chunlinli/defuse.