Latent Variable Causal Discovery under Selection Bias

TL;DR

This paper introduces a novel approach using rank constraints in covariance matrices to address the challenge of causal discovery involving latent variables under selection bias, a previously underexplored area.

Contribution

It develops a graph-theoretic framework for rank constraints in linear Gaussian models, enabling identification of latent variable models under selection bias.

Findings

Rank constraints retain meaningful information despite selection bias.

The one-factor model can be identified under selection bias using these constraints.

Simulations and real-world data validate the approach.

Abstract

Addressing selection bias in latent variable causal discovery is important yet underexplored, largely due to a lack of suitable statistical tools: While various tools beyond basic conditional independencies have been developed to handle latent variables, none have been adapted for selection bias. We make an attempt by studying rank constraints, which, as a generalization to conditional independence constraints, exploits the ranks of covariance submatrices in linear Gaussian models. We show that although selection can significantly complicate the joint distribution, interestingly, the ranks in the biased covariance matrices still preserve meaningful information about both causal structures and selection mechanisms. We provide a graph-theoretic characterization of such rank constraints. Using this tool, we demonstrate that the one-factor model, a classical latent variable model, can be identified under selection bias. Simulations and real-world experiments confirm the effectiveness of using our rank constraints.