Causal Discovery in Linear Models with Unobserved Variables and Measurement Error

TL;DR

This paper develops a method for causal discovery in linear models with unobserved variables and measurement error, providing conditions for identifiability and algorithms to recover causal structures.

Contribution

It introduces the LV-SEM-ME model, characterizes identifiability under certain conditions, and offers algorithms to recover causal structures despite unobserved variables and measurement errors.

Findings

Identifiability of causal models is characterized under a separability condition.

Graphical criteria for equivalence classes of models are provided.

Recovery algorithms enumerate all models in the equivalence class of the true model.

Abstract

The presence of unobserved common causes and measurement error poses two major obstacles to causal structure learning, since ignoring either source of complexity can induce spurious causal relations among variables of interest. We study causal structure learning in linear systems where both challenges may occur simultaneously. We introduce a causal model called LV-SEM-ME, which contains four types of variables: directly observed variables, variables that are not directly observed but are measured with error, the corresponding measurements, and variables that are neither observed nor measured. Under a separability condition-namely, identifiability of the mixing matrix associated with the exogenous noise terms of the observed variables-together with certain faithfulness assumptions, we characterize the extent of identifiability and the corresponding observational equivalence classes. We provide graphical characterizations of these equivalence classes and develop recovery algorithms that enumerate all models in the equivalence class of the ground truth. We also establish, via a four-node union model that subsumes instrumental variable, front-door, and negative-control-outcome settings, a form of identification robustness: the target effect remains identifiable in the broader LV-SEM-ME model even when the assumptions underlying the specialized identification formulas for the corresponding submodels need not all hold simultaneously.