Characterize when variance stratification suffices for cumulant-based causal ordering

Determine when variance stratification suffices for reliable causal ordering by the federated and centralized cumulant-based LiNGAM estimators.

Background

The paper shows that FedRCD, FedISHC, FedHC, HC, and HC-LiNGAM can rank variables primarily through a variance ladder induced by directed paths in the DAG rather than through the population asymmetry encoded by higher-order cumulants. This behavior is called variance stratification and is closely related to varsortability in scale-dependent causal discovery methods.

The authors leave unresolved the conditions under which this stratification signal is sufficient for accurate causal ordering. In particular, the paper does not characterize how the result depends on graph structure, noise distributions, edge weights, sample size, or the degree of variance monotonicity along directed paths.