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.

翻译：从分散数据中学习贝叶斯网络结构面临两大挑战：(i) 确保参与者的严格隐私保证，(ii) 避免随着维度增加而扩大的通信成本。在本工作中，我们提出Fed-Sparse-BNSL，一种新颖的联邦学习方法，用于学习线性高斯贝叶斯网络结构，同时应对上述两个挑战。通过将差分隐私与贪心更新相结合，仅针对每个参与者的少量相关边，Fed-Sparse-BNSL高效利用隐私预算，同时保持低通信成本。我们精心的算法设计保持了模型的可识别性，并实现了精确的结构估计。在合成与真实数据集上的实验表明，Fed-Sparse-BNSL在提供显著更强的隐私性和通信效率的同时，达到了接近非私有基线的效用。