Efficient DAG selection and asymptotic theory for nonlinear SEMs

Develop efficient methods to select directed acyclic graph (DAG) structures for nonlinear structural equation models (SEMs) from observational data, and establish asymptotic theory for these methods analogous to the posterior DAG selection consistency proved in the linear SEM setting. The goal is to provide algorithms and theoretical guarantees that remain valid when the structural relationships are nonlinear.

Background

The paper establishes posterior DAG selection consistency for linear acyclic SEMs under general (Gaussian scale-mixture) error distributions using a Bayesian approach with a Laplace working likelihood. This advances identifiability and consistency beyond Gaussian models and allows mixtures of Gaussian and non-Gaussian errors.

Extending these guarantees to nonlinear SEMs is identified as an open direction. The authors note that accommodating nonlinearity with basis expansions typically requires the number of basis functions to grow with the sample size, which induces high-dimensional challenges even when the number of variables is fixed, creating new theoretical hurdles for consistent structure learning.