mlsanityData to 7 Oct 2026

Towards Federated Bayesian Network Structure Learning with Continuous Optimization

arXiv 2110.09356 ↗First posted 18 Oct 2021cs.LG stat.MLcited by 31

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Abstract (arXiv)

Traditionally, Bayesian network structure learning is often carried out at a central site, in which all data is gathered. However, in practice, data may be distributed across different parties (e.g., companies, devices) who intend to collectively learn a Bayesian network, but are not willing to disclose information related to their data owing to privacy or security concerns. In this work, we present a federated learning approach to estimate the structure of Bayesian network from data that is horizontally partitioned across different parties. We develop a distributed structure learning method based on continuous optimization, using the alternating direction method of multipliers (ADMM), such that only the model parameters have to be exchanged during the optimization process. We demonstrate the flexibility of our approach by adopting it for both linear and nonlinear cases. Experimental results on synthetic and real datasets show that it achieves an improved performance over the other methods, especially when there is a relatively large number of clients and each has a limited sample size.

Key facts. Cited by 31 papers in the map (data through 7 Oct 2026). Builds on 26 of its 82 references that are in the map. First posted on arXiv 18 Oct 2021.

Builds on

26 of 82 references.

References · 26

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
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14 more
  1. 2020DYNOTEARS: Structure Learning from Time-Series Datacited by 198
  2. 2020On the Role of Sparsity and DAG Constraints for Learning Linear DAGscited by 186
  3. 2019Secure Federated Matrix Factorizationcited by 102
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 8; 2023: 6; 2024: 6; 2025: 3; 2026: 7.

31 papers.

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  1. 2023Structure Learning with Continuous Optimization: A Sober Look and Beyondcited by 34
  2. 2023Bayesian Federated Learning: A Surveycited by 22
  3. 2021FedDAG: Federated DAG Structure Learningcited by 17
  4. 2024Federated Causal Discovery from Heterogeneous Datacited by 15
  5. 2022Distributed Learning of Generalized Linear Causal Networkscited by 13
  6. 2022Towards Privacy-Aware Causal Structure Learning in Federated Settingcited by 11
  7. 2023Federated Causality Learning with Explainable Adaptive Optimizationcited by 11
  8. 2023Towards Practical Federated Causal Structure Learningcited by 9
  9. 2022Multiscale Causal Structure Learningcited by 7
  10. 2022VertiBayes: Learning Bayesian network parameters from vertically partitioned data with missing valuescited by 5
  11. 2025FedGES: A Federated Learning Approach for BN Structure Learningcited by 4
  12. 2022Differentiable Invariant Causal Discoverycited by 3
19 more
  1. 2022On the Sparse DAG Structure Learning Based on Adaptive Lassocited by 3
  2. 2024Embarrassingly Parallel GFlowNetscited by 3
  3. 2024psiDAG: Projected Stochastic Approximation Iteration for DAG Structure Learningcited by 3
  4. 2023Directed Acyclic Graphs With Tearscited by 2
  5. 2025Regret-Based Federated Causal Discovery with Unknown Interventionscited by 2
  6. 2022Federated Causal Discovery From Interventionscited by 1
  7. 2023Learning Personalized Brain Functional Connectivity of MDD Patients from Multiple Sites via Federated Bayesian Networkscited by 1
  8. 2024CCBNet: Confidential Collaborative Bayesian Networks Inferencecited by 1
  9. 2024Interventional Causal Structure Discovery over Graphical Models with Convergence and Optimality Guaranteescited by 1
  10. 2024Revisiting Differentiable Structure Learning: Inconsistency of ℓ1 Penalty and Beyondcited by 1
  11. 2025Differentially Private and Federated Structure Learning in Bayesian Networkscited by 1
  12. 2022Differentiable and Transportable Structure Learningcited by 0
  13. 2026Federated Concept-Based Models: Interpretable models with distributed supervisioncited by 0
  14. 2026Uncertainty Quantification in Federated Granger Causality Learningcited by 0
  15. 2026Federated Learning of Nonlinear Temporal Dynamics with Graph Attention-based Cross-Client Interpretabilitycited by 0
  16. 2026Preserving Data Privacy in Learning Causal Structure with Fully Homomorphic Encryptioncited by 0
  17. 2026Beyond Weights and Gradients: A Taxonomy of Federated Learning Messagescited by 0
  18. 2026A Survey on Federated Causal Discovery and Inferencecited by 0
  19. 2026Federated Causal Discovery via Regression-Directed Cumulantscited by 0