Parameter identification in linear non-Gaussian causal models under general confounding

TL;DR

This paper develops a graphical criterion for determining the identifiability of causal effects in linear non-Gaussian models with arbitrary confounding, including non-linear latent variables and feedback loops.

Contribution

It introduces a necessary and sufficient graphical criterion for generic identifiability in complex latent variable models with an efficient algorithm.

Findings

Graphical criterion for causal effect identifiability

Polynomial-time algorithm for the criterion

Estimation heuristics and model generalizations

Abstract

Linear non-Gaussian causal models postulate that each random variable is a linear function of parent variables and non-Gaussian exogenous error terms. We study identification of the linear coefficients when such models contain latent variables. Our focus is on the commonly studied acyclic setting, where each model corresponds to a directed acyclic graph (DAG). For this case, prior literature has demonstrated that connections to overcomplete independent component analysis yield effective criteria to decide parameter identifiability in latent variable models. However, this connection is based on the assumption that the observed variables linearly depend on the latent variables. Departing from this assumption, we treat models that allow for arbitrary non-linear latent confounding. Our main result is a graphical criterion that is necessary and sufficient for deciding the generic identifiability of direct causal effects. Moreover, we provide an algorithmic implementation of the criterion with a run time that is polynomial in the number of observed variables. Finally, we report on estimation heuristics based on the identification result and explore a generalization to models with feedback loops.