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：从去中心化数据中学习贝叶斯网络结构面临两大挑战：(i) 为参与者提供严格的隐私保障，(ii) 避免通信成本随维度增长而急剧上升。本研究提出 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，同时应对上述挑战。该方法将差分隐私与针对每位参与者仅更新少量相关边的贪心策略相结合，在高效利用隐私预算的同时保持较低的通信开销。我们通过精心的算法设计保持了模型可识别性，并实现了准确的结构估计。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保护与通信效率的同时，其效用可接近非隐私基线方法。