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Causal Discovery from Poisson Branching Structural Causal Model Using High-Order Cumulant with Path Analysis
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Proposes the Poisson Branching Structural Causal Model (PB-SCM) with binomial thinning and Poisson noise, and uses high-order cumulants and path counts to show causal order is identifiable under graphical conditions, with a likelihood-plus-cumulant-test algorithm for count data.
Problem
Causal discovery from count data with an inherent branching structure (binomial thinning plus Poisson innovations), where standard causal discovery only identifies up to Markov equivalence and the direction of a single causal pair is non-identifiable.
Approach
Models count causal relations as PB-SCM and shows that high-order joint cumulants of Poisson branching variables encode the number of directed paths between variables, so causal order is identifiable when the cause is a root with at least two directed paths to the effect, or when a dominant common ancestor has a path to the effect avoiding the cause. Learns skeleton by penalized likelihood (PGF-ba
Key results
- On synthetic data with n=30000 and 10 vertices, PB-SCM outperforms OCD, PC and GES across sample size, vertex count and indegree sweeps (F1 reported in figures).
- On a football events dataset, PB-SCM identifies five of six cause-effect pairs among Foul, Yellow card, 2nd Yellow card, Red card and Substitution, missing Foul to Red card.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Denser graph structure (higher indegree rate) | PB-SCM · Synthetic sensitivity experiments | F1 | Helped |
| Increasing number of vertices | PB-SCM · Synthetic sensitivity experiments | F1 | Hurt |
| Increasing sample size | PB-SCM · Synthetic sensitivity experiments | F1 | Helped |
| Adding a BIC penalty to likelihood for skeleton learning | PB-SCM skeleton learning · Synthetic experiments | excess redundant edges | Helped |
| Adding an extra directed path Z->C->Y not passing X | causal direction identifiability · Graph example | identifiability of X->Y | Helped |
| Foul -> Red card direction test on football data | PB-SCM · Football events dataset | correct identification of cause-effect pair | No clear effect |
Surprising findings
- Denser graphs help identifiability: additional paths from a dominant common ancestor can make the causal order identifiable, so sparsity is not always beneficial for this method.
Limitations
- High-order cumulant estimation has large variance, degrading performance as the number of vertices grows.
- Non-identifiability persists for some graph configurations, e.g., when a dominant common ancestor's paths all pass through the cause.
- Real-world evaluation is limited to a single football events dataset with no ground truth beyond domain rules.
Experimental setup
Datasets: football events dataset (Kaggle)
Benchmarks: football events dataset
Metrics: F1
Baselines: OCD PC GES
Builds on: Poisson Bayesian network identifiability integer-valued autoregressive model BIC
Closest papers by meaning
- On the Identifiability of Poisson Branching Structural Causal Model Using Probability Generating Function (NeurIPS 2024 · similarity 0.95)
- Identification of Causal Structure with Latent Variables Based on Higher Order Cumulants (AAAI 2024 · similarity 0.89)
- Learning Structural Causal Models from Ordering: Identifiable Flow Models (AAAI 2025 · similarity 0.87)
- Discovering Mixtures of Structural Causal Models from Time Series Data (ICML 2024 · similarity 0.87)
- Foundations of Testing for Finite-Sample Causal Discovery (ICML 2024 · similarity 0.86)
- Hybrid Top-Down Global Causal Discovery with Local Search for Linear and Nonlinear Additive Noise Models (NeurIPS 2024 · similarity 0.86)
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