🤖 AI Summary
This paper addresses causal structure learning for nonlinear directed acyclic graphs (DAGs) under latent confounding with Gaussian noise. We propose DeFuSE: a two-stage method that first performs deconfounding correction to mitigate latent-variable bias, then jointly estimates the causal ordering and nonlinear functional relationships via a sequential neural network architecture. Key contributions include: (i) the first identifiability result for latent confounding in nonlinear DAG models; (ii) introduction of a sublinear growth assumption to ensure model identifiability; and (iii) formulation of a strong causal minimality condition, with theoretical proof of estimation consistency. Implemented using feedforward neural networks, DeFuSE balances scalability with rigorous statistical guarantees. Experiments demonstrate substantial improvements over state-of-the-art methods that either ignore confounding or assume linearity, on both synthetic benchmarks and real-world gene regulatory network inference. An open-source Python implementation is publicly available.
📝 Abstract
Abstract 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. Supplementary materials for this article are available online.
