Nonlinear Causal Discovery with Confounders

TL;DR

This paper presents DeFuSE, a scalable neural network-based method for nonlinear causal discovery in the presence of confounders, with proven identifiability and consistency, demonstrated through simulations and gene network analysis.

Contribution

Introduction of DeFuSE, a novel method combining deconfounding and sequential estimation for nonlinear causal discovery with confounders, supported by theoretical guarantees.

Findings

DeFuSE outperforms existing methods in simulations.

DeFuSE accurately estimates causal order in nonlinear models.

Application to gene networks shows practical utility.

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.