Causal discovery under mean independence and linearity
For researchers and practitioners in causal inference, LiMIAM relaxes a key assumption of LiNGAM, making causal discovery more robust to common forms of noise dependence.
LiMIAM replaces the fragile independence assumption in causal discovery with weaker mean-independence restrictions, enabling correct causal order recovery under dependent noise. DirectLiMIAM outperforms LiNGAM in simulations and recovers a realistic causal ordering in an oil market application.
Causal discovery methods such as LiNGAM identify causal structure from observational data by assuming mutually independent disturbances. This assumption is fragile: shared volatility, common scale effects, or other forms of dependence can cause the methods to recover the wrong causal order, even with infinite data. We introduce the Linear Mean-Independent Acyclic Model (LiMIAM), which replaces full independence with weaker one-sided mean-independence restrictions on the disturbances. Under finite-order consequences of these restrictions, source nodes are generically identifiable, and hence a compatible causal order can be recovered recursively. Our proof is constructive and leads to DirectLiMIAM, a sequential residual-based algorithm for causal discovery under dependent noise. In simulations with mean-independent but dependent disturbances, DirectLiMIAM outperforms LiNGAM methods. A large-scale empirical application to the oil market highlights the implausibility of the independence assumption and the ability of DirectLiMIAM to recover a realistic causal ordering, from policy to production and from prices to inflation.