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Federated Causality Learning with Explainable Adaptive Optimization
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Proposes FedCausal, a federated DAG-learning method that aggregates local NOTEARS-style causal models via a global acyclicity-constrained optimization, exchanging only first-layer parameters to handle non-iid client data.
Problem
Learning a unified global causal DAG from horizontally partitioned, privacy-restricted client data whose distributions may differ (non-iid), where existing federated or distributed causal discovery methods either need centralized data, share too many parameters, or cannot handle heterogeneity.
Approach
Replace weighted averaging of local causal matrices with a server-side optimization that pulls a global matrix toward each client's local matrix under an explicit NOTEARS acyclicity constraint, with clients adding a proximal penalty; for nonlinear models only the first MLP layer is shared. The authors argue this objective reduces to centralized NOTEARS/NOTEARS-MLP on iid data while allowing differ
Key results
- On Sachs (11 variables, 10 clients), FedCausal achieves SHD 15 and FDR 52.63%, versus NO-ALL SHD 18 and FedDAG SHD 26.
- On 40-node non-iid synthetic data, FedCausal's local-graph TPR is 92.4% with FDR 4.4%, versus FedDAG TPR 82.4% and FDR 10.8%.
- The paper reports FedCausal's global acyclicity term h reaches about 4.2e-12 on 40-node non-iid data, while NO-Avg reaches about 0.22.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use FedCausal instead of NO-ALL | Sachs causal discovery · Sachs | SHD: 18 -> 15 | Helped |
| Add the global acyclicity constraint (ablation) | FedCausal · Sachs | FDR: 69.23 -> 52.63 | Helped |
| Add the global acyclicity constraint (ablation) | FedCausal · non-iid synthetic, 40 nodes | TPR: 84.7$\pm$3.4 -> 92.4$\pm$1.9 | Helped |
| Add the global acyclicity constraint (ablation) | FedCausal · non-iid synthetic, 40 nodes | FDR: 8.3$\pm$5.0 -> 4.4$\pm$2.8 | Helped |
| Omit the global acyclicity constraint (ablation) | FedCausal · iid linear and nonlinear synthetic data | FDR | Hurt |
| Omit the global acyclicity constraint (ablation) | FedCausal · non-iid synthetic data | TPR | Hurt |
| Average independently learned local graphs instead of optimizing the global graph | NO-Avg · non-iid synthetic data | acyclicity | Hurt |
Surprising findings
- FedCausal outperforms the centralized NO-ALL oracle on several iid linear settings, which the authors attribute to ensemble-like effects across clients.
- NO-Avg (naive weighted averaging of local graphs) yields very high FDR and SHD, even when its TPR is high.
Limitations
- Theoretical consistency results hold only under homogeneous-data assumptions; heterogeneous-case adaptivity is argued informally.
- FedDAG baseline could not be run on 80 nodes because only hyperparameters for 10, 20, 40 nodes were provided, and FedDAG is sensitive to hyperparameters.
Experimental setup
Datasets: Sachs protein signaling dataset synthetic ER/SF DAG data with LG, ANM-MLP, ADD-GP, MIM models
Benchmarks: Sachs protein signaling dataset synthetic ER/SF graphs with 10, 20, 40, 80 nodes
Metrics: TPR FDR SHD NNZ h(theta) acyclicity value
Baselines: FedDAG NOTEARS-ADMM NO-ALL NO-Avg NO-w/oAcy PC GES
Builds on: NOTEARS NOTEARS-MLP NOTEARS-ADMM FedDAG
Closest papers by meaning
- Federated Causal Discovery from Heterogeneous Data (ICLR 2024 · similarity 0.90)
- Federated Causal Structure Learning with Non-identical Variable Sets (ICML 2025 · similarity 0.90)
- FedCSL: A Scalable and Accurate Approach to Federated Causal Structure Learning (AAAI 2024 · similarity 0.89)
- Causal Discovery with Fewer Conditional Independence Tests (ICML 2024 · similarity 0.87)
- Adaptive Online Experimental Design for Causal Discovery (ICML 2024 · similarity 0.87)
- Stable Differentiable Causal Discovery (ICML 2024 · similarity 0.87)
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