Research map / Probabilistic and scientific modeling / Causal discovery
Stable Differentiable Causal Discovery
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Proposes SDCD, a two-stage differentiable causal discovery method that uses the spectral radius as a stable acyclicity constraint and an edge-preselection stage for sparse graphs, scaling to thousands of variables.
Problem
Differentiable causal discovery (DCD) for DAG structure learning is numerically unstable and scales poorly beyond tens of variables due to its acyclicity constraints.
Approach
Replaces power-series trace acyclicity penalties (NOTEARS exp, log-det, inverse) with the spectral radius constraint, proven E-, V- and D-stable and computable in O(d^2) via power iteration, and adds a stage-1 edge preselection (masking unlikely edges) before penalized DCD in stage 2.
Key results
- SDCD is the only method among those evaluated to scale above 200 variables with nontrivial SHD; runs under 15 minutes on GPU for d=500 and scales to 4,000 variables in under 2h45.
- DCDI crashes for d>40 and DAGMA fails to converge within 6 hours for as few as 30 variables, while SDCD achieves the best SHD at every scale on observational data.
- SDCD outperforms DCDI on all sparse DCDI datasets (s=1); it is worse only on d=10, s=4 graphs with edge density 88.9%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SDCD instead of existing methods | Causal discovery on observational simulations · Observational simulations | SHD | Helped |
| Use SDCD instead of the compared methods | Causal discovery with interventional data · Interventional simulations | SHD | Helped |
| Use SDCD instead of existing methods | Causal discovery across graph sizes · Observational simulations | convergence speed | Helped |
| Remove stage 1 edge preselection (ablation) | SDCD · Causal discovery simulations | convergence speed | Hurt |
| Remove stage 1 edge preselection (ablation) | SDCD · Causal discovery simulations | accuracy | Hurt |
| Replace the spectral acyclicity constraint with a PST constraint (ablation) | SDCD stage 2 · Causal discovery simulations | performance | Hurt |
Surprising findings
- NO-TEARS and NO-BEARS perform similarly to the trivial sortnregress baseline.
- DCD-FG scales well but yields exceptionally high SHD due to predicting very dense graphs.
Limitations
- No hyperparameter optimization; a single fixed parameter set is used across experiments.
- Theoretical correctness of stage 1 relies on strong assumptions (model class expressiveness, faithfulness, infinite data).
Experimental setup
Datasets: simulated observational and interventional data (random graphs with neural-network conditionals, Gaussian interventions) DCDI simulated datasets
Benchmarks: simulated observational data (varying d, s=4) simulated interventional data (varying proportion intervened) DCDI simulated datasets
Metrics: structural Hamming distance (SHD) runtime
Baselines: DCDI DCD-FG GIES NO-TEARS NO-BEARS DAGMA SCORE sortnregress
Builds on: NOTEARS DCDI DAGMA NO-BEARS
Closest papers by meaning
- THE ROBUSTNESS OF DIFFERENTIABLE CAUSAL DISCOVERY IN MISSPECIFIED SCENARIOS (ICLR 2025 · similarity 0.91)
- Differentiable Cyclic Causal Discovery Under Unmeasured Confounders (NeurIPS 2025 · similarity 0.91)
- Causal Discovery with Fewer Conditional Independence Tests (ICML 2024 · similarity 0.90)
- Differentiable Constraint-Based Causal Discovery (NeurIPS 2025 · similarity 0.90)
- Differentiable Causal Discovery for Latent Hierarchical Causal Models (ICLR 2025 · similarity 0.89)
- On Causal Discovery in the Presence of Deterministic Relations (NeurIPS 2024 · similarity 0.89)
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