Research map / Probabilistic and scientific modeling / Causal discovery
THE ROBUSTNESS OF DIFFERENTIABLE CAUSAL DISCOVERY IN MISSPECIFIED SCENARIOS
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Benchmarks twelve causal discovery methods (constraint-, score-, FCM-, and differentiable-based) on synthetic data under eight i.i.d./model-assumption violations and finds differentiable methods robust except under scale variation.
Problem
Causal discovery algorithms rely on unverifiable assumptions (faithfulness, causal sufficiency, i.i.d., equal noise, linearity), which real data often violate; it is unclear how robust mainstream methods, especially differentiable ones, are under such misspecification.
Approach
Large-scale empirical benchmark of 12 causal discovery methods across eight misspecified scenarios (latent confounders, measurement error, autoregressive, heterogeneity, scale variation, missing data, unfaithfulness, mechanism violation), with a theoretical explanation based on noise-variance ratio for linear least-squares methods.
Key results
- Under linear setting with 10-node ER-2 graphs, NOTEARS, DAGMA and GOLEM achieve near-best SHD in vanilla (1.2-1.5) and competitive SHD under confounding and heterogeneity, while PC/GES are worse.
- Under scale-variant data, linear differentiable methods such as NOTEARS degrade sharply (SHD 18.0 vs 1.5 vanilla), performing worse than PC and GES.
- In the nonlinear setting, DAGMA attains the best mechanism-violation SHD (3.3) versus CAM (17.8), showing CAM's advantage is tied to its Gaussian-process assumption.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use differentiable causal discovery methods instead of other benchmark methods | Linear causal discovery · Linear ER-2, 10 nodes, scale-variant | SHD | Hurt |
| Use differentiable causal discovery methods instead of other benchmark methods | Nonlinear causal discovery · Nonlinear ER-2, 10 nodes, scale-variant | SHD | Mixed |
| Use linear differentiable causal discovery methods | Linear causal discovery · Linear ER-2, 10 nodes, heterogeneous | SHD: 5.5 | Helped |
| Use linear differentiable causal discovery methods | Linear causal discovery · Linear ER-2, 10 nodes, missing | SHD: 1.5 | Helped |
| Use linear differentiable causal discovery methods | Linear causal discovery · Linear ER-2, 10 nodes, mechanism violation | SHD: 18.6 | Mixed |
| Use nonlinear differentiable causal discovery methods | Nonlinear causal discovery · Nonlinear ER-2, 10 nodes, mechanism violation | SHD: 5.9 -> 3.3 | Helped |
| Use NOTEARS-MLP instead of CAM | Causal discovery in MLP setting · MLP ER-2, 10 nodes, heterogeneous | SHD: 19.9 -> 14.5 | Helped |
| Use CAM instead of NOTEARS-MLP | Causal discovery in MLP setting · MLP ER-2, 10 nodes, scale-variant | SHD: 18.2 -> 12.4 | Helped |
Surprising findings
- Linear differentiable methods remain competitive under nonlinear mechanism violation, despite PC and GES handling nonlinearity.
- CAM, the best method in the nonlinear vanilla setting, performs poorly under mechanism violation.
Limitations
- Only non-temporal causal discovery methods are evaluated.
- Evaluation limited to synthetic data and a single real-world dataset (Sachs) in appendix.
- Scale-variant robustness for nonlinear differentiable methods is left unresolved.
Experimental setup
Datasets: synthetic ER and SF graphs with d in {10,20,50} Sachs (real-world, appendix)
Benchmarks: synthetic ER-2 and SF graphs under eight misspecified scenarios Sachs
Metrics: SHD SID
Baselines: PC GES DirectLiNGAM CAM Var-SortnRegress R2-SortnRegress NOTEARS GOLEM NOTEARS-MLP GraN-DAG NoCurl DAGMA
Builds on: NOTEARS DAGMA Var-Sortability GOLEM equal-variance theory
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