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Latent Variable Causal Discovery under Selection Bias

ICML 2025 · Probabilistic and scientific modeling › Causal discovery · approach: Identifiability with hidden confounders · 0 citations (OpenAlex)

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Generalizes rank constraints (t-separation) to data subject to linear selection bias and uses them to identify one-factor latent causal structures under selection, with experiments on synthetic and World Value Survey / Big Five data.

Problem

Latent variable causal discovery is hard when data are subject to selection bias, because existing latent-variable tools (beyond CI constraints) assume random sampling and no tool beyond CI handles selection.

Approach

Shows that ranks of covariance submatrices in linear Gaussian models remain informative under linear selection mechanisms; gives a graphical criterion (t-separation on a selection-augmented graph with response nodes) for these generalized rank constraints and applies it to recover CIs among latent variables in the one-factor model, then runs FCI on them.

Key results

• On synthetic data with Gaussian errors, the proposed rank-based method yields fewer differing edge marks than FCI, PC and BOSS across 5-20 latent variables, with the gap widening as the number of variables grows.
• Applied to World Value Survey data for Canada, China and Germany, the method finds potential selection patterns (e.g., selection associated with Social Trust) and nation-specific selection.
• Theory shows the rank of selected covariance equals the rank of the selection-augmented covariance minus the number of selection variables, with a graphical t-separation criterion (Theorem 1).

Measured effects reported in the paper

Surprising findings

• Tetrad (latent) and inverse Tetrad (selection) structures produce identical rank patterns among four observed variables, so ranks alone cannot distinguish latent variables from selection bias in general.
• Some CI-equivalent graphs with selection and latent variables are distinguishable only via rank constraints.

Limitations

• A complete characterization of rank equivalence classes (analogous to MAGs) is not yet developed.
• Assumes linear Gaussian models with linear selection mechanisms; non-Gaussian X breaks the rank property.
• Requires known oracle clustering of measurements to latent variables in the one-factor model.

Experimental setup

Datasets: World Value Survey Big Five Personality dataset synthetic linear SEM data with truncated probit selection

Benchmarks: synthetic linear SEM graphs (5-20 latent variables) World Value Survey Big Five

Metrics: difference of edge marks between estimated and true PAG SHD of skeleton

Baselines: FCI PC BOSS

Builds on: rank constraints (Sullivant et al., 2010) t-separation FCI one-factor model (Silva et al., 2003)

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