Causal discovery under mean independence and linearity

TL;DR

This paper introduces LiMIAM, a causal discovery model that relaxes the independence assumption to mean-independence, enabling more accurate causal inference in dependent noise scenarios.

Contribution

The paper proposes LiMIAM and DirectLiMIAM, novel methods for causal discovery under mean-independence, with proven identifiability and improved performance over existing methods.

Findings

DirectLiMIAM outperforms LiNGAM in simulations with dependent disturbances.

LiMIAM can recover causal orderings under weaker assumptions than traditional methods.

Application to the oil market demonstrates realistic causal inference from observational data.

Abstract

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.