Nonlinear Causal Discovery with Confounders

Chunlin Li, Xiaotong Shen, Wei Pan

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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 Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)1205-1214
Number of pages10
JournalJournal of the American Statistical Association
Issue number546
StatePublished - 2024

Bibliographical note

Publisher Copyright:
© 2023 American Statistical Association.


  • Deconfounding
  • Directed acyclic graph
  • Gene regulatory networks
  • Neural networks
  • Variable selection


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