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Causal Effect Identification in LiNGAM Models with Latent Confounders
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Gives necessary and sufficient graphical criteria for generic identifiability of total and direct causal effects in linear non-Gaussian latent-variable acyclic models (lvLiNGAM), with and without a known graph, plus polynomial-time certification and a graph-constrained RICA estimator.
Problem
Identifying which causal effects (direct or total) between observed variables can be uniquely recovered from observational data in linear non-Gaussian acyclic models with latent confounders, both when the causal graph is known and when it is unknown.
Approach
Derives complete graphical characterizations of generic identifiability of total and direct causal effects in lvLiNGAM by analyzing when column permutations of the mixing matrix preserve graph structure, yielding polynomial-time checkable criteria, and adapts RICA to estimate effects with the known graph restricting the parameterization to edges.
Key results
- Identification algorithms handle graphs with a thousand nodes in about a second.
- With known graph, all sampled random graphs' edge causal effects were identifiable in the experiments (500 graphs per setting).
- GRICA consistently recovers the direct causal effect with few samples and significantly outperforms RICA on larger Erdős-Rényi graphs (one latent/five observed; two latent/ten observed).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Graphical RICA instead of RICA | Causal effect estimation on G1 and G2 · G1 and G2, varying sample size | relative error | Helped |
| Use Cross-Moment instead of Graphical RICA | Causal effect estimation on G1 · G1, sufficiently many samples | relative error | Helped |
| Use RICA instead of Graphical RICA | Causal effect estimation on G1 and G2 · G1 and G2, varying sample size | relative error | Hurt |
| Use Graphical RICA instead of Cross-Moment | Causal effect estimation on G1 · G1, varying noise on W | relative error | No clear effect |
| Use Graphical RICA with a noiseless proxy observation of L1 | Causal effect estimation on G3 · G3, varying noise on W and Z | relative error | Helped |
| Add observation noise on W | Other algorithms evaluated on G3 · G3, varying noise on W and Z | relative error | Hurt |
| Use Graphical RICA instead of RICA | Mixing-matrix estimation on larger random graphs · Erdős–Rényi graphs with two latent and ten observed variables | normalized Frobenius loss | Helped |
Surprising findings
- Without knowledge of the graph, the total effect of T on Y in the instrumental variable graph is not identifiable, although it is with a known graph.
Limitations
- Assumes the number of latent variables is known.
- Results are generic identifiability (hold outside a measure-zero set), and estimator has no consistency guarantees.
- Restricted to linear models with non-Gaussian noise and acyclic graphs.
Experimental setup
Datasets: synthetic data from linear non-Gaussian latent variable models on Erdős-Rényi random graphs
Benchmarks: synthetic lvLiNGAM graphs G1, G2, G3 Erdős-Rényi random graphs
Metrics: probability of identifiability relative error normalized Frobenius loss run time
Baselines: RICA Cross-Moment method
Builds on: RICA overcomplete ICA identifiability (Salehkaleybar et al.) Gessel-Viennot-Lindström lemma
Closest papers by meaning
- Causal Effect Identification in lvLiNGAM from Higher-Order Cumulants (ICML 2025 · similarity 0.92)
- Identifiability Guarantees for Causal Disentanglement from Purely Observational Data (NeurIPS 2024 · similarity 0.90)
- Identifiable Latent Polynomial Causal Models through the Lens of Change (ICLR 2024 · similarity 0.90)
- Identifying Causal Effects Under Functional Dependencies (NeurIPS 2024 · similarity 0.89)
- On the Parameter Identifiability of Partially Observed Linear Causal Models (NeurIPS 2024 · similarity 0.89)
- Coarsening Linear Non-Gaussian Causal Models with Cycles (NeurIPS 2026 · similarity 0.89)
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