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Learning Linear Causal Representations from General Environments: Identifiability and Intrinsic Ambiguity
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Shows that linear causal representations learned from general (unrestricted) multi-environment data are identifiable up to surrounded-node ambiguity, proposes the LiNGCReL algorithm, and proves SNA is intrinsic even for non-parametric models with soft interventions.
Problem
Identifiability of latent causal graphs and unmixing functions from multi-environment observational data when interventions are general or soft rather than single-node hard interventions.
Approach
For linear non-Gaussian causal models with linear mixing, identifiability holds from general environments with no similarity constraints across environments, but latent variables are only recovered up to surrounded-node ambiguity; a LiNGAM-inspired orthogonal-projection algorithm (LiNGCReL) recovers the graph and unmixing up to this ambiguity, and SNA is shown unavoidable even with soft interventi
Key results
- LiNGCReL recovers the ground-truth causal graph in about 80% of sampled models within each category (d=5, 8, 10).
- Median average SNA error across latent variables is below 1% in the experiments.
- For nodes with nonempty surrounding set, the true error is much larger than the SNA error, consistent with the predicted ambiguity.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use LiNGCReL to learn the causal graph and latent variables from multiple environments | Random causal models, d=5, 8, 10 · Random causal models, d=5, 8, 10 | graph recovery accuracy: about 80% | Helped |
| Use LiNGCReL to learn latent variables up to surrounded-node ambiguity | Random causal models, d=5, 8, 10 · Random causal models, d=5, 8, 10 | median average SNA error: smaller than 1% | Helped |
| Increase the number of environments from K=d to K=20 while fixing the total number of samples | LiNGCReL · Random causal models, d=5 | performance | No clear effect |
| Set the threshold tl to 0.15 (ablation) | LiNGCReL · Random causal models, d=5, K=5 | SNA error and graph recovery accuracy | Helped |
Surprising findings
- Diversity of environments helps: Theta(d^2) single-node interventions are necessary and sufficient for identification up to SNA, and general environments give identifiability where single-node interventions were assumed.
- Even with single-node soft interventions on non-parametric models, SNA cannot be removed, so soft interventions are strictly weaker than hard ones.
Limitations
- Identification is only up to surrounded-node ambiguity, so latent variables are not fully recovered.
- Theory and algorithm assume linear causal models with linear mixing and non-Gaussian independent noise; the non-parametric result requires soft interventions with non-degeneracy conditions.
- Algorithm is described for the infinite-sample regime; finite-sample rank estimation requires a sensitive tolerance hyperparameter.
Experimental setup
Datasets: synthetic linear causal models with generalized Gaussian noise
Benchmarks: synthetic randomly generated linear causal models (d=5, 8, 10)
Metrics: graph recovery accuracy SNA error true error
Builds on: LiNGAM surrounded-node ambiguity (SNA) transitive-closure identifiability for soft interventions
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