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FedCSL: A Scalable and Accurate Approach to Federated Causal Structure Learning
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Proposes FedCSL, a federated causal structure learning method that learns local causal neighbors per client, aggregates them with sample-size-inferred p-value weights, and orients a global skeleton, scaling to high-dimensional data under uneven sample allocation.
Problem
Federated causal structure learning is hard to scale to high-dimensional data because existing methods run expensive global CSL at each client, and accuracy degrades when clients hold uneven sample sizes that are private and unknown to the server.
Approach
A federated local-to-global pipeline (causal neighbor learning via HITON-PC, weighted skeleton construction, and weighted orientation via BDeu hill-climbing) where client weights are inferred from the distribution of empty-set G2 p-values, without encryption or revealing sample sizes.
Key results
- On benchmark BN datasets with 12 clients, FedCSL's F1 on Child is 20%-42% higher than the best baseline FedPC.
- On Pigs and Gene, FedCSL runs over 10 times faster than all baselines (e.g., 322.6s vs 3198.5s for FedPC on Pigs with 12 clients).
- Removing the weighted aggregation (FedCSL w/o weighting) yields lower F1 and higher SHD on all five benchmark BN datasets.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use FedCSL instead of the baselines | Federated CSL on Sachs · Sachs, 2, 3, and 8 clients | SHD | Helped |
| Use FedCSL instead of the baselines | Federated CSL on Sachs · Sachs, 5 and 12 clients | SHD | Hurt |
| Add the weighted aggregation strategy (ablation) | FedCSL · Child, Insurance, Alarm, Pigs, and Gene | F1 score | Helped |
| Add the weighted aggregation strategy (ablation) | FedCSL · Child, Insurance, Alarm, Pigs, and Gene | SHD | Helped |
| Use FedCSL instead of FedPC | Federated CSL on Child · Child BN benchmark, uneven allocation | F1 score: 20%˜42% higher | Helped |
Surprising findings
- On the Sachs real dataset, FedCSL does not beat all baselines at 5 and 12 clients, though differences in SHD are minimal.
Limitations
- Assumes horizontal federated setting with uniformly sampled data from the same DAG; no data heterogeneity considered.
- Does not handle latent variables.
- Weighting relies on a heuristic hypothesis (Hypothesis 1) validated empirically rather than fully proven.
Experimental setup
Datasets: Child Insurance Alarm Pigs Gene Sachs high-dimensional synthetic DAG (5,000 variables)
Benchmarks: Child Insurance Alarm Pigs Gene Sachs high-dimensional synthetic datasets
Metrics: SHD F1 score running time
Baselines: NOTEARS-ADMM NOTEARS-MLP-ADMM GS-FedDAG AS-FedDAG FedPC ADL-AllData ADL-Avg ADL-Best ADL-Voting
Builds on: HITON-PC FedPC NOTEARS ADL
Closest papers by meaning
- Federated Causal Structure Learning with Non-identical Variable Sets (ICML 2025 · similarity 0.92)
- Federated Causality Learning with Explainable Adaptive Optimization (AAAI 2024 · similarity 0.89)
- Federated Causal Discovery from Heterogeneous Data (ICLR 2024 · similarity 0.87)
- Subgraph Federated Learning via Spectral Methods (NeurIPS 2025 · similarity 0.87)
- FedSC: Provable Federated Self-supervised Learning with Spectral Contrastive Objective over Non-i.i.d. Data (ICML 2024 · similarity 0.86)
- Federated Causally Invariant Feature Learning (AAAI 2025 · similarity 0.86)
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