mlsanityData to 7 Oct 2026

Differentially Private and Federated Structure Learning in Bayesian Networks

arXiv 2512.01708 ↗First posted 1 Dec 2025stat.ML cs.LGcited by 1

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Abstract (arXiv)

Learning the structure of a Bayesian network from decentralized data poses two major challenges: (i) ensuring rigorous privacy guarantees for participants, and (ii) avoiding communication costs that scale poorly with dimensionality. In this work, we introduce Fed-Sparse-BNSL, a novel federated method for learning linear Gaussian Bayesian network structures that addresses both challenges. By combining differential privacy with greedy updates that target only a few relevant edges per participant, Fed-Sparse-BNSL efficiently uses the privacy budget while keeping communication costs low. Our careful algorithmic design preserves model identifiability and enables accurate structure estimation. Experiments on synthetic and real datasets demonstrate that Fed-Sparse-BNSL achieves utility close to non-private baselines while offering substantially stronger privacy and communication efficiency.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 26 of its 50 references that are in the map. First posted on arXiv 1 Dec 2025.

Builds on

26 of 50 references.

References · 26

  1. 2016Communication-Efficient Learning of Deep Networks from Decentralized Datacited by 7,592
  2. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 745
  3. 2020Inverting Gradients -- How easy is it to break privacy in federated learning?cited by 707
  4. 2016Concentrated Differential Privacy: Simplifications, Extensions, and Lower Boundscited by 339
  5. 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 209
  6. 2019Learning Sparse Nonparametric DAGscited by 207
  7. 2020On the Role of Sparsity and DAG Constraints for Learning Linear DAGscited by 186
  8. 2019Masked Gradient-Based Causal Structure Learningcited by 89
  9. 2013High-dimensional learning of linear causal networks via inverse covariance estimationcited by 86
  10. 2021A survey of Bayesian Network structure learningcited by 85
  11. 2018Revisiting differentially private linear regression: optimal and adaptive prediction & estimation in unbounded domaincited by 60
  12. 2019Causal Discovery Toolbox: Uncover causal relationships in Pythoncited by 49
14 more
  1. 2015Coordinate Descent Converges Faster with the Gauss-Southwell Rule Than Random Selectioncited by 39
  2. 2020On the Convergence of Continuous Constrained Optimization for Structure Learningcited by 38
  3. 2023Structure Learning with Continuous Optimization: A Sober Look and Beyondcited by 34
  4. 2021Towards Federated Bayesian Network Structure Learning with Continuous Optimizationcited by 31
  5. 2021FedDAG: Federated DAG Structure Learningcited by 17
  6. 2021The Permute-and-Flip Mechanism is Identical to Report-Noisy-Max with Exponential Noisecited by 14
  7. 2020Towards practical differentially private causal graph discoverycited by 10
  8. 2021Differentially Private Coordinate Descent for Composite Empirical Risk Minimizationcited by 10
  9. 2023Towards Practical Federated Causal Structure Learningcited by 9
  10. 2018Efficient Greedy Coordinate Descent for Composite Problemscited by 8
  11. 2021Correlation inference attacks against machine learning modelscited by 7
  12. 2022VertiBayes: Learning Bayesian network parameters from vertically partitioned data with missing valuescited by 5
  13. 2022High-Dimensional Private Empirical Risk Minimization by Greedy Coordinate Descentcited by 4
  14. 2025FedGES: A Federated Learning Approach for BN Structure Learningcited by 4

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Citing papers per year: 2026: 1.

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  1. 2026A Survey on Federated Causal Discovery and Inferencecited by 0