Sample Dependence-Aware Blind Source Separation for Linear Causal Discovery

Abstract

Causal discovery seeks to determine directional relationships among variables in complex systems, yet observational data alone generally do not identify causal direction. Complete identification therefore requires assumptions beyond linearity and acyclicity. A key approach is the Linear Non-Gaussian Acyclic Model (LiNGAM), which formulates linear structural equation model estimation as a blind source separation (BSS) problem. LiNGAM treats disturbances as mutually independent random variables under independent sampling, relying on higher-order statistics (HOS) and non-Gaussianity for identifiability. This restricts identifiability when multiple disturbances are Gaussian and ignores potentially informative temporal dependence. To broaden causal identifiability, we formulate linear acyclic causal discovery with mutually independent disturbance processes and transfer established BSS identification conditions to causal structure recovery. Under this formulation, replacing the mutual information cost with mutual information rate enables identification under a broader class of disturbances, including Gaussian processes with nonproportional covariance functions. Synthetic experiments reveal the limitations of methods relying solely on HOS or sample dependence, while their joint exploitation provides near-perfect causal recovery across the tested disturbance settings. Experiments on real functional magnetic resonance imaging (fMRI) data further demonstrate that jointly exploiting HOS and sample dependence improves the bootstrap stability of estimated ancestral directionality.