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A Meta-Learning Approach to Bayesian Causal Discovery
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Proposes the Bayesian Causal Neural Process (BCNP), a transformer encoder-decoder meta-learner that samples acyclic DAGs from the posterior by parametrising permutation (Gumbel-Sinkhorn) and lower-triangular Bernoulli matrices, and compares it to AVICI, CSIvA, DiBS and BayesDAG on synthetic and Syntren data.
Problem
Approximating the Bayesian posterior over causal DAGs is hard due to the huge graph space and the marginal likelihood over functional mechanisms; existing amortised meta-learning methods (AVICI, CSIvA) only target the MAP or marginal edge probabilities and fail to sample valid acyclic graphs from th
Approach
Amortise posterior inference over DAGs with a neural process whose decoder directly samples DAGs as Q A Q^T, where Q is a Gumbel-Sinkhorn permutation and A is a lower-triangular Bernoulli matrix produced by parameter attention with shared parameters, making samples acyclic by construction, permutation equivariant in nodes, and edge-dependent.
Key results
- On Syntren, BCNP achieves AUC 0.84 and log probability -76.35, the best among methods (DiBS AUC 0.81, log prob -83.31).
- On the unidentifiable two-variable case, BCNP outputs X1->X2 and X2->X1 at 0.4979 and 0.4897 with almost no empty graphs (0.0124), whereas AVICI outputs empty graphs 31.9% of the time and cyclic/bidirectional graphs 18.8%.
- On 20-variable Linear ER60, BCNP ER60 reaches AUC 0.85 and expected edge F1 0.36, versus AVICI at 0.83 and 0.31 and DiBS at 0.40 AUC.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use BCNP instead of DiBS for posterior graph prediction | Bayesian causal discovery on Syntren · Syntren | AUC: 0.81 ± 0.02 -> 0.84 ± 0.02 | Helped |
| Use BCNP instead of AVICI for posterior graph prediction | Bayesian causal discovery on Syntren · Syntren | Expected SHD: 48.94 ± 2.37 -> 50.87 ± 1.92 | Hurt |
| Use BCNP instead of AVICI for posterior graph prediction | Bayesian causal discovery on Syntren · Syntren | Expected Edge F1: 0.09 ± 0.01 -> 0.17 ± 0.01 | Helped |
| Use BCNP ER60 instead of AVICI | Bayesian causal discovery on Linear ER60 · Linear ER60 | AUC: 0.83 ± 0.01 -> 0.85 ± 0.01 | Helped |
| Use BCNP ER60 instead of BayesDAG | Bayesian causal discovery on Linear ER60 · Linear ER60 | Expected SHD: 63.51 ± 0.40 -> 76.52 ± 0.92 | Hurt |
| Use BCNP ER60 instead of AVICI | Bayesian causal discovery on NeuralNet ER60 · NeuralNet ER60 | AUC: 0.79 ± 0.01 -> 0.85 ± 0.00 | Helped |
| Use BCNP ER60 instead of DiBS | Bayesian causal discovery on NeuralNet ER60 · NeuralNet ER60 | Expected SHD: 65.72 ± 0.17 -> 70.40 ± 0.35 | Hurt |
| Use BCNP ER60 instead of AVICI | Bayesian causal discovery on NeuralNet ER60 · NeuralNet ER60 | Expected Edge F1: 0.29 ± 0.01 -> 0.40 ± 0.00 | Helped |
| Train BCNP on a mixture of datasets instead of the GPCDE-specific ER60 distribution | BCNP · GPCDE ER60 | AUC: 0.72 ± 0.01 -> 0.77 ± 0.01 | Helped |
| Use BCNP All Data instead of DiBS | Bayesian causal discovery on GPCDE ER60 · GPCDE ER60 | Expected SHD: 64.22 ± 0.22 -> 80.28 ± 0.77 | Hurt |
Surprising findings
- AVICI outputs bidirectional and empty graphs in the unidentifiable two-variable case, despite strong marginal edge metrics, showing marginal-only metrics hide poor DAG sampling.
- BayesDAG achieves the lowest expected SHD on several linear datasets despite poor AUC and log probability.
Limitations
- CSIvA baseline uses a smaller width due to autoregressive memory constraints, so comparisons are not fully matched unless the same-width experiments are considered.
- Explicit Bayesian baselines required hyperparameter choices (e.g., selecting BayesDAG by AUC rather than expected SHD) and log-probability constants added to DiBS, which may affect fairness.
- Accuracy under distribution shift between training prior and target data is not rigorously characterised, as the authors acknowledge.
Experimental setup
Datasets: Synthetic Bayesian causal model data (Linear, NeuralNet, GPCDE with ER20/40/60 graphs) Syntren gene expression simulator data
Benchmarks: Two-variable normalised linear Gaussian (unidentifiable) Synthetic 20-node Linear/NeuralNet/GPCDE ER20/40/60 Syntren (10 datasets, 20 nodes)
Metrics: AUC log Bernoulli probability expected SHD expected edge F1 proportion of sampled graph types
Baselines: DiBS BayesDAG AVICI CSIvA
Builds on: Neural processes AVICI CSIvA Gumbel-Sinkhorn BayesDAG
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