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On the Parameter Identifiability of Partially Observed Linear Causal Models
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Studies parameter identifiability of linear Gaussian causal models with latent variables given a known graph, derives sufficient and necessary graphical conditions, and proposes a likelihood-based estimator (gradient descent on Gaussian likelihood with LogDet) that recovers edge coefficients.
Problem
Whether edge coefficients of linear causal models can be recovered from partially observed data given the causal graph, when latent variables may be present and may be connected to each other and to observed variables.
Approach
Generalizes prior parameter identifiability work by allowing all variables (including latent ones) to have arbitrary edges among them, gives graphical sufficient conditions (with a provably necessary part) and a maximum-likelihood estimator that explicitly models latent variables, solved by gradient descent.
Key results
- Estimator-TR achieves restricted MSE of 0.008, 0.002, 0.001 at 2k, 5k, 10k samples on observed-only edges, versus GES at 0.41, 0.35, 0.35.
- Parameter estimation takes around 10 seconds, 2 minutes, and 10 minutes for graphs with 20, 50, and 100 variables.
- For graphs without latent variables, estimates are nearly identical to GES at 5k and 10k samples.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| explicitly model latent variables rather than use a method that does not allow latent variables | Estimator-TR vs GES · Observed-edge restricted, 2k, 5k, and 10k samples | MSE: 0.41 -> 0.008; 0.35 -> 0.002; 0.35 -> 0.001 | Helped |
Surprising findings
- Edges among observed variables can be wrongly estimated by methods ignoring latent variables, since latent confounders bias their coefficients even when restricted to observed edges.
Limitations
- Sufficient condition is not necessary and sufficient; some identifiable cases fall outside the graphical condition.
- Group sign indeterminacy means signs of some coefficients can flip unless anchored by prior knowledge.
- Identifiability holds only generically (Lebesgue measure zero exceptions), and structure is assumed given.
Experimental setup
Datasets: synthetic linear Gaussian graphs Big Five personality questionnaire data
Benchmarks: synthetic graphs with 20, 50, 100 variables
Metrics: MSE of edge coefficients MSE up to orthogonal transformation runtime
Baselines: GES Estimator-TR
Builds on: NOTEARS generic identifiability of linear structural equation models
Closest papers by meaning
- Identification of Partially Observed Linear Causal Models: Graphical Conditions for the Non-Gaussian and Heterogeneous Cases (NeurIPS 2021 · 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 0.89)
- Causal Effect Identification in LiNGAM Models with Latent Confounders (ICML 2024 · similarity 0.89)
- Identifying Causal Effects Under Functional Dependencies (NeurIPS 2024 · similarity 0.89)
- Tight Partial Identification of Causal Effects with Marginal Distribution of Unmeasured Confounders (ICML 2024 · similarity 0.89)
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