Latent Variable Causal Discovery under Selection Bias
This addresses an underexplored issue in causal inference for researchers dealing with biased data, though it is incremental as it adapts existing rank constraint methods to a new context.
The paper tackled the problem of latent variable causal discovery under selection bias by developing rank constraints as a statistical tool, demonstrating that the one-factor model can be identified under such bias with effectiveness confirmed in simulations and real-world experiments.
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.