The Blessing of Linear Non-Gaussian Models: Powerful Independent Subspace Inference for Latent-Variable Causal Discovery

The linear non-Gaussian model is a classical parametric model for causal discovery, known for its strong identifiability. A key ingredient underlying such identifiability is independence induced by linear transformations. For example, given two random vectors $\mathbf{X}$ and $\mathbf{Z}$, one may seek a transformation ${\omega }^{\top }\mathbf{X}$ such that ${\omega }^{\top }\mathbf{X}\perp \mathbf{Z}$, where $\omega$ may arise from linear regression or more general constructions. In the presence of latent confounders, two established tools, generalized independent noise (GIN) and transformed independent noise (TIN), exploit such constraints to characterize independent linear transformations. Despite their success in causal identification, existing implementations do not fully exploit the statistical structure of linear non-Gaussian models, which may compromise the reliability of causal identification. To address this issue, building on the characterization of independence through constant conditional means and variances, we construct a fixed linear operator whose kernel exactly characterizes all independent directions, enabling unified estimation and testing using only low-order information. We develop a paired-bootstrap GIN test with pointwise asymptotic Type I error control and a jointly calibrated TIN rank estimator. Synthetic and real-world experiments across several settings show gains in GIN testing power, TIN dimension recovery, and downstream latent-variable causal discovery.