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Federated Causal Structure Learning with Non-identical Variable Sets

ICML 2025 · Federated learning and privacy › Personalized and heterogeneous FL · approach: Federated learning with pretrained models

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Proposes FedCDnv, a federated causal structure learning method for clients with non-identical (partially overlapping) variable sets, using theories to flag spurious dependencies and a two-level priority selection strategy (TPSS) to aggregate stable causal relationships.

Problem

Federated causal structure learning when clients observe overlapping but non-identical variable sets, where non-overlapping variable pairs create spurious dependencies and existing aggregation ignores the varying importance of edges within local graphs.

Approach

Classifies variable pairs as overlapping or non-overlapping, derives theorems/lemmas to mark definite causal and non-causal relations, defines stable relations via an interval of CI-test significance levels, and aggregates local FCI graphs on the server with a two-level priority selection (TPSS) weighted by sample size and p-value scaling.

Key results

On the Sachs real-world dataset, FedCDnv reaches F1-edge 0.6967 versus 0.5823 for the best baseline FCI-base, roughly a 10-point gain.
On Sachs, FedCDnv achieves F1-orientation 0.2861, higher than FedCDnv-vote (0.2544), CDUIOV (0.1211) and FCI-base (0.2488).
On synthetic data, FedCDnv reports orientation F1 about 10% higher than compared methods; on benchmarks it gains 8-12% F1-orientation in four networks.

Measured effects reported in the paper

What was changed	Where	Measured	Effect
Use FedCDnv instead of FedCDnv-vote's voting strategy (ablation)	FedCDnv · Sachs	F1-edge: 0.5778 ± 0.0998 -> 0.6967 ± 0.0316	Helped
Use FedCDnv instead of FedCDnv-vote's voting strategy (ablation)	FedCDnv · Sachs	F1-orie: 0.2544 ± 0.0384 -> 0.2861 ± 0.0840	Helped
Use FedCDnv instead of FCI-base	Federated causal structure learning with non-identical variable sets · Sachs	F1-edge: 0.5823 ± 0.1289 -> 0.6967 ± 0.0316	Helped
Use FedCDnv instead of CDUIOV	Federated causal structure learning with non-identical variable sets · Sachs	F1-orie: 0.1211 ± 0.0021 -> 0.2861 ± 0.0840	Helped
Extract only definite relationships using the proposed theories	FedCDnv · Synthetic networks with 10 to 150 variables	FDR-C	Mixed
Extract definite non-causal relationships using the proposed theories	FedCDnv · Synthetic networks with 10 to 150 variables	FDR-nC	Helped

Surprising findings

CDUIOV achieves the highest orientation precision on Sachs (0.8843) but with very low recall (0.0858), a trade-off attributed to its reliance on intervention targets.
Definite causal relations have only about 1% lower average FDR than all identified causal relations, a modest effect.

Limitations

Current theories for identifying definite relationships are acknowledged as not yet comprehensive.
Assumes absolute latent confounders but no selection bias; privacy protection relies on p-value scaling without formal guarantees.
Absolute accuracy on Sachs is modest (orientation F1 about 0.29).

Experimental setup

Datasets: Erdős-Rényi synthetic DAG data Child Alarm Insurance Barley Child3 Alarm3 Sachs

Benchmarks: Child Alarm Insurance Barley Child3 Alarm3 Sachs

Metrics: precision recall F1-edge F1-orientation FDR

Baselines: FedCDnv-vote CDUIOV CD-MiNi FCI-base Notears-ADMM FedPC FedCSL

Builds on: FCI RFCI Zhang orientation rules FedPC CD-MiNi

Closest papers by meaning

FedCSL: A Scalable and Accurate Approach to Federated Causal Structure Learning (AAAI 2024 · similarity 0.92)
Federated Causality Learning with Explainable Adaptive Optimization (AAAI 2024 · similarity 0.90)
Federated Causal Discovery from Heterogeneous Data (ICLR 2024 · similarity 0.88)
Decoupled Subgraph Federated Learning (ICLR 2025 · similarity 0.87)
Federated Causally Invariant Feature Learning (AAAI 2025 · similarity 0.87)
Federated Granger Causality Learning For Interdependent Clients With State Space Representation (ICLR 2025 · similarity 0.86)

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