Nonlinear Causal Discovery with Confounders

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