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A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variables
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Proposes RLCD, a three-phase rank-based causal discovery algorithm that identifies latent variables (including causally related ones) and the Markov equivalence class of linear latent causal graphs from covariance rank constraints.
Problem
Causal discovery from observed data when latent variables may be present almost anywhere in the causal graph (confounders, mediators, effects, hierarchical structures), including adjacency among observed variables, without strong graphical constraints.
Approach
Uses rank deficiency of sub-covariance matrices over observed variables (trek-separation) instead of conditional independence to detect nonadjacency and latent variables, with atomic covers as minimal identifiable units; RLCD locates latent variables and their cardinalities and recovers the Markov equivalence class under weaker graphical conditions.
Key results
- On synthetic latent-tree graphs with 10k samples, RLCD reaches skeleton F1 0.98 over all variables versus 0.60 for Hier. rank and 0.37 for PC.
- On latent general graphs with 10k samples, RLCD reaches F1 0.80 over all variables versus 0.45 for Hier. rank and 0.36 for RCD.
- On the Big Five data, RLCD recovers clusters largely matching the five personality dimensions, with latent variables L1-L6 and plausible indicator-level links.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use RLCD instead of Hier. rank | Latent causal discovery · Latent+tree, 10k samples | F1 score for skeleton among all variables: 0.60 (0.01) -> 0.98 (0.02) | Helped |
| Use RLCD instead of Hier. rank | Latent causal discovery · Latent+measurement, 10k samples | F1 score for skeleton among all variables: 0.53 (0.05) -> 0.91 (0.09) | Helped |
| Use RLCD instead of Hier. rank | Latent causal discovery · Latent general, 10k samples | F1 score for skeleton among all variables: 0.45 (0.04) -> 0.80 (0.05) | Helped |
| Use RLCD instead of PC | Latent causal discovery · Latent+tree, 10k samples | F1 score for skeleton among observed variables: 0.44 (0.00) -> 0.97 (0.04) | Helped |
| Use RLCD instead of PC | Latent causal discovery · Latent+measurement, 10k samples | F1 score for skeleton among observed variables: 0.48 (0.02) -> 0.95 (0.05) | Helped |
| Use RLCD instead of PC | Latent causal discovery · Latent general, 10k samples | F1 score for skeleton among observed variables: 0.45 (0.01) -> 0.78 (0.06) | Helped |
Limitations
- Cannot directly handle cyclic graphs
- Restricted to linear causal models
- Identifiability requires graphical conditions (basic condition, collider condition) and faithfulness
Experimental setup
Datasets: Big Five personality dataset (openpsychometrics.org, ~20,000 samples, 50 indicators)
Benchmarks: synthetic latent linear causal graphs Big Five personality dataset
Metrics: F1 score for skeleton among observed variables F1 score for skeleton among all variables
Baselines: Hier. rank PC FCI RCD GIN
Builds on: PC algorithm trek-separation theory Hierarchical rank method GIN
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