# Towards Federated Bayesian Network Structure Learning with Continuous Optimization

arXiv: https://arxiv.org/abs/2110.09356 · HTML: https://mlsanity.com/paper/2110.09356/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 82 references that are in the map.
- First posted on arXiv 18 Oct 2021.

## Builds on (most cited first, 26 of 26)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Secure Federated Matrix Factorization](https://mlsanity.com/paper/1906.05108/) (2019)
- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [Masked Gradient-Based Causal Structure Learning](https://mlsanity.com/paper/1910.08527/) (2019)
- [DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networks](https://mlsanity.com/paper/2010.09133/) (2020)
- [Convergence Analysis of Alternating Direction Method of Multipliers for a Family of Nonconvex Problems](https://mlsanity.com/paper/1410.1390/) (2014)
- [Differentiable Causal Discovery Under Unmeasured Confounding](https://mlsanity.com/paper/2010.06978/) (2020)
- [A Graph Autoencoder Approach to Causal Structure Learning](https://mlsanity.com/paper/1911.07420/) (2019)
- [DAGs with No Curl: An Efficient DAG Structure Learning Approach](https://mlsanity.com/paper/2106.07197/) (2021)
- [Constraint-based Causal Discovery from Multiple Interventions over Overlapping Variable Sets](https://mlsanity.com/paper/1403.2150/) (2014)
- [Structural Agnostic Modeling: Adversarial Learning of Causal Graphs](https://mlsanity.com/paper/1803.04929/) (2018)
- [On the Convergence of Continuous Constrained Optimization for Structure Learning](https://mlsanity.com/paper/2011.11150/) (2020)
- [Structural Intervention Distance (SID) for Evaluating Causal Graphs](https://mlsanity.com/paper/1306.1043/) (2013)

## Built on by (most cited first, 30 of 31)

- [Structure Learning with Continuous Optimization: A Sober Look and Beyond](https://mlsanity.com/paper/2304.02146/) (2023)
- [Bayesian Federated Learning: A Survey](https://mlsanity.com/paper/2304.13267/) (2023)
- [FedDAG: Federated DAG Structure Learning](https://mlsanity.com/paper/2112.03555/) (2021)
- [Federated Causal Discovery from Heterogeneous Data](https://mlsanity.com/paper/2402.13241/) (2024)
- [Distributed Learning of Generalized Linear Causal Networks](https://mlsanity.com/paper/2201.09194/) (2022)
- [Towards Privacy-Aware Causal Structure Learning in Federated Setting](https://mlsanity.com/paper/2211.06919/) (2022)
- [Federated Causality Learning with Explainable Adaptive Optimization](https://mlsanity.com/paper/2312.05540/) (2023)
- [Towards Practical Federated Causal Structure Learning](https://mlsanity.com/paper/2306.09433/) (2023)
- [Multiscale Causal Structure Learning](https://mlsanity.com/paper/2207.07908/) (2022)
- [VertiBayes: Learning Bayesian network parameters from vertically partitioned data with missing values](https://mlsanity.com/paper/2210.17228/) (2022)
- [psiDAG: Projected Stochastic Approximation Iteration for DAG Structure Learning](https://mlsanity.com/paper/2410.23862/) (2024)
- [FedGES: A Federated Learning Approach for BN Structure Learning](https://mlsanity.com/paper/2502.01538/) (2025)
- [Differentiable Invariant Causal Discovery](https://mlsanity.com/paper/2205.15638/) (2022)
- [On the Sparse DAG Structure Learning Based on Adaptive Lasso](https://mlsanity.com/paper/2209.02946/) (2022)
- [Embarrassingly Parallel GFlowNets](https://mlsanity.com/paper/2406.03288/) (2024)
- [Directed Acyclic Graphs With Tears](https://mlsanity.com/paper/2302.02160/) (2023)
- [Regret-Based Federated Causal Discovery with Unknown Interventions](https://mlsanity.com/paper/2512.23626/) (2025)
- [Federated Causal Discovery From Interventions](https://mlsanity.com/paper/2211.03846/) (2022)
- [Learning Personalized Brain Functional Connectivity of MDD Patients from Multiple Sites via Federated Bayesian Networks](https://mlsanity.com/paper/2301.02423/) (2023)
- [CCBNet: Confidential Collaborative Bayesian Networks Inference](https://mlsanity.com/paper/2405.15055/) (2024)
- [Interventional Causal Structure Discovery over Graphical Models with Convergence and Optimality Guarantees](https://mlsanity.com/paper/2408.04819/) (2024)
- [Revisiting Differentiable Structure Learning: Inconsistency of ℓ1 Penalty and Beyond](https://mlsanity.com/paper/2410.18396/) (2024)
- [Differentially Private and Federated Structure Learning in Bayesian Networks](https://mlsanity.com/paper/2512.01708/) (2025)
- [Differentiable and Transportable Structure Learning](https://mlsanity.com/paper/2206.06354/) (2022)
- [Federated Concept-Based Models: Interpretable models with distributed supervision](https://mlsanity.com/paper/2602.04093/) (2026)
- [Uncertainty Quantification in Federated Granger Causality Learning](https://mlsanity.com/paper/2602.13004/) (2026)
- [Federated Learning of Nonlinear Temporal Dynamics with Graph Attention-based Cross-Client Interpretability](https://mlsanity.com/paper/2602.13485/) (2026)
- [Preserving Data Privacy in Learning Causal Structure with Fully Homomorphic Encryption](https://mlsanity.com/paper/2606.05129/) (2026)
- [Beyond Weights and Gradients: A Taxonomy of Federated Learning Messages](https://mlsanity.com/paper/2606.16891/) (2026)
- [A Survey on Federated Causal Discovery and Inference](https://mlsanity.com/paper/2606.23741/) (2026)

## 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.