# Differentially Private and Federated Structure Learning in Bayesian Networks

arXiv: https://arxiv.org/abs/2512.01708 · HTML: https://mlsanity.com/paper/2512.01708/

## Key facts

- Cited by 1 papers 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 (most cited first, 26 of 26)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Inverting Gradients -- How easy is it to break privacy in federated learning?](https://mlsanity.com/paper/2003.14053/) (2020)
- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Masked Gradient-Based Causal Structure Learning](https://mlsanity.com/paper/1910.08527/) (2019)
- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [Revisiting differentially private linear regression: optimal and adaptive prediction & estimation in unbounded domain](https://mlsanity.com/paper/1803.02596/) (2018)
- [Causal Discovery Toolbox: Uncover causal relationships in Python](https://mlsanity.com/paper/1903.02278/) (2019)
- [Coordinate Descent Converges Faster with the Gauss-Southwell Rule Than Random Selection](https://mlsanity.com/paper/1506.00552/) (2015)
- [On the Convergence of Continuous Constrained Optimization for Structure Learning](https://mlsanity.com/paper/2011.11150/) (2020)
- [Structure Learning with Continuous Optimization: A Sober Look and Beyond](https://mlsanity.com/paper/2304.02146/) (2023)
- [Towards Federated Bayesian Network Structure Learning with Continuous Optimization](https://mlsanity.com/paper/2110.09356/) (2021)
- [FedDAG: Federated DAG Structure Learning](https://mlsanity.com/paper/2112.03555/) (2021)
- [The Permute-and-Flip Mechanism is Identical to Report-Noisy-Max with Exponential Noise](https://mlsanity.com/paper/2105.07260/) (2021)
- [Towards practical differentially private causal graph discovery](https://mlsanity.com/paper/2006.08598/) (2020)
- [Differentially Private Coordinate Descent for Composite Empirical Risk Minimization](https://mlsanity.com/paper/2110.11688/) (2021)
- [Towards Practical Federated Causal Structure Learning](https://mlsanity.com/paper/2306.09433/) (2023)
- [Efficient Greedy Coordinate Descent for Composite Problems](https://mlsanity.com/paper/1810.06999/) (2018)
- [Correlation inference attacks against machine learning models](https://mlsanity.com/paper/2112.08806/) (2021)
- [VertiBayes: Learning Bayesian network parameters from vertically partitioned data with missing values](https://mlsanity.com/paper/2210.17228/) (2022)
- [High-Dimensional Private Empirical Risk Minimization by Greedy Coordinate Descent](https://mlsanity.com/paper/2207.01560/) (2022)
- [FedGES: A Federated Learning Approach for BN Structure Learning](https://mlsanity.com/paper/2502.01538/) (2025)

## Built on by (most cited first, 1 of 1)

- [A Survey on Federated Causal Discovery and Inference](https://mlsanity.com/paper/2606.23741/) (2026)

## 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.